HISTORICAL ET AND MODERN ETs

Posted by: alfredo capurso

HISTORICAL ET AND MODERN ETs - 01/16/10 02:38 PM


In all this sharing, I would like to make one point and three questions.

In my opinion, 12th root of two ET may well be considered a Historical Temperament too, since it pays for the "pure octaves" ancient dogma, and today it could well be referred to as the first algebraic/geometrical model, just by acknowledging other new ET models.

Why do I get the impression that Time stopped with 12th root of two ET?

People featuring non-equal temperaments or UTs say that they have more "colour", that "tempering" from just results in (in meaning) tone's colour. This may be fair enough. Personally, I'm in favour of beats and you may well know why.

What I do not understand is: what is difficult about acknowledging modern ETs, i.e. new algebraic geometrical models, new degrees of harmoniousness, new tonal effects, new spectral fusions, and accepting that also 12th root of two ET could evolve, actually it has evolved.

What is then "true" ET?
Does (in your opinion) modernity make people giddy?

a.c.

.
Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 01/16/10 05:08 PM

Two very different things - unequal putting the variety of beatspeeds in non-chromatic order; sometimes featuring equal beating intervals.

Equal -modern or otherwise puts variety of beatspeeds in chromatic order. The size of the octave is irrelevant to Equal or not.

Ron Koval
chicagoland
Posted by: Emmery

Re: HISTORICAL ET AND MODERN ETs - 01/16/10 05:50 PM

Quotes by a.c.

"Why do I get the impression that Time stopped with 12th root of two ET?"

Because we live in a fast paced era in which things come and go quickly, yet the 12th root of 2 ET has been used predominantly in our music with great success and only small change in the last 90 years.

"...what is difficult about acknowledging modern ETs..."

Same thing as acknowledging anything new or different, having an open mind, a willingness to not fear change, and an understanding that polarity leaves no freedom to incorporate something along with something else. Polarizing our tastes creates an all or nothing/take it or leave it attitude. All temperaments have value given the right circumstances and music. A technician may have difficulty making a living out of exclusively tuning some of them (historical temperaments).

"What is then "true" ET?"

A division of an octave or pseudo octave into equal parts on a logarithmic scale.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/16/10 06:42 PM


Ron, you write:

..."Two very different things - unequal putting the variety of beatspeeds in non-chromatic order; sometimes featuring equal beating intervals."...

About chromatic or "non-chromatic order", Bill Bremmer wrote something similar to: who will ever check the progression of 3rds?

I understood that Bill as well would prefere to talk about harmoniousness and effects. If so, there is some more and new (Modern ET) harmoniousness and effects to be acknowledged...

..."Equal -modern or otherwise puts variety of beatspeeds in chromatic order."...

Where is the problem? I do not think it should be a problem of "chromatic or not chromatic", it could be a theme: harmoniousness and resonance + all the qualities or effects you can think of.

..."The size of the octave is irrelevant to Equal or not."...

Well, not really. Historical ET (12th root of two) theorizes non-tuneable pure octaves, modern ETs temper (and tune) the octaves.

Emmery, you write:

..."yet the 12th root of 2 ET has been used predominantly in our music with great success and only small change in the last 90 years."...

Ok, but what about putting in practice what is theorized by 12th root of two ET (pure octaves)? Can we really say, as you say, that it "has been used...with great success and only small change in the last 90 years."? In my opinion the debate on its acceptance and its practicability is still open.

..."What is then "true" ET?"

You say: "A division of an octave or pseudo octave into equal parts on a logarithmic scale."...

I do not know if this is still correct. Cordier's ET has a 7 semitones module, Stopper's has a 19 semitones module, Chas has an infinite-number-of-semitones module. This is to say that yes, the semitones are equal and on a logarithmic scale, but Modern ETs do not fix their module on the octave anymore. This is the improvement, did you mean that with "pseudo octaves"?

In any case, Modern ETs modules do make a difference, both for us (tuners) and for the piano's performance.

Regards, a.c.

.

Posted by: Emmery

Re: HISTORICAL ET AND MODERN ETs - 01/16/10 06:53 PM

You are correct about the module...I should also include the expanded versions in my definition. For practical purposes, the majority of tuners use the octave as the base.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/16/10 07:19 PM


..."I should also include the expanded versions in my definition. For practical purposes, the majority of tuners use the octave as the base."...

Yes, me too, the octave interrelated with two 4ths and two 5ths, so to control 2:1, 4:3 and 3:2 ratios.

Previously you wrote:..."Same thing as acknowledging anything new or different, having an open mind, a willingness to not fear change, and an understanding that polarity leaves no freedom to incorporate something along with something else. Polarizing our tastes creates an all or nothing/take it or leave it attitude. All temperaments have value given the right circumstances and music."...

I like this, thanks. You say polarity, I'd say useless rivality.

a.c.
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Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 01/16/10 08:39 PM

All good points. Thank you, Emmery, for not taking the mock and ridicule tact this time. Along the lines of the "What did you do today?" thread, the one Steinway customer I took today when I usually avoid working if I can, specifically sought me out and asked the the EBVT III by name. He has a model B Steinway, purchased from the local Steinway dealer. He did not want ET which is all that dealer's technicians offer. Although I know that two of that dealer's technicians are familiar with other temperaments and they have done them often, that Steinway dealer forbids them to tune any Steinway pianos in anything but ET.

Not being able to get the tuning he wanted, the customer sought me out for the first time. He also had three other keyboard instruments, all early types, various types of harpsichords.

That Steinway dealership opened in 2006 after Steinway abandoned their former local dealership with whom they had been for 90 years. My prediction is that the new dealership will fail within a few years and close. The local Yamaha dealer closed about 2 years ago leaving this area with no Yamaha representation. They also chose to mock and ridicule the use of non-equal temperaments. Their technicians also mocked and ridiculed PTG. As many times as they were invited to attend PTG functions, they refused.

They would tell their customers all of what I often see written here, all of the theories about why ET is best, etc., but the problem was that what they actually did instead was reverse well. Time after time, year after year, I was asked to tune a Yamaha piano by an owner who had not been satisfied by the service provided by the Yamaha dealer technicians.

Temperament itself wasn't the only issue, I must say. The Yamaha dealer also mocked and ridiculed the installation and use of Dampp-Chaser systems. The salesmen and technicians enjoyed their guffaws as they called the humidity control systems, "washer-drier combinations". They laughed harder at the "crazy guys" who tuned "hysterical" temperaments.

The dealer and its technicians put themselves out of business because of the aggregate choices they made. Yamaha required every piano to undergo a "Service Bond" procedure. There was a card supplied with each piano. The technician was supposed to remove the action, re-align all hammers, tighten all flanges and at the very least, adjust the capstans on each and every piano after 6 months. Yamaha paid the dealer $40 for each of those cards which were returned.

The "Service Bond" was never intended to be a "free tuning" and was supposed to be performed the second time the piano was serviced in the home or wherever the piano went, not the first. The dealer, however was mainly interested in profits and competition. The dealer paid those technicians $40 to do the first "free" tuning. The technicians checked all of the boxes and fraudulently signed their names to work they had never done, time after time, year after year.

I do have a degree of sympathy for a technician who would be required to perform 2-3 hours of work for only $40. Who would ever do that? So, as you might expect, they spent about a half hour turning some tuning pins to result in a reverse-well tuning at whatever pitch the piano had sunk to.

The dealer had sold Yamaha pianos to virtually all area schools, both public and private. Many times over, the comment from the music teacher was that the first "free" tuning had not been satisfactory. Those teachers were not required to engage RPTs but it was a strong suggestion from the Area Arts Administrator. The teachers, one by one, independently of each other but perhaps in consultation with each other, found the technicians who made their pianos sound best, play best and whose tunings lasted the longest. Virtually all of them chose RPTs who tuned non-equal temperaments. Dampp-chaser systems were installed and maintained. Actions were tightened, aligned and regulated.

The private homes, schools, churches, restaurants and hotels in this area have all mostly been serviced by RPTs who tune non-equal temperaments for about two decades. The Yamaha dealer is long out of business and so are its former technicians.

The theory of ET, as I recall, goes back to ancient China, many centuries before the modern piano was ever conceived. In the mid 19th Century, Helmholtz published a list of theoretical frequencies for it. In the early 20th Century, William Braide-White wrote a book on how to tune it. Most technicians bought and studied that book over most of the 20th Century. Well-Temperament or any other kind of non-equal temperament became rarely heard of or was unknown completely.

In the 20th Century, there was only one tuning, ET. Nothing else was ever talked about, known, considered or even remotely possible as far as anyone who tuned a piano was concerned. The problem was and still is, that the ET which is imagined only in the mind, as a theoretical idea, most of the time, never really happened.

Today, 10 years into the 21st Century, true ET does, in fact happen more often than it used to for most of the 20th Century. Aural tuning has improved mostly through the presence of PTG and schools which now teach methods which came about solely from the existence of PTG. ETDs of course, now allow any tuner to tune ET to a satisfactory degree.

I witness nearly every day, this thread included, the hypothesis that ET is the "holy grail". It can be the one and only perfect solution. I used to believe that too. But I have moved beyond that hypothesis over two decades ago. I know what the reality is. I know what the pianists prefer. I go with what I know works for me and what makes me a very fine living.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 01/17/10 04:00 AM

Bill I can promise you that most of the European tuners have never heard of William Braid White ! we have similar documents here, but mostly the tuning is being told by apprenticing, the basis of the formation came from the piano factories and the tuners that worked there.

Even talking about the size of octaves and partial match in tuning is an analytic point of view which is not used here, what is told is good tone, good octaves, recognizing the good toning interval,and listening , listening, listening. No explanation is given on why suddenly, that octave is good, but you learn to recognize the alignment of partials between the 2 notes and the tone quality it provides (indeed all the apprenticing is octave/stretch based).

Yesterday I talked a little about tuning and tempering with the professional pianist, that had some views about it (which is not really often).

He stated that older temperament have their utility if you want to play the music related to it, (in the tonality they accept)
That when playing classical music the quality of the 5th and 12th prevails, while tunings more based on even progression of RBI intervals but with less attention given to the SBI quality could be more suited for modern music.

I have talked of the organ effect and he agreed that it should be magnificent, but if at the expense of modulation in farther tonalities he stated that it would not then suitable for daily use.

moving from an octave based idea to other directions may help to obtain a more pure output. I believe that we have to be told how the instrument are tuned and have comparison provided so to decide which suits the best which music.

Then, on a performance piano, or one used in many different venues, I see no possibility to change temperament then fight with stability for weeks.

So this limitation is a huge one.










Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/17/10 08:06 AM


I would really like if we managed to elaborate on this first posted thread's issue:

..."what is difficult about acknowledging modern ETs, i.e. new algebraic geometrical models, new degrees of harmoniousness, new tonal effects, new spectral fusions, and accepting that also 12th root of two ET could evolve, actually it has evolved."...

So here the point is not whether ET or any other temperament is the holy gral, but:

While 12th root of two ET has never been practicable, Modern ETs today are finally practicable. Moreover, Modern ETs have new degrees of harmoniousness and new tonal effects, due to new spectral fusions.

Why not wanting to get to know about all this?
Why keeping on relating ET to 12th root of two, when today ET has evolved?

For what I read, it seems that ET can only be 12th root of two, and this is why I get the impression that Time stopped with it.

Pleas tell me, would anyone talk about "true UT"?

Actually, Modern ETs can well prove that the pure-octaves ET Theory was inadeguate (for practical tuning), Modern ETs can well prove that the theoretical octave geometry was an arbitrary assumption.

We also know how difficult, for all tuners, the tuning of 12th root of two was and is.

Sholud not we stop talking about true ET and open to the new performances of Modern ETs?

Regards, a.c.

.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/17/10 10:11 AM


Kamin, you report and write:

..."I have talked of the organ effect and he agreed that it should be magnificent, but if at the expense of modulation in farther tonalities he stated that it would not then suitable for daily use."...

Talking about Modern ETs, Stopper stated quite recently that his pure 12ths tuning gains that kind of effect (organ) on any key, preserving any change in tonality.

Do not you think this could be, and maybe should be, enough for wanting to know more about ET's evolution and more about this Modern pure-12ths ET aural tuning?

I remember you asking for practical directions and I agree, I think they should be given (for free).

..."moving from an octave based idea to other directions may help to obtain a more pure output."...

It certainly does. But, say that we do not consider Cordier's pro experience, Stopper's experience, your experience, my experience, say we do not consider any pro tuner's experience, who has ever been able to tune Historical ET and its pure-octaves theoretical base? Nobody. In my opinion, all tuners have directed towards ET's evolution, towards Modern ET Theories and models.

..."I believe that we have to be told how the instrument are tuned and have comparison provided so to decide which suits the best which music."...

I agree (sob!), and I ask: where is the problem nowadays? Tuners could easly be told. Why Modern ETs are meeting (here, in my opinion) with resistance? Just because it is not admitted that ET could evolve? Why are we still talking about "true ET" and yet referring to Historical 12th root of two ET?

a.c.

.
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 01/17/10 12:53 PM

Alfredo, the only interest I have in ET is to teach it well enough to novices so they can pass the PTG exam, never to tune it for any pianist. I also work on the perfection of ET when I conduct a "master tuning" for one of the PTG exams but I never work in those ways when I tune any piano for the public. I do not think of tuning of any kind in terms of mathematics, so any such discussion is beyond my understanding. Therefore, I cannot participate in that.

Kamin, from what you say, the teaching of piano tuning is 40 years behind what it is in the USA. The only way anyone can learn it is from a teacher and lots of practice. That keeps the number of piano technicians who are really good very small because only a few people can learn that way. However, I find it difficult to believe, especially in Germany and Austria that technicians there are not just as familiar with the same advanced concepts as we are in North America.

The concept of octave sizes and that ET can be tuned within any size octave is something only recently understood. There is no mention of it in older books on tuning. It is something I have come to understand only by my association and participation with PTG and working on the tuning exams. I wrote a PTG Journal article about that 2 years ago. The only books on piano tuning which have any material about octave sizes or types are not the basic books but the advanced concept books such as "On Pitch" by Rick Baldassin.

There were teachers such as Virgil Smith who taught that the technician should learn to listen to the "whole sound". He did not use CM3s, only 4ths & 5ths and he would only tune a fine grand piano, usually a Steinway. He did not listen to isolated partials and advised technicians not to do that. I used to attend his sessions in the 1980's. He tuned a beautiful sounding piano back then. From what I know today, he did not tune a "pure" temperament octave. It was always stretched slightly beyond the point of true beatlessness. He could and would only explain this in very vague terms; not the way it is explained today.

In the last decade, his health has deteriorated. The last report I heard from a technician who attended perhaps his last session was that he could no longer tune a true ET. PTG no longer hires him to teach piano tuning. He recently wrote a very small, thin book on piano tuning. It does not contain and advanced concepts, only the vague, "whole sound" idea from which any technician wishing to improve knowledge and skills can gain nothing of practical value.

Similarly, Franz Mohr would teach piano tuning at PTG functions. He always got a very large audience. Everyone wanted to see how Steinway's best technician would tune the piano. Of course, he would only tune a large Steinway piano. He would often say that he is the world's luckiest piano technician because he did not have to tune any other kind of piano. He used a temperament octave from A3-A4 which very few people used. He tuned only 4ths & 5ths but had quick and odd ways to check that which nobody could follow or understand.

He could not explain what he did. He could only use vague terms such as, "You have to make it shine, you know". Nobody who attended his sessions really learned much if anything at all which they could use in their own practice. They only got some inspiration from it. There was no information about what to do with a small piano. The book he wrote was a pleasure to read but contained really only anecdotes about his life as a technician and absolutely no useful information about how to tune any piano. I also witnessed Franz Mohr tune a piano in a non-ET but he denied that was true. For him, ET was his only model but he did admit that he was not perfect. He is a very religious man. So, to him, no human being is ever perfect. He only ever attempts to tune ET and if the results are something else, it is not what he intended, it is only what actually happened on that particular occasion.

Both of these technicians always said the same thing the pianist you asked about temperament said. Most pianists in this country, most piano technicians and most music educators would say the same thing. I have often communicated with a very intelligent scholar in Mexico. He says that virtually all pianists and music educators in his country only know of ET and believe that there is no other possibility for the modern piano. Yet, what the piano tuners actually do is almost never really ET. When I asked Franz Mohr about non-ET, he said the same thing you said, "Then, on a performance piano, or one used in many different venues, I see no possibility to change temperament then fight with stability for weeks."

However, there are other technicians who have taught other ways to tune pianos. Certainly, people in France did not read Braide-White's book but they would have read whatever was available in France. The world has long been sold on ET and ET only. Nearly everyone believes it is the only way to tune a piano. The problem with that, as I see it, is that many technicians have not been able to use the information presented in such material adequately or correctly. Their results are imperfect. They firmly believe what they do is ET and they believe only in ET. That is very clear to me and quite well understood. However, their lack of knowledge about any other possibilities prevents them from ever knowing that what they actually do is often not really ET. In far too many cases, it never was, is not now and never will be ET until they learn more information and better techniques.

In my area, many of us have long been far beyond the narrow concept of ET only. Some of us never tune any pianos in ET but we never encounter any of the problems which all of the ET only technicians only theorize would happen. We simply do not believe those theories and we ignore completely all of the warnings because our experience over many years has told us they simply are not true. There are also other technicians in other parts of the USA (and I know some in Canada) who never or almost never tune in ET.

There are dozens of them just among those I know of. However, if you consider that perhaps 50 or fewer technicians (or maybe even 100-200)do what I do and believe what I do, out of the approximately 4,000 technicians who belong to PTG and however many more technicians there may be, yes, that is a very small minority. Just because we are a minority, it does not mean that we are all wrong and the rest are all right. We do what we do because we believe in what we do and we find acceptance of it. There has always been a growing number of technicians who have expressed interest in these concepts during the entire time I have worked with them. Some have tried different ideas and embraced them, others have chosen to only occasionally perform non-ETs in certain circumstances.

From the top down, PTG itself used to have the same beliefs and attitude about non-ET but it long ago came to understand that the use of non-ET represented an expansion of knowledge and skills, not a digression. It chose to honor the person most responsible for advocating that expansion with its highest honor at the last convention. PTG still teaches ET and still uses ET as the model for its exams and probably always will, even though ET was never specified as a rule. PTG regularly presents programs on how to tune non-ETs and also offers performances in non-ETs at its events. It has done so for many years although certainly not at each and every event each and every time.

From the beginning, the PTG Standardized Tuning Exam was based upon what most tuners practiced. The tolerances for it were based upon what the very best technicians could do at the high end and about what 50% of technicians could barely or not quite accomplish at the low end. Since almost all tuners tuned ET and only thought in terms of ET, the tuning exams have always been based on ET but once again, ET is not specified. PTG left open the possibility that tuning could evolve to a point where the majority of tuners do something else.

The tolerances for the exam have been raised over time to make it more difficult. When it was seen that too many technicians could pass the exam too easily, the tolerances were raised. The exam "master tuning" model has also evolved. Technicians consult with each other about how to create an ET model which is closer to perfection each time they do it. They don't do that with mathematical theory on paper or with calculators. However, they do compare the statistical results and ponder the numerical results of purely aural tuning and look for ways to improve aural tuning. The octave size analysis has been one of those recent areas of research.

I am not against purely mathematical analysis of tuning, ET or otherwise. I simply don't have the mathematical skills to participate in that nor do I have much interest in acquiring them. I also am not against the exploration of the effects octave size and/or stretching techniques have on ET. I know there are differences which technicians and pianists can perceive but I also believe that to combine that knowledge with other ideas for temperament provides for a much broader area to explore. To me, limiting oneself only to ET and its perfection is to impose a very unnecessary constraint which denies the world of music the many possibilities which the piano has to offer.
Posted by: RPD

Re: HISTORICAL ET AND MODERN ETs - 01/17/10 01:18 PM

Originally Posted By: Bill Bremmer RPT
The only books on piano tuning which have any material about octave sizes or types are not the basic books but the advanced concept books such as "On Pitch" by Rick Baldassin.


An excellent book, filled with explanation that reveals itself like the peeling of an onion. Its been my nightstand read for many months.

RPD
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 01/17/10 01:50 PM

Originally Posted By: alfredo capurso

Kamin, you report and write:

..."I have talked of the organ effect and he agreed that it should be magnificent, but if at the expense of modulation in farther tonalities he stated that it would not then suitable for daily use."...


The pipe organ effect is not, nor ever has been a goal for tuning. It is simply an observation of what happens when the octaves are tuned in a particular way. When those octaves are combined with equal beating M3s and M6s the way they are in the EBVT III, the effect is truly stunning.

Yes, I heard a hint of that effect when I heard the Stopper tuning but it was not the same as when the piano is tuned in the EBVT or EBVT III.

The effect only happens really when a long C Major arpeggio is played across the entire keyboard with the damper pedal held and the piano is allowed to ring. That is not playing music. It is nothing more than a curiosity.

That is not to say that my customers are unimpressed by it, they most certainly are. For them, it is a confirmation that the piano is now very well tuned. So, the recent mockery and ridicule there was against Rafael who knows what the pipe organ effect really is as well as its value, was particularly insulting. At the same time that it was insulting, it also blatantly demonstrated the ignorance of the person who chose to mock and ridicule.

There was also an example in a musical context which Patrick offered when the pipe organ effect was briefly heard. It just so happened that his musical example captured that effect. He enjoyed the experience and so did I. I can't imagine any pianist who might hear that same effect when the context of music may cause it to exhibit itself who would want the piano technician to eliminate it.

Tuning the piano in standard ET with the octaves tuned the way they most often are will not yield that effect. Therefore, most people have never heard it and probably never will. That will not persuade any of us who know how to produce it from doing so. There will never be any pianist for whom we ever tune a piano who will ever ask us to change the tuning so that the pipe organ effect cannot be heard.

You all will get a chance to hear exactly what that effect is and you will all understand exactly why it has been called the "pipe organ effect" very soon next month when I go to Grandpianoman's home to tune his piano. We will make sound clips of that effect alone. We will also play various selections of different music of different styles in various keys with all possible modulations for everyone to hear and to form their own opinion.

While I certainly don't expect that by putting the sound files on this forum that suddenly the entire world will want to have its pianos tuned in the EBVT III, I do expect that over time, there will be more and more technicians who become interested in it as they hear them.

Here is one such message from last Friday, the name and other identifying information has been redacted for that person's privacy:

Date: Friday, January 15, 2010 7:13 PM
From: charles *****
To: BillBremmerRPT
Subject: Thanks!
Size: 7 KB
Mr. Bremmer:

My name is Charles *******. I live in ******, and have been in the Tuning business for +20 years, but have only seriously pursued building a business for the past 5. I am an associate in the PTG in ******, and I service the northwest part of *****, *****, and into ***** on occasion. I am a retired school principal, and continue to teach band after 32 years. I lack a dissertation in the completion of a Doctorate in Education. I am a performing church and concert organist, and this year am Grand Master of Masons in the state of *****. I have been the principal organist for the ******. for +30 years. I have been fortunate to study and perform piano for many years with many outstanding teachers and collegues. After my tenure as Grand Master, I am going to complete my quest for RPT status in memory of my mentor, Robert *****, RPT, who began my desire to be an outstanding tuner/tech, and was my friend and hero.

I do not get to attend the PTG meetings in ***** since they meet while I teach school, but I have developed a great friendship with our President, and consult with him frequently.

I began this letter with a quick bio to defend the statement that I TRULY APPRECIATE THE CONTRIBUTIONS THAT YOU MAKE on the Piano World Forums. I have quietly studied the content for a number of years, and have received a tremendous amount of knowledge that has improved my skill. I have tuned your EBVT both with tunelab in the temperament, and aurally, and I assure you that as a pianist with almost 50 years of experience, it makes the music and the piano come alive. [Bold face added for emphasis].

I just feel that I need you to know that there are many techs who aspire to perfection that read and listen to the content who will probably never post on that site, but still appreciate your unselfish efforts to improve a profession that was unapproachable not that many years ago.

You have to contend with a few "techs" who sling crap in an effort to improve their station. Please do not let them get you down, and remember, you are doing great things to improve the craft.

Sincerely,

Charles *****

These kind of messages are frequent. The traffic on my website is particularly impressive, especially the sources from where that traffic originated and the number of downloads of specific information there have been. This is true for ET tuning methods as well as the EBVT.

So, I am not the least bit concerned about being seen as a "maverick" tuner with unconventional ideas who will soon fade into obscurity.

Today, I received this message:

Date: Sunday, January 17, 2010 5:10 AM
From: Ken *****
To: BillBremmerRPT
Subject: Piano Technician mentoring
Size: 5 KB
Greetings Mr. Bremmer --

I am a recent addition to the world of Piano Technicians. I have been through the course from the ***** School (5 years to complete, but that is a longer story) and have applied for membership in the PTG. Last week I attended the local meeting of the PTG/Madison chapter and had my application signed by *****. I desire to work for the RPT, and would like to take you up on the offer of assistance in study as stated on your website....

I live relatively close to Madison so travel is not a problem. My schedule is very open (I am a statistic of the economy) so whenever it suits you, I would be grateful for your guidance.

I have decided that being a Piano Technician is my new career, so you can rest assured that I take this quite seriously and with great interest. I have three pianos of my own (one is a player) that I work on and I have done some work for others.

I look forward to your reply.

With Best Regards,

Ken *****

I am quite interested, actually to find out just what this person's temperament sounds like after 5 years of study. Considering the school he mentioned, I know that the method is a 4ths & 5ths sequence. If he can do a reasonably good temperament using that method, I will work with him on how he can improve tuning using that method.

If, however the results are actually reverse well as I fully expect them to be, we will start all over and use the ET via Marpurg. I won't say one word about the EBVT unless he asks about it. If he does, I will tell him that I will teach him to tune that after he becomes an RPT. I will not charge this student one red cent to tutor him. It will be my contribution to PTG.

Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 01/17/10 10:15 PM

Originally Posted By: alfredo capurso

I would really like if we managed to elaborate on this first posted thread's issue:

..."what is difficult about acknowledging modern ETs, i.e. new algebraic geometrical models, new degrees of harmoniousness, new tonal effects, new spectral fusions, and accepting that also 12th root of two ET could evolve, actually it has evolved."...


There is nothing difficult about acknowledging modern ET's - except that in all the pages written, there hasn't been anything new at the tuning level about these new approaches. Simply an ET with a different width to the octave. While this may be new "across the pond", technicians over here have been experimenting with this since the early 1980's or before.

Ron Koval
chicagoland
Posted by: BDB

Re: HISTORICAL ET AND MODERN ETs - 01/17/10 11:28 PM

I am not convinced that there is anything new at all, except for the proliferation of electronic devices. They have redefined the way that we talk about things, without necessarily changing anything that people are doing, now or in the past.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 01/18/10 05:31 AM

Originally Posted By: RonTuner
Originally Posted By: alfredo capurso

I would really like if we managed to elaborate on this first posted thread's issue:

..."what is difficult about acknowledging modern ETs, i.e. new algebraic geometrical models, new degrees of harmoniousness, new tonal effects, new spectral fusions, and accepting that also 12th root of two ET could evolve, actually it has evolved."...


There is nothing difficult about acknowledging modern ET's - except that in all the pages written, there hasn't been anything new at the tuning level about these new approaches. Simply an ET with a different width to the octave.
Ron Koval
chicagoland


I respectfully disagree, the octave begin to be a side effect when the tuning is based on another tempering than 12.

Octaves are not "tuned" in Cordier, 10ths are (for what I know) they are checked in the same way that we check 5ths 4ths in usual tuning (or 10 ths 17ths, depending which method we use)
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 01/18/10 07:12 AM

Originally Posted By: alfredo capurso

Kamin, you report and write:

..."I have talked of the organ effect and he agreed that it should be magnificent, but if at the expense of modulation in farther tonalities he stated that it would not then suitable for daily use."...

Talking about Modern ETs, Stopper stated quite recently that his pure 12ths tuning gains that kind of effect (organ) on any key, preserving any change in tonality.

Do not you think this could be, and maybe should be, enough for wanting to know more about ET's evolution and more about this Modern pure-12ths ET aural tuning?

I remember you asking for practical directions and I agree, I think they should be given (for free).

..."moving from an octave based idea to other directions may help to obtain a more pure output."...

It certainly does. But, say that we do not consider Cordier's pro experience, Stopper's experience, your experience, my experience, say we do not consider any pro tuner's experience, who has ever been able to tune Historical ET and its pure-octaves theoretical base? Nobody. In my opinion, all tuners have directed towards ET's evolution, towards Modern ET Theories and models.

..."I believe that we have to be told how the instrument are tuned and have comparison provided so to decide which suits the best which music."...

I agree (sob!), and I ask: where is the problem nowadays? Tuners could easly be told. Why Modern ETs are meeting (here, in my opinion) with resistance? Just because it is not admitted that ET could evolve? Why are we still talking about "true ET" and yet referring to Historical 12th root of two ET?

a.c.

.



Hello ALfredo,
(sorry I forget to answer ) of course I am interested in by different valuable approach that could conciliate the theory
and the practical way to do things. I am not sure that it would be easy to pass those kind of concepts.

The idea to have advice of the actual acoustician and research people is a good one.

They may however state that mostly piano tuning is involved (which does not seem to raise a lot of interest those days !).

Indeed I am impatient to listen and to have a close understanding of a different way to do things.

I also believe that justness is instrument (and conditions) based, so theorizing may open a window on a part of the subject only.

I have promised myself to give holidays to my estimated colleagues and refrain to write as extensively , even if I appreciate the discussions. I'll keep an eye and answer only if really need.
Yes I like to have more insight and at last more recordings of Bernhard Stopper tunings (as I am expecting that EVBT tuning record).

I am surprised than so little of the forum members are willing to record some of the pianos they work on.
Discussions are good, but listening is more interesting to me, be it with headsets on a computer card with a MP3.

Pianos, are used to play music, so thats what we should be able to show in the end it is easier those days than ever.

See you soon !

ISaac









Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 01/18/10 07:39 AM

Alfredo:

I think you are doing what some other posters here also do: construct a straw man that you can knock down to prove a point.

As soon as iH is considered, twelfth root of two ET along with any root of anything ET is shown to be an inadequate model.

I wonder why we can’t get beyond thinking of tuning theory in this way. Perhaps it would be harder on the self-promotion aspect of the discussions.
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 01/18/10 09:33 AM

Let us not forget that ET can be constructed within virtually any conceivably sized octave from slightly narrow to wide enough that the 5ths become pure. All of the classic books teach only one possibility but tests for the octaves were not understood as well as they are today. For example, on one page, Braide-White gives the test for a 4:2 octave but on another, he shows a test for a 6:3 octave, apparently believing them to be equivalent.

Indeed, they both can sound very similar on some pianos. I can imagine that in Braide-White's time, a large, low inharmonicity piano would yield very little, if any aurally perceptible difference between a 4:2 and a 6:3 octave in the midrange. When working with other examiners on a moderate inharmonicity piano and trying to find the compromise between a 4:2 and 6:3 octave, the tests applied to each for the A3-A4 octave would both sound about the same to all three of us. When that happened, we left the octave tuned that way. If we were to narrow or widen the octave even slightly, one test would favor over the other but when we found the point where they both sounded alike, we deemed it to be the best compromise. Ideally, neither test would be perfect, the 4:2 would be slightly wide and the 6:3 slightly narrow but sometimes, we could not really get that.

Up until about 12 years ago, I thought in terms of ET being only one possibility. After all, the word "equal" is one that can't take a modifier. A temperament cannot be "more equal" or "less equal", it is either equal or it is not. Of course, a temperament can be almost equal and for that, we use the Latin word, "quasi" (equal).

Back then, Kent Swafford pointed out to me that a temperament can still be equal, regardless of the size of octave. That statement had slipped my mind until in 1999, at a Chicago Chapter PTG meeting, Virgil Smith tuned two Steinway Model M pianos, one with the temperament octave about 1/2 beat per second narrow and the other with the temperament octave about 1/2 beat per second wide. There was clearly a difference in character between the two pianos. Virgil said at the time that his usual practice was to tune the wider octave but for a very few customers who did not seem to like the results of that technique, he would tune using the narrowed octave.

In sound files posted by Grandpianoman recently, we heard a piano tuned with the RCT in default stretch mode which I presume to be the compromise between the 4:2 and 6:3 octave, although it could have been as narrow as 4:2, I don't know for sure without inquiring. The other was the Stopper tuning. I did hear a distinct difference between the two and my preference was for the Stopper tuning. I liked what I perceived as "clarity". Others seemed to prefer the RCT tuning, calling it "warm" or "mellow".

So, there is no doubt that there are effects to be heard and appreciated or disliked as the case may be when one establishes the central octave size when tuning ET. It is clear to me that Alfredo has found to his own satisfaction an octave size that he finds appealing. Now, from what I gather, he does not think in terms of a single octave but rather a double octave. Whatever the size of that double octave is, all of the pitches within it are equally placed. Apparently, Herr Stopper thinks in terms of an octave and 5th and from what I gather, that interval is beatless and all pitches are placed equally within it.

Each of the above will yield single octaves however, of a distinct width and they will be somewhat wider than absolutely beatless. As I see it, they cannot be very different from each other although they are probably not exactly the same. It seems to me that whatever the difference may be is more intellectual than anything else, the thought process behind creating the construction with the results of both being fairly close, if not exactly alike. Either thought process would seem to be as valid as the other. Only the satisfaction of the technician who uses the method and the recipient of the work, the pianist matter in the end.

If a performing artist went one day to Italy and Alfredo tuned the piano, the artist would use it and like it. If he went the next day to Germany and Herr Stopper tuned the piano, the artist would probably like his work just as well. Other factors would naturally be present such as different makes and models of pianos. So, a direct comparison between the Stopper tuning and Alfredo's CHAS method is virtually impossible. It would still be next to impossible even if the two pianos were side by side because they would still be two different pianos, even if they were the same make and model.
Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 01/19/10 09:14 AM

Originally Posted By: Kamin
Originally Posted By: RonTuner
Originally Posted By: alfredo capurso

I would really like if we managed to elaborate on this first posted thread's issue:

..."what is difficult about acknowledging modern ETs, i.e. new algebraic geometrical models, new degrees of harmoniousness, new tonal effects, new spectral fusions, and accepting that also 12th root of two ET could evolve, actually it has evolved."...


There is nothing difficult about acknowledging modern ET's - except that in all the pages written, there hasn't been anything new at the tuning level about these new approaches. Simply an ET with a different width to the octave.
Ron Koval
chicagoland


I respectfully disagree, the octave begin to be a side effect when the tuning is based on another tempering than 12.

Octaves are not "tuned" in Cordier, 10ths are (for what I know) they are checked in the same way that we check 5ths 4ths in usual tuning (or 10 ths 17ths, depending which method we use)



Well, ok - let's see some data. It should be pretty easy for those of you that think that you have something very new to list the tuning targets for a common piano model - we can discuss the partials to list as well as the model of piano that we all have available. Then we can look at how that compares to other methods of calcualting a tuning as well as standard aural approches and see the results...

Ron Koval
chicagoland
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 01/19/10 09:37 AM

Excellent challenge, Ron. I am drooling, but not holding my breath. Hopefully I won't have to hold my nose.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/20/10 03:11 PM

Ron,

I appreciate very much your positive intentions. I'm travelling, this is why I'm taking some time to reply.

..."list the tuning targets for a common piano model"...

Could you explain what you mean?

..."we can discuss the partials to list as well as the model of piano that we all have available."...

May I ask you to articulate your idea, and we could think of all the necessary comparesons.

..."Then we can look at how that compares to other methods of calcualting a tuning as well as standard aural approches and see the results..."...

Could you go deeper on this, by saying what you mean with "methods of calculating a tuning" and "standard aural approaches"? These of yours may be the starting points indeed.

Regards, a.c.

.
Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 01/20/10 03:49 PM

Hi Alfredo

While the math is important and interesting to some, I'm interested in the final product (tuning).

To measure a tuning, for example, in the US, we have the registered piano technician's exam. From A0 - B3, each note is measured at the 4th partial level against a machine to list an offset from a pitch standard. Likewise, from C4 -B4 the 2nd partial is measured. From C5 -C8, the 1st partial is measured. Any partial could be chosen, these are just the standards here.

So we could all compare tunings on a similar piano, we would agree on a piano. Steinway B, Yamaha P22 etc.. - doesn't matter, as long as we use the same model. Each individual piano may have it's own unique signature tuning, but those of the same model usually will end up with similar stretches if the same tuning approach is used.

For those of us using multiple machines over the years, we are accustomed to choosing alternate stretches. RCT has built in octave tuning styles from 1-9. These use the inharmonicity data collected during the measuring phase to calculate the width of the octaves in different regions of the piano. Further input through the custom equalizer function allows for more control from the technician. Tunelab and Verituner also have custom settings to force the machine to use a different method to calculate a tuning - usually choosing a different partial match, a blend of partial matches as well as any additional or lessening of stretch. I haven't used the SAT much, but understand that the double octave beat control also allows for technician input to create a different tuning style.

Standard aural approaches refers again to the registered piano technician's exam which is a standardized tuning approach for testing purposes.

Even without full tuning data, just 1 or two notes per octaves allows the visualization of stretch parameters. We might find out that your approach produces the same overall tuning stretch as RCT with OTS7, for example. (just a random example.)

Ron Koval
chicagoland
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 01/20/10 06:26 PM

Ron, do you know what the default stretch for the A3-A4 octave on the RCT would be? How about the Verituner? Is it a 4:2 octave + 1 cent, the way the SAT FAC program works? Adding 1 cent to a 4:2 octave usually accomplishes the compromise between a 4:2 and 6:3 octave. Enquiring minds want to know, lol.
Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 01/20/10 09:11 PM

Hi Bill

Default for the Average style in the Verituner A3-A4 octave is a 4:2 octave, .32 beats/sec wide of pure. I think I have the RCT info at work...

Ron Koval
chicagoland
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 01/21/10 12:26 AM

I am unsure those softwares know how to build a temperament with anything else than 12 or 13 notes , for what I know. I asked when wanting to have a pure fifth tuning)

May be Tunelab ( could you confirm Mr Scott please ?)

Seem to me that there is always a "temperament approach" (if not none of the HT could be used)
Even Verituner which is based on a multi partial analysis and weighting have a different process to compute the temperament than to expand the tuning in the piano.

Making a temperament and use octaves partial match to reproduce it within the scale is the logical all EDT may strive for, it seem evident that they try to act as most tuners do.

Asking them to use a partial relation to compute the temperament is not possible (pure 5Th, pure 12Th, semi pure 12th-15th, etc)


Comparing tunings on similar pianos may be possible without much trouble, assuming the same music samples is played on the pianos and they are in the same room.

Voicing and sound ability of the pianos have not much to do in that, from a musical point of view ( I believe).

Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/21/10 07:03 PM

Originally Posted By: RonTuner
Hi Alfredo

While the math is important and interesting to some, I'm interested in the final product (tuning).

To measure a tuning, for example, in the US, we have the registered piano technician's exam. From A0 - B3, each note is measured at the 4th partial level against a machine to list an offset from a pitch standard. Likewise, from C4 -B4 the 2nd partial is measured. From C5 -C8, the 1st partial is measured. Any partial could be chosen, these are just the standards here.

So we could all compare tunings on a similar piano, we would agree on a piano. Steinway B, Yamaha P22 etc.. - doesn't matter, as long as we use the same model. Each individual piano may have it's own unique signature tuning, but those of the same model usually will end up with similar stretches if the same tuning approach is used.

For those of us using multiple machines over the years, we are accustomed to choosing alternate stretches. RCT has built in octave tuning styles from 1-9. These use the inharmonicity data collected during the measuring phase to calculate the width of the octaves in different regions of the piano. Further input through the custom equalizer function allows for more control from the technician. Tunelab and Verituner also have custom settings to force the machine to use a different method to calculate a tuning - usually choosing a different partial match, a blend of partial matches as well as any additional or lessening of stretch. I haven't used the SAT much, but understand that the double octave beat control also allows for technician input to create a different tuning style.

Standard aural approaches refers again to the registered piano technician's exam which is a standardized tuning approach for testing purposes.

Even without full tuning data, just 1 or two notes per octaves allows the visualization of stretch parameters. We might find out that your approach produces the same overall tuning stretch as RCT with OTS7, for example. (just a random example.)

Ron Koval
chicagoland



So, we may only have to agree on the use of one precise ETD and one precise piano make and model. Correct?

I should tune as I normally do, measure the frequencies and list the offset from our ETD's pitch standard. Would this be correct?

Kamin, you write:..."I am unsure those softwares know how to build a temperament with anything else than 12 or 13 notes , for what I know. I asked when wanting to have a pure fifth tuning)

May be Tunelab ( could you confirm Mr Scott please ?)"...

I wonder too.

Regards, a.c.

.

Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 01/21/10 08:27 PM

Originally Posted By: RonTuner
Hi Bill

Default for the Average style in the Verituner A3-A4 octave is a 4:2 octave, .32 beats/sec wide of pure. I think I have the RCT info at work...

Ron Koval
chicagoland


Ron,

This is the first I have heard that a 4:2 octave sounds anything but "pure". Granted, .32 beats per second is a very slow beat but any 4:2 octave I ever tuned (by direct interval) sounded "pure" to me.

This does, however bring a little light to some of the math that Tooner has done. A 4:2 octave is, after all, wider than a 2:1. As I always thought of them, the 4:2 octave was just on the "edge" of creating an audible beat while a 2:1 is solidly "pure". .32 beats per second can still qualify (I suppose) as being on the edge since you would only hear a very slow beat that occurs over 3 full seconds. That would be difficult to perceive but I find it hard to believe that it could even be that much.

The instructions I give in the ET via Marpurg sequence tell the tuner to approach the octave from the wide side, narrowing the octave just to the point where the beat apparently stops. That approach will generally test out aurally for a 4:2 octave.

The opposite approach, to widen a narrow octave just until the beat apparently stops will usually test out aurally as a 2:1 octave.
Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 01/21/10 11:33 PM

Originally Posted By: alfredo capurso



So, we may only have to agree on the use of one precise ETD and one precise piano make and model. Correct?

I should tune as I normally do, measure the frequencies and list the offset from our ETD's pitch standard. Would this be correct?



.



Yes, a specific piano, but almost any of the electronic tuning devices should be able to measure the notes.

Something like
Yamaha c6

A2 110hz 4th partial -1 cent
A3 220 hz 2nd partial -.59 cent
A4 440 hz 1st partial 0.0
A5 880 hz 1st partial +2.85 cents
A6 1760hz 1st partial +13.9 cents

Cents will be easier for us to work with... I'm not sure I can translate Hz... Maybe Jeff can?

Ron Koval
chicagoland
A
Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 01/21/10 11:37 PM

Originally Posted By: Bill Bremmer RPT
Originally Posted By: RonTuner
Hi Bill

Default for the Average style in the Verituner A3-A4 octave is a 4:2 octave, .32 beats/sec wide of pure. I think I have the RCT info at work...

Ron Koval
chicagoland


Ron,

This is the first I have heard that a 4:2 octave sounds anything but "pure". Granted, .32 beats per second is a very slow beat but any 4:2 octave I ever tuned (by direct interval) sounded "pure" to me.

.


I looked up the RCT values and they are the same for OTS 4 and for the RPT exam emulation mode. 4:2 +.32 beats/sec (OTS values from 1-9) It seems they both target a place somewhere between a 4:2 and a 6:3 octave for an average tuning approach. I'm not sure what the default tuning is for Tunelab.

Ron Koval
chicagoland
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 01/22/10 03:45 AM

Originally Posted By: Bill Bremmer RPT
Originally Posted By: RonTuner
Hi Bill

Default for the Average style in the Verituner A3-A4 octave is a 4:2 octave, .32 beats/sec wide of pure. I think I have the RCT info at work...

Ron Koval
chicagoland


Ron,

This is the first I have heard that a 4:2 octave sounds anything but "pure". Granted, .32 beats per second is a very slow beat but any 4:2 octave I ever tuned (by direct interval) sounded "pure" to me.



approximatively the same size in the "Pleyel" temperament based on a ladder of 3 thirds , F3-F4, then the progression follows the same kind of stretch to the treble until it is definitively too large.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 01/22/10 07:47 AM

Bill & Ron:

Here are some calculations from a Charles Walter Console in a simulator with A3 having an iH of 0.24 and A4 having an iH of 0.67:

A3 = -0.72 cents
2:1 = 0 bps
4:2 = -0.45 bps
6:3 = -1.8 bps

A3 = -1.6 cents
2:1 = +0.22 bps
4:2 = 0 bps
6:3 = -1.22 bps

A3 = -3.07 cents
2:1 = +0.6
4:2 = +0.75
6:3 = 0 bps

A3 = -2.48 cents
2:1 = +0.45 bps
4:2 = +0.45 bps
6:3 = -0.45 bps

Notice how when the 4:2 and 6:3 are equal beating, the 2:1 is also equal beating! This is always the case and I suspect that is why the compromise is so popular. I also suspect that this may be the origin of Virgil Smith’s “Natural Beat”. Not that all octaves should be tuned this way, but here is an about ½ bps wide 2:1 octave and is a guide or standard that can be used for all 2:1 octaves to be tuned to. It is really just speculation on my part, and I do not tune pianos that are large enough that I would try to tune this way.

I agree with what Bill said about coming from below tends to tune more of a 2:1 octave and tuning from above more of a 4:2 octave. I no longer trust myself to tune octaves where I do not have to. Instead I use 4ths and 5ths on plain strings below about C6, and then check octaves and 12ths etc.

Hope this helps. If you give me other sample iH values I can easily provide additional beat rates and cent deviations, or other values you may be interested in as well.
Posted by: accordeur

Re: HISTORICAL ET AND MODERN ETs - 01/22/10 09:01 AM

Tunelab average tuning.

A0 -5.83
A1 -2.83
A2 -1.94
A3 -1.06
A4 0.00
A5 2.96
A6 9.18
A7 24.37
C8 30.96
Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 01/22/10 10:41 AM

Before tossing numbers around - can we find a specific model of piano that we can all use for testing?

Easy for me:

Baldwin SF10, 243
Kawai RX-A
Steinway B, L, M, D
Yamaha CFIII, G7, C6, U1, P22

Harder, but possible
Yamaha C3, G1
Couple of Kawai grands - have to check the model - I know one is a GS-40 and another is a KG-2C...
Petrof 7' - I can get the model number

Ron Koval
chicagoland
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 01/22/10 10:54 AM

Sure, how about Yamaha U1? I have that in the simulator.

I'll post the same numbers for a U1 in a little while if that is agreeable, or are there other numbers you'd like?
Posted by: accordeur

Re: HISTORICAL ET AND MODERN ETs - 01/22/10 11:49 AM

tunelab steinway D

A0 -2.50
A1 -0.81
A2 -0.37
A3 -0.16
A4 0.00
A5 2.13
A6 8.12
A7 25.30
C8 33.25
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 01/22/10 12:05 PM

All:

Here is what I get with a Yamaha U1. iH is 0.2 for A3 and 0.57 for A4:

A3 = -0.61 cents
2:1 = 0 bps
4:2 = -0.34 bps
6:3 = -1.38 bps

A3 = -1.28 cents
2:1 = +0.17 bps
4:2 = 0 bps
6:3 = -0.87 bps

A3 = -2.42 cents
2:1 = +0.46
4:2 = +0.58
6:3 = 0 bps

A3 = -1.96 cents, or 0.68 cents wide of 4:2
2:1 = +0.35 bps
4:2 = +0.35 bps
6:3 = -0.35 bps

And 1 cent wide of 4:2

A3 = -2.28 cents
2:1 = +0.43 bps
4:2 = +0.51 bps
6:3 = -0.11 bps

And as a spill over from another Topic, here is the result from tuning F3-C4 P5 at -0.5 bps and C4-F4 P4 at 1.0 bps.

F4 = -0.43 cents, 0.39 iH
C4 = -0.86 cents, 0.26 iH
F3 = -1.47 cents, 0.13 iH

F3-F4 4:2 = +0.08 bps, or 0.2 cents wide of 4:2, and 0.23 cents from a 4:2/6:3 compromise.

And F3-C4 P5 6:4 partial match = -1.31 bps.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/22/10 07:14 PM


Hello.

Ron, you say:

..."can we find a specific model of piano that we can all use for testing? Easy for me:

Baldwin SF10, 243
Kawai RX-A
Steinway B, L, M, D
Yamaha CFIII, G7, C6, U1, P22..."


I share your proposal. I shall try to reduce the choise, so that we will eventually choose (look for and work on) one precise model. We'd better check the factory and the serial number too (for equal strings age/scaling?), yes? Any reasonable preference?

Kawai RX
Steinway B, D
Yamaha CFIII, C6, U1

Regards, a.c.

.
Posted by: Gadzar

Re: HISTORICAL ET AND MODERN ETs - 01/23/10 02:14 AM

Ron,

Cents are easy translated to hz, the formula is:

f' = f * 2^(cents/1200)

so:

110 hz - 1 cent = 110*2^(-1/1200) = 109.94 hz
220 hz - 0.59 cents = 220*2^(-0.59/1200) = 219.93 hz
880 hz + 2.85 cents = 880*2^(2.85/1200) = 881.45 hz
1760hz + 13.9 cents = 1760*2^(13.9/1200) = 1,774.19 hz
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/24/10 04:16 PM

Ron, you write:

..."There is nothing difficult about acknowledging modern ET's - except that in all the pages written, there hasn't been anything new at the tuning level about these new approaches. Simply an ET with a different width to the octave. While this may be new "across the pond", technicians over here have been experimenting with this since the early 1980's or before."...

While waiting for the favorite piano's choise, I'll try to explain what is new - at the tuning level - about Modern ET models.

Modern ET models establish new geometrical progressions rules and new tuning references: Cordier's model fixes pure-5ths, Stopper's model's fixes pure 12ths, Chas describes only beating intervals in the sound set, i.e. all intervals contribute to a beating whole.

You write:..."there hasn't been anything new at the tuning level about these new approaches"...

I do not think this is correct. You can well understand that a model and/or a Theory can change the approach to tuning and the relative targets. This could be the case for all the different and yet actual "true ET" tunings, actual true ETs (sometime Reverse Well) that have got no rules for 5ths and octaves and 12ths and 15ths, true ET that I can only call quasi-12th root of two ET (or what?), and yet today Modern ETs are able to rule also those "mysterious" intervals.

You write:..."While this may be new "across the pond", technicians over here have been experimenting with this since the early 1980's or before."...

You see Ron, here we are not talking about experiments, but truly new and finished and approved Modern ET Theory and models. I cannot really say when experimenting started "across the pond", but I can tell you about what my experimenting gained: it gained Chas ET Theory, in fact a Modern, approved and practicable ET model that can renew our tuning referencies once for all.

Modern ETs do not put an end to experimentations nor they limit the freedom in choosing other kind of temperaments. Modern ETs simply represent 12th root of two ET's evolution, i.e. the evolution of the first algebraic geometrical progression.

Regards, a.c.

.
Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 02/03/10 02:25 PM

Sorry - I had a serious side-track...

Let's go with the U1 - looks like that's the easiest for all of us to work with.

I'll be back again to post some numbers. We still need come up with which partials would be most appropriate to measure/post.

Might not be till next week

Ron Koval
chicagoland
Posted by: TimR

Re: HISTORICAL ET AND MODERN ETs - 02/03/10 04:33 PM

I wonder if this might be a case where the digital piano might actually be an advantage, rather than competition.

As far as I know digital pianos mimic an acoustic one to the best of their ability, including the inharmonicities of one tuned to some version of ET.

DPs now outsell acoustics 2 to 1 or so, right? So there's a pretty good user base.

Seems to me it would be possible to adjust the DP to mimic some of the ET variants now in use, and if people liked this enough they might start demanding their acoustics be tuned the same way.

Piano techs might even take on retuning digitals as an extra income generator.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/05/10 06:43 PM

Ron,

I do not know what a side-track is but I hope you are well.

For me Ya U1 is fine. Let's get down to the most appropriate partial and you may decide, I do not use ETDs normally...and let's choose a precise ETD, if you agree.

Best regards, a.c.
Posted by: RonTuner

Re: HISTORICAL ET AND MODERN ETs - 02/05/10 07:16 PM

Side track is like a train taking a track that leads off to the side - instead of staying continuing on the journey. (kindof a detour) I'm fine, just was busy with other things...

Any ETD that can measure and give a cents value of a specific partial should work - I think Jeff has Tunelab, I'll look into the partials this week. I want to make sure that the measured partials are strong, clear and make sense for that particular piano.



Ron Koval
chicagoland
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/06/10 05:58 AM

Ron:

I do not have an ETD at all. I have a simulator with iH curves derived from Verituner files. A U1 is one of the files.

The simulator provides beatrates when given the iH and either hertz or cent offsets of the fundementals. It also produces curves for iH, cents and beat rates. By adjusting each note to simulate a tuning sequence, the result of the sequence can be evaluted.

Although the simulator is set up for entering the fundamental frequency or cent deviation, this is not a problem. I wrote the program myself and can modify it to accept the cent deviations of partials. And if the iH curve of the U1 in the files is much different than what others are using, a new file can be made and used.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 02/06/10 06:24 AM

Jeff, what makes a difference is that when the string is stroked by the hammer , the spectra is different, all iH comes in play and modify the audible pitch - I see it that way.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/14/10 02:58 PM

Jake, you wrote:

"Thanks for posting these recordings. Were tuning sequences and checks ever written out for these two temperaments? (I remember seeing some lists of steps, and guesses, but not precise sequences.)"...

Chas ET tuning sequence has been published in PW, here is a recent version, written for another forum:

..."Here is the sequence I routinely use for Chas Preparatory Tuning:

sharp or flat is referred to the note (centre string) I'm ment to tune. The already-tuned note is in bracket -

Step 1 – A4 – from 440.0 Hz to 442.0 Hz (concert or studio) - from 442.0 to 443.0 (for flat pianos)
------------------------------------------------------------------------------------------------
Step 2 – (A4)-A3 - tiny little flat, just on the beating threshold - beat raises after 2 or 3 secs and rolls slowly
------------------------------------------------------------------------------------------------
Step 3 – (A3)-D4-((A4)) - sharp, close to 1 beat/sec. – D4-(A4) faintly beating
------------------------------------------------------------------------------------------------
Step 4 – (A3)-E4 - flat
check overlaping 5ths and adjacent 4ths to set up Chas octave:
A3-E4 about 1,5 beat/3s - sensibly faster than D4-A4
E4-A4 about 2 beats/1s - sensibly faster than A3-D4
------------------------------------------------------------------------------------------------
Step 5 – (E4)-B3 – flat - tiny little faster beat than A3-D4, sensibly slower beat than E4-A4
------------------------------------------------------------------------------------------------
Step 6 – (B3)-F#4 - flat - little slower beat than A3-E4 since 5ths have already inverted -
faster beat than D4-A4 - evaluate M6 A3-F#4
------------------------------------------------------------------------------------------------
Step 7 – (F#4)-C#4 – flat - faster beat than E4-B3, sensibly slower beat than E4-A4
evaluate two M3’s progression + one M6
------------------------------------------------------------------------------------------------
Step 8 – (C#4)-G#4 – flat - slower beat than B3-F#4, tiny little faster than D4-A4
evaluate three M3’s progression + two M6’s progression
------------------------------------------------------------------------------------------------
Step 9 – (G#4)-D#4 – flat - tiny little slower beat than E4-(A4), faster than F#4-C#4
evaluate four M3’s progression
------------------------------------------------------------------------------------------------
Step 10 – (D#4)-A#3 – flat - tiny little faster beat than A3-D4, tiny little slower than E4-B3
evaluate five M3’s progression
------------------------------------------------------------------------------------------------
Step 11 – (A#3)-F4 – flat - tiny little slower beat than A3-E4,
tiny little faster beat than B3-F#4
evaluate seven M3’s progression
------------------------------------------------------------------------------------------------
So far, apart from A3-D4, I have stretched "flat" - now I’ll stretch "sharp"
------------------------------------------------------------------------------------------------
Step 12 – (D4)-G4 – sharp - tiny little slower beat than G#4-D#4, faster beat than F#4-C#4
evaluate eight M3’s progression + three M6’s progression
------------------------------------------------------------------------------------------------
Step 13 – (G4)-C4 - sharp - tiny little slower beat than B3-F#4,
tiny little faster beat than C#4-G#4 evaluate nine M3’s progression + four M6’s progression
--------------------------------------------------------------------------------------------
Beats curves are meant to be tuned temporarly. While I'm tuning, I bear all (few) doubts in mind.
------------------------------------------------------------------------------------------------
Step 14 – (A#3)-A#4 – sharp - increase octaves beat’s speed very slowly – 5ths go very, very slowly towards pure – F4-A#4 tiny little faster beat than D4-A4, as for the next 4ths
------------------------------------------------------------------------------------------------
From the octave beat threshold, first signs of beating come to me in a shorter and shorter lapse of time, this helps to S-shape octaves stretch
------------------------------------------------------------------------------------------------
Step 15 – (B3)-B4 - sharp - increase octaves beats rate very, very slowly - 5ths towards pure
------------------------------------------------------------------------------------------------
Step 16 – (C4)-C5 - sharp - increase octaves beats rate very slowly - 5ths towards pure
------------------------------------------------------------------------------------------------
Step 17 – (C#4)-C#5 - sharp - increase octaves beats rate very slowly – 5ths start transiting pure - evaluate one M10
------------------------------------------------------------------------------------------------
Step 18 – (D4)-D5 - sharp - increase octaves beats rate very slowly – 5ths are transiting pure - evaluate M10’s progression
------------------------------------------------------------------------------------------------
Step 19 – (D#4)-D#5 - sharp - increase octaves beats speed very slowly – 5ths are transiting pure - evaluate M10’s progression
------------------------------------------------------------------------------------------------
Step 20 – (E4)-E5 - sharp - increase octaves beats speed very slowly –
5ths have transited pure, evaluate M10’s progression –
chromatic M12s, like A3-E5 must be constant and temporarly tuned pure (on normally out of tune pianos) -
Step 21 – (F4)-F5 – sharp
Step 22 – (F#4)-F#5 – sharp
Step 23 – (G4)-G5 – sharp
Step 24 – (G#4)-G#5 – sharp
------------------------------------------------------------------------------------------------
Step 25 – A4-A5 – chromatic double octaves like A3-A5 must be constant and temporarly beat with a rate of about 3b/2s, or 3/2 bps - check the wideness of A3-A4
increase octaves beats speed very slowly –
5ths are very slowly widening, evaluate M10’s progression –
------------------------------------------------------------------------------------------------
Step 26 – (A#4)-A#5 – sharp - check 10ths, pure 12ths, wide 15ths, let 5ths go slowly wider
Step 27 – (B4)-B5 – sharp - check 10ths, pure 12ths, wide 15ths, let 5ths go slowly wider
Step 28 – (C5)-C6 – sharp - check 10ths, pure 12ths, wide 15ths, let 5ths go slowly wider
---------------------------------------------------------------------------------------------
Go back down for G#3 to lower notes using SBI and RBI, improve A#4 with F#3, never lose control of beats progressions for all intervals. 5ths will get slower, so will 4ths. Unison all these registers from left hand moving right, except last muted string on C6, then go up to higher notes. Chas delta-wide 15ths and delta-narrow 12ths beat’s rate is about 1b/3s or 1/3 bps.

Tune middle string first, then unison previous note’s right string (C6), next left (C#6), tune next middle (D6), unison previous right (C#6), next left, tune next middle and so on, checking also M17ths progression. While tuning, do not stop evaluating strings and sound-board rigidity/elasticity, so to be able to conveniently tune centre strings."

- . - . - . -

About Cordier's and Stopper's sequencies unfortunatelly I can not help you, I'd hope they were available.

..."Strange about the Chas--I recently reread the long thread\argument in which the ideas behind it were first put forth. Over 30 pages. And it turned out to have a lovely sound. (That 53 meg file is what first convinced me.)"...

In my opinion, it is not so strange...it takes time for the tuning to settle, it takes time for people to acknowledge.

..."Seems as though we have a stunning set of choices--good methods of reaching ET, the EBVT, the beautiful Stopper temperament, the CHAS."...

Yes, we have modern ETs that should be acknowledged as soon as possible, since they allow us to really and easly tune progressive and coherent intervals.

..."I've only been learning about temperaments for the past year--not sure I'll ever catch up to a full understanding."...

I'd take a chance by stopping doubts about understanding, the all issue is absolutelly at hand.

..."Is there at least a conference, here--recent temperaments?"...

You are preciselly on one issue I'm after. I think it is time to gather together and refresh the actual knowledge about modern ETs.

Regards, a.c.

.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 02/14/10 04:30 PM

Merci.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 02/14/10 05:49 PM

bout Cordier's and Stopper's sequencies unfortunatelly I can not help you, I'd hope they were available.

I can provide the original Cordier method ans sequence, all is derived from a "pure 5th" hence the ocatve have a 3.5 cts enlarging.

The double octave get very wide...

After some thinking and may criticisms received, in 1982 Serge Cordier proposed something smoother wher the octave is only enlarged by 1.5 cts (1/3 bps) and the 5th became pure again only at a6 level.

That one is near the Chas for the plain wire. (no sequence for that option, but I have the one used by a collegue that use more or less the same).

But the approach stay based on the "pure 5th" intention, the 12th double octave relation is not the basis (in fact I was said that the twelve enlarge around 2.5 bps in the high treble (which is not much, but for some reason I believe that resonance begin to lower as soon as the 12the enlarge).

All those sequences are in French for today. I'll try to post them on the Canadian forum to see if someone have the desire to put it in English. Because the notes names is different in the French terminology (a3 is A440Hz) translation is necessary.
May be I will do that myself, or my colleague could if time permit.

Same basic process to stick on RBI progressiveness, but beat synchronism on P5th is tested with classical tests)
That tuning was even told at an university for some years in France, so we have tuners that use it regularly, it is not so often but not rare (many are from the south of France, as the University was in Montpellier). Some church organs (I have to look for twhich ones) have been tuned in Cordier, so the enlarged octave is not only to be used on inharmonic instruments (Jean Guillou who is a well known organist and play at the Ste Eustache church on magnificent organs, in Paris, is very found of that tuning) .

Should be interesting. records would be a plus indeed.


Best regards.
Posted by: Bernhard Stopper

Re: HISTORICAL ET AND MODERN ETs - 02/15/10 03:08 AM

Originally Posted By: Kamin

After some thinking and may criticisms received, in 1982 Serge Cordier proposed something smoother wher the octave is only enlarged by 1.5 cts (1/3 bps) and the 5th became pure again only at a6 level.



I believe you are slightly off the timeline here.

Codier published his book initially in 1982. Although the tuner colleagues attacked him immediately for his "too wide" octaves, he listed about 30 references from well known pianists applauding to his new tuning at the end of his book and confirming him what he was doing. I doubt that he gave up his model and proposed a smaller octave already in the year where is book was released.

Public criticism of his model came up the first time to my knowledge with my publication of the temperament based on pure duodecimes in euro piano in 1988, (translated and published also for the french tuning community, Cordier probably got knowlegde of it), where i strived the philosophical incoherence of Cordier´s pure fifth model, as the model is based on a pure 3/2 interval, which itself consists of two other pure intervals (i.e. the duodecime "3" and the octave "2"), which are both not pure in Cordier´s pure fifth ET model.

I appreciate if you can provide some provable facts that Cordier revised his model already in the year his book was published.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 02/15/10 03:44 AM

I'll have to verify those historical points as I am only refering to what a colleague wrote me . He tunes the "Cordier" and that modified version (he slighly adapted to his liking he says).

I have an extract (in French) from the writing of Cordier abouit that othe way. Indeed if the book was in 82 that modified method could not be at the same time.:

Voici ce que Cordier écrivait en 1982 à propos d'un tempérament intermédiaire :
"parmi toutes les solutions intermédiaires entre la gamme bien tempérée et le tempérament à quintes justes , l'une d'entre elles retiendra davantage notre attention : celle où la nécessité d'aboutir à un tempérament égal ne s'exerce pas davantage au détriment de la justesse de la quinte que de celle de l'octave mais où le prix à payer au tempérament paraît également réparti entre les deux intervalles . C'est précisément le cas lorsqu'on ne raccourci la quinte que de 1 cent (au lieu de deux dans la gamme tempérée) , ce qui permet de n'agrandir l'octave que de 1,7 cents (au lieu de 3,4 dans le tempérament égal en quintes justes) . Une octave et une quinte ayant la même note de basse présentent alors la même rapidité soit , par exemple , 0,3 bat/secpour fa2- fa3 et fa2-do3 ce qui est pratiquement imperceptible . "
Plus loin :
"C'est pourquoi nous avons récemment défini et réalisé un accord où la quinte , raccourcie de 1 cent dans le médium retrouve progressivement sa justesse pour l'atteindre au niveau de la quinte la4-mi5 (notation française (a5e6 in english) ndlr ) et l'outrepasser ensuite ... "


Indeed all that is dated 1882. Not from a second writing; my mistake, due also to the fact that Cordier stated something slighly different from his first eaasy a few years after, having not studied the points closely, I'll let my colleague chime in on the subject.

I guess we can say that Cordier opened the way, he was looking for the "secret" of concert tuners if I recall well the way things are stated at the beginning of its writing.

I also recall hearing cordier tunings that adbsorb iH on small pianos and that lend to a too vivid major harmony on low iH pianos (while may be the way it is used only conducts to that result)

To me a "pure fifth" at the piano will have differnt size depending of the iH, is not it the case or does it depend of the way the pure inteval is checked ?

Your point on the fact that 5th based on 2 others intervals yet pure is clear. for sure the 12ths weights more than the 5ths, very strange that it have not been evoqued more before.

SO to build an historical temperament one would better use a cycle of 12ths ?











Posted by: Bernhard Stopper

Re: HISTORICAL ET AND MODERN ETs - 02/15/10 08:17 AM



OK, this text is from the last chapter of his book, where he writes about infinite intermediate possibilities (page 260). His intention was not to revise his model, but to explain that infinite possibilites between pure octaves and pure fifths exist, and that the pure fifths tempermant is superior to such intermediate solutions. This appears clearly some sentences later (page 261), where he is discarding this intermediate solutions by favorising the pure fifths in these statements:

"...Dans le premier Cas (pure fifths) on trouvera le piano brilliant, á la rigueur un peu haut, dans le second (with the intermediate solutions), on le trouvera tout simplement faux..."
and
"...Il ne presente pas á un meme niveau que le TEQJ (Cordier temperament) dont les rapiditées sont isochrones ou quasi isochrones et favorise donc moin..."

So the text you have interpreted as a rethinking and refinement of his pure fifth model, was rather an argumentation against the intermediate solutions. This is a nice example how the sense of a text can be converted into it´s opposite by leaving out important parts.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 02/15/10 10:32 AM


For what I know Serge Cordier did not train as a concert technician, I have seen no mention of the way the temperament octave is (generally) opened , in his book (I have read very fast).

I thought he focused on beats synchronism within the 5th, as he did not mention differnces in beats depending of the level of the partials, I did not see where he wanted to go (at the piano)

What makes me state that "second version" was the way things have been preseneted to me by my colleague. In the end I understand that for every day's work he uses that modified version (that he arranage to his liking he said) . With octave then at 1.7 cts and 1/3 bps for the 5th as for the octave.

It is in any case different than taking the 12th as the ruler of the tuning.

And again beats are seen as "the enemy of resonance" .

We have as tuners little learning to the question of resonance and harmony it is normal that false or one sided ideas are going around. (for instance the tuned duplexes)

In my view that should be the role of the ones who can explain to make those concepts and principles availeable to us.

Most of the colleagues I tolk of Chas and of your tuning ask for a temperament sequance and method to try those tunings. They seem generally speaking open to have the pôssibility to try something different, to analyse it as possible, and then decide with a more complete knowledge what looks more suiteable for them to their dayly work.

Those new informations are highly welcome, be it to seasoned tuners (more to seasoned tuners probably) than to beginners.

Do you have the envy or possibility to add your part to this ?

I find that the affirmation that a new way to determine the pitches of ET is not so excessive, at last for the piano it can't be questionned.
It always will be a compromizing question, but being aware of the kind of compromizing we are using, being able to compare the effect of differnt compromizing approaches sure may help the tuner to work more confidently.

What amazes me is that all this for a good part is using what some are or have been yet doing since a long time.

Many things we do are not done in conscience (particularely when tuning)because we have to learn to work fast.

Talking of Cordier, did he wrote some addendum or only stated something different from his book "piano and orchestral justness ?

The Cordier tuners here are very sure they provide a "better" tuning, with more clarity in the treble. To me this is mostly because they are confident in the way they stretch the tuning, they have a method. I see most others are presenting tuning as an art 'which certainly it is'.
Some find a way or another to stick to some rule.

It is good news that we begin to really analyse which ratios we use, and what is the result of those ones in terms of departing from the natural behaviour of the piano string.(while I understand well it can be of no interest to some, of course)
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/16/10 06:43 AM


Yes Isaac,

also in my opinion it is foundamental for tuners to know what and why having to look for. This is how I understand Bill Bremmer's satisfaction when he features EBVT. If a tuner can rely on a re-foundable form, even if it is a non-equal temperament he/she may eventually know that his/her job has been done. And as I say (opinion), any intentional tuning form is better than any unhinged quasi-ET attempt. If anything, the intentional tuning of a precise form may say something about that one tuner and his/her own preferencies.

Good if you manage to post Cordier's sequence. Have you tryed it? BTW, do you think is worth contacting that university and ask what is left with that model?

Also, if really Cordier's model has been applyed to pipe organs, you may argue about the efficiency of theoretical models for harmonic and inharmonic tones, what I consider a crucial, very relevant issue, as this argument (O) is being abused. ((O) is my opinion).

Stopper,

I join the others requesting your practical tuning sequence, it should not take long for you and all of us may get some benefits.

About Cordier's pure 5ths model you write:

..."Public criticism of his model came up the first time to my knowledge with my publication of the temperament based on pure duodecimes in euro piano in 1988, (translated and published also for the french tuning community, Cordier probably got knowlegde of it), where i strived the philosophical incoherence of Cordier´s pure fifth model, as the model is based on a pure 3/2 interval, which itself consists of two other pure intervals (i.e. the duodecime "3" and the octave "2"), which are both not pure in Cordier´s pure fifth ET model."...

It would be nice if you managed to deepen about that (is Cordier still alive?). Also you may explain the theoretical and philosophical aspects regarding pure 12ths theory.

For instance, you claim pure 12ths superiority on the basis of some (practical?) beat symmetries (wich you could post here too), and I would ask you how this is related with a single theoretical pure ratio. In other words, how do zero-beating (12ths) symmetries cohere with beating symmetries?

Also, would you say that zero-beating intervals can still be theorized? And if yes, would you say for what purpose?

I took seven months to realize one more bottom question: not acknowledging a substantial difference between 12th root of two and Modern ETs. So, I think it is up to us explaining how the first ET has evolved and how modern theory can now take tuners to a practicable and naturally-harmonious form.

Bill Bremmer was mentioning some help that may come from PTG's mathematicians, like Robert Scott. I still hope they'll join us in renewing the equal tempering horizon.

Regards, a.c.

.

Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/21/10 04:36 PM


Bernhard Stopper,

I join the others requesting your practical tuning sequence, it should not take long for you and all of us may get some benefits.

About Cordier's pure 5ths model you write:

..."Public criticism of his model came up the first time to my knowledge with my publication of the temperament based on pure duodecimes in euro piano in 1988, (translated and published also for the french tuning community, Cordier probably got knowlegde of it), where i strived the philosophical incoherence of Cordier´s pure fifth model, as the model is based on a pure 3/2 interval, which itself consists of two other pure intervals (i.e. the duodecime "3" and the octave "2"), which are both not pure in Cordier´s pure fifth ET model."...

It would be nice if you managed to deepen about that (is Cordier still alive?). Also you may explain the theoretical and philosophical aspects regarding pure 12ths theory.

For instance, you claim pure 12ths superiority on the basis of some (practical?) beat symmetries (wich you could post here too), and I would ask you how this is related with a single theoretical pure ratio. In other words, how do zero-beating (12ths) symmetries cohere with beating symmetries?

Also, would you say that zero-beating intervals can still be theorized? And if yes, would you say for what purpose?

I took seven months to realize one more bottom question: not acknowledging a substantial difference between 12th root of two and Modern ETs. So, I think it is up to us explaining how the first ET has evolved and how modern theory can now take tuners to a practicable and naturally-harmonious form.

Bill Bremmer was mentioning some help that may come from PTG's mathematicians, like Robert Scott. I still hope they'll join us in renewing the equal tempering horizon.

a.c.

.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/22/10 08:02 AM

Alfredo:

I would also like to hear more about aurally tuning the Stopper temperament. It seems to be based on a "sweet spot" between the 3:1 and 6:2 partial matches of the P12. It may be another one of those artistic things that cannot be explained, only experienced.

But let me warn you about looking at the theory of pure twelfths. It is not about the 19th root of 3 any more than ET is about the 12th root of 2. These ratios are meaningless when dealing with inharmonic tones. Until you accept this concept, you will not be able to understand nor contribute to any discussion of inharmonic tuning theory.

But then to accept this concept is also to leave Chas theory behind because Chas theory is about frequency ratios. It would be “a bitter pill for you to swallow”, Acquaintance.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 02/22/10 08:45 AM

Jeff I am unsure you understand well the effect of inharmonicity on piano tone. Ih only give you room for enlarging the intervals from the basic relations, this does not mean that the relation can't be tuned.

I am still expecting links for records of "pure 5ths" based tuning on an organ. It have been done (I wonder about the speed of the thirds !).

To me that is the whole partial match approach ans listening that complicate our job. Most often, the good tuners tune "in the tone" without focusing on a particular partial level (which is a good method to learn, but can be left aside after-that, in my opinion).
Or at last listen to the beating at the most fundamental level availeable.




Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/22/10 11:02 AM

Isaac:

We seem to have more and more in common. Likewise, Isaac, I am unsure you understand well the effect of inharmonicity on piano tuning.

Consider the m3-M6 test for a 6:3 octave. If an octave in the middle of a piano is tuned to sound beatless, the 6:3 octave test will show that the octave is narrower than the 6:3 partial match; the m3 will beat faster than the M6. This means that the effects of iH on the beat rate of these intervals is opposite of what would be expected from merely “stretched” intervals. If the intervals were merely stretched due to iH, the m3 would beat slower than the M6! You see, iH affects the beat rates of some intervals in a way that is opposite to the stretching effect of iH.

But now I also agree with you about there being more important things to listen to than beat rates. Although the complex interaction of many beat rates due to difference tones are, I believe, what gives some intervals “color”, the ear can normally only separate a few of the strongest and obvious ones. It is a start but, as you say, tuning “in the tone” is a more advanced way.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/22/10 05:03 PM


Jeff, you wrote:

..."I would also like to hear more about aurally tuning the Stopper temperament."...

So would I. I find strange that Stopper has not released its pure 12ths aural tuning sequence, and that he is not replying on his approach's incongruencies.

..."It seems to be based on a "sweet spot" between the 3:1 and 6:2 partial matches of the P12. It may be another one of those artistic things that cannot be explained, only experienced."...

Well, he himself could say what it is, not you nor me.

..."But let me warn you about looking at the theory of pure twelfths. It is not about the 19th root of 3 any more than ET is about the 12th root of 2.

Sorry, but yours is a wrong reduction.
ET is about geometrical progressions and equally distant notes.
12th root of two is only the first ET, the ET based on a pure, zero beating octave. Modern ETs models have well improved that first attempt to use a geometry we can find in nature.

...”These ratios are meaningless when dealing with inharmonic tones."...

I've acknowledged your opinion about ET models and how meaningless you think they are. And more, I've acknowledged your approach to tuning, to beats, to tuning-checks and, to a certain extent, I've also acknowledged your taste in terms of piano performance.

...”Until you accept this concept, you will not be able to understand nor contribute to any discussion of inharmonic tuning theory."...

Talking about iH, (O) we have said enough in Chas Topic. About the existence of “inharmonic tuning theories”, this is the first time I hear of this category. Do you have an "inharmonic tuning theory"?

Also, you'd better realize that my contribute is meant to go towards Temperamental Theories and the sharing of the latest ET's evolution. In other words, the latest variant of the first ET. Would you like a realistic refresh? Have a look:

http://www.huygens-fokker.org/docs/bibliography.html

..."But then to accept this concept is also to leave Chas theory behind because Chas theory is about frequency ratios."...

Well, you too may take advantage by letting me say what Chas Theory is about.
Chas theory is about proportional differences. When you are ready, you can read (maybe re-read) sections 2.0 and 3.0 in the research report and simply acknowledge what is written in there. So, in Chas case, the frequencies values are for the first time derived from proportional differences.

...”It would be “a bitter pill for you to swallow”.

If only you knew how sweet the tuning of Chas form can be, you would not worry about bitterness any more.

a.c.

CHAS Tuning MP3 on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

.
_________
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 02/22/10 08:20 PM

ANd now it seem to be ready to be tested in the Pianoteq software (even on the demo version).

The first comments of the users are as usual, more harmony, increase of harmonic resonance, sweet sound, etc...

As what said the pianists when hearing their piano , they speak of "beauty". Even when making good tunings, you fairly know that is not the word that comes in mouth of pianists naturally...

If you knew Alfredo, you would understand that he could take a lot of bitter pills , he have a natural medecine that protects againts that bitter taste (if not he would have left that forum for long !!)..

Please Alfredo, have a look at the logic of the "scala " file provided for Pianoteq. (an incremental ratio non one octave, reproduced all along the keyboard) At first it sound as Chas.

Best regards to all !
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/23/10 07:08 AM

Alfredo and Isaac:

I am not talking about how a tuning sounds. I am talking about the validity of tuning theories.

Fixed frequency ratios are not valid for inharmonic tones. That is why the Railsback curve is not a stratight line.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 02/23/10 09:50 AM

I have to say that I'm not so sure about that Scala file for Pianoteq: it's based on just one octave, with an offset of 1 cent per octave. In other words, it's a Scala file instead of a tuning.

I hear the beats on the octaves, but I'm not sure I would recognize the sound as similar to the recordings I've heard using CHas as the spine for the tuning.

One problem is that, using the scala file, the 3:1 checks on 12ths from A4 (which is A3 in PianoTeq) don't show an accurate result. And of course, since the Scala file just repeats the intervals with the subtraction or addition of a cent, the gradual widenings and narrowings of intervals are left out. Everything just has a cent subtracted or added to it at each octave.

It may be necessary to use PianoTeq Pro's Detune Note Edit pane and Spectrum profile NE pane, tuning by ear and by partial checks, along with the Unison detune NE pane, to get closer to the aural tuning that sounds like a CHas-based tuning.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/23/10 10:04 AM

Jake:

Are you listening to harmonic or inharmonic tones?
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 02/23/10 10:33 AM

Jeff:

EDIT: You guys may have moved on to discuss other things, so I'm sorry if I'm responding to an earlier concern. But here's what I understand about the earlier concern:

I'd rather stay out of this battle, but I worry that there may be a mix-up. My impression is that you and Alfredo are sometimes talking about apples and oranges. His CHas is a theoretical variation on theoretical ET and focus, to me, seems to be on harmonic partials. He's not arguing for using fixed freqs in an actual tuning. In other words, my impression is that his temperament bears the same relation to a tuning as theoretical ET bears to a tuning--it's the map, but once he leaves the Mathematics Department, the trip is taken by listening to the piano to get the beats he wants and by doing partial checks. In the academic document, on the other hand, he's arguing for the general, theoretical point of departure. (If recordings of a piano tuned using the two octave approach had appeared earlier, would the entire discussion have gone better?)

In the version of the theory that I recently read, he doesn't claim that the temperament is a universal cure for IH. The claim is more along the lines of--conventional ET based on 12 repeating steps encourages inharmonicity, but if you use 24 steps, which sharps the notes just slightly from conventional ET, IH tends to naturally get reduced, and many partials beat in a sweet way. The math then demonstrates why the beating happens. I think the original doc may have started with more math, and then gone from there, so that the impression was that a formula was being imposed on a piano. In a way, it is--he's writing for a Math Department. But the math was arrived at from experience--it essentially explains why some partials match up and how some beat in a pleasing way if you use a different multiple for creating the theoretical intervals. (And then go in and tune the damned thing--but he can't say that in a math paper...Forgive me for this simplification, Alfredo. Is it roughly accurate?)

Sorry to wade into this entire battle.

Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 02/23/10 10:51 AM

Jeff,

We're cross-posting. Were you asking if I was listening to harmonic or enharmonic partials when listening to the sound based on the scala file in PianoTeq? Actually, I was going in and looking at the partial structure in the Spectrum note edit pane. (I don't know if you know PianoTeq. The pro version lets you repitch a note, or load a Scala file, and see the freqs of each partial. The older version of the program didn't always accurately show the freqs. The latest one, released about a week ago, does.)

That's really why I think that a manual tuning is best in PianoTeq--if you open the Detune NE pane and the Spectrum NE pane, you can change the pitch of each note and watch the effect on the freq of each partial. It's a little more complex, than that, really--since you can control the length of the "string," you can in a sense design the IH, and thus the effect of the pitch change, on each note.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/23/10 12:03 PM

Jake:

Thanks for the response. You probably do not want to get into this “battle.” There are disagreements on a number of levels…

I believe I understand what you are trying saying about a theoretical tuning being a map that is departed from when actually tuning. I call this doing the right thing for the wrong reason.

No, I do not have PianoTeq. And we should be careful to not confuse the word enharmonic with the word inharmonic. It was probably just a typo. If the frequencies of the upper partials that the pane display are exact multiples of the first partial, then the tones are harmonic. If they are not exact multiples I would think that somewhere the iH for each note is displayed.

The reason I ask about if the tones are inharmonic is what this can mean to the relationship between octave types and the justness of 12ths. The “more iH” (meaning either the value for a particular note is greater for a given logarithmic iH slope or the logarithmic iH slope is less steep for the given value of a particular note) the narrower the octave type can be with the result being just 12ths. For example: a “high iH” piano may produce beatless 12ths when tuned with 4:2 octaves in a particular part of the scale while a “low iH” would need to be tuned with 6:3 octaves to produce beatless 12ths in the same part of the scale.

The difficulty with using frequency ratios as a “map to take a departure from” is that taking the 19 root of 3, for example, and saying this will produce beatless 12ths does nothing in predicting the resulting octave type which will be a function of iH. And the same problem happens when using a “map” with equal beating 12ths and 15ths. The result depends on the piano’s iH, and the frequency ratio is really irrelevant and even misleading.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 02/23/10 01:57 PM

Yes, I meant "inharmonic," of course.

Pianoteq doesn't display the IH of a note, in the sense of determining the spread between some partials, or the difference between some partials and their idealized Fourier harmonic, and then performing a calculation that gives results such as IH = X. It instead just shows the freqs for each partial and lets you change the tension and\or length of the string. (I'd actually like to learn more about the way IH is calculated as a value--don't different people\companies\ETD's use different formulas for the calculation?)

Are you saying that he should discuss the details of IH --the way it varies with piano and string and octave and note--in the formal paper? I'll really have to look at paper again to review the discussion of IH.

Is it the use of the root that is worrisome, since it creates a formula that neglects IH as a variable? (But theoretical ET divides the octave up and ignores IH as a variable?)

If he spoke of a range of possible results, instead of absolutes, would his argument be stronger-a range of results for modern, well-designed pianos? I don't really know at all--I'm far from being qualified to evaluate the argument. (Let alone understand all of the math...)But let's remember--thinking aloud, here--that the formal paper states the argument only for the 24 note temperament, and not for the entire piano, so the variation might be fairly wide, but less wide than the variations caused by IH in ET over the same notes? That could become an entirely different paper--the testing of the theory on many, many pianos, instead of providing the mathematical proof required by a Mathematics Department (which is very different from the proofs required in physics, biology, etc...), which would generate the range of variations.

I don't know, really.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/23/10 02:36 PM

Jake:

I don't know, really.

No better place to start!

Sorry, I do not want to discuss Alfredo’s paper anymore. Everything I have to say about it has already been said. You can look it up if you care to.

Not too long I could also say, I don't know, really. Let me give you the path that I followed and how I look at the effects of iH.

Inharmonicity is explained in:

http://www.afn.org/~afn49304/youngnew.htm#ftnote8

And here is a link to the iH curves for a number of pianos:

http://www.goptools.com/gallery.htm

Wikipedia has some good pages on cent to frequency conversions and on inharmonicity.

Inharmonicity is the difference between what the fundamental pitch of a string should vibrate at when ignoring the stiffness and what it actually vibrates at in cents. Each partial is higher in pitch than exact multiples of the theoretical fundamental by the iH in cents times the square of the partial number. Higher partials are affected by iH much, much more than lower partials.

The iH of the strings of a piano are not all the same. For the unwound strings the iH doubles at around every 8 semi-tones for large pianos and less than doubles for smaller ones when going up the scale. For the wound strings the lowest notes have more iH than the higher ones.

There are three ways that iH effects tuning. First, the octaves are tuned wider than a 2:1 ratio. This also makes the cents between the fundamentals of intervals greater than theoretical. Second, the higher the nearly coincidental partials are in an interval the more iH causes them to beat as if they were narrower than they are. Third, since iH is a logarithmic curve, the effect is of wider intervals to beat as if they were more wider than narrower intervals. The combined effects are largely self cancelling on well scaled pianos.

I better stop here for now. But Let me also mention that the general beat rate of some intervals more than double each octave and others less than double.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 02/24/10 01:26 AM

Originally Posted By: Jake Jackson
I have to say that I'm not so sure about that Scala file for Pianoteq: it's based on just one octave, with an offset of 1 cent per octave. In other words, it's a Scala file instead of a tuning.

I hear the beats on the octaves, but I'm not sure I would recognize the sound as similar to the recordings I've heard using CHas as the spine for the tuning.

One problem is that, using the scala file, the 3:1 checks on 12ths from A4 (which is A3 in PianoTeq) don't show an accurate result. And of course, since the Scala file just repeats the intervals with the subtraction or addition of a cent, the gradual widenings and narrowings of intervals are left out. Everything just has a cent subtracted or added to it at each octave.


Hello Jake, this occur (the correct application of the formula by "Nikkos" in the scala file) because of your interest in tunings and temperaments, so thank you for your opening of mind.

Philippe Guillaume, the pianoteq developper, was a piano technician before graduating to a doctorate in maths and begin to teach Applied maths.


ALfredo will answer on that later, but at first he said that Nikos (who made the file) correclty applied the theory, and understood the value of s (S=1).

The Chas ratio is provided on an octave, which is copied afterthat all along the scale.
If I understand well, when stretch = 1 in Pianoteq the inharmonicity is corrected at the 2:1 level. (makes a very compact ET, the stretch added afterthat apply out of the temperament zone , as in tuning, hence the little change in harmony. Listening to Rachmaninoff while passing from standard ET to Chas is an amazing experience ! I even believe that the scala file make the piano tone more realisitic.

If any difference exist they may be due to the non use of 3d and 4th partial. But immediately a first listening the Chas effect is noticeable, as a nice opening of the tuning (even with harpsichord tone).
To be complete, some colleagues are tuning with that kind of tone, probably not managed similar but in the same kind of harmony. For what I understand the ones that learned the Cordier "fall" in that kind of tone (while making the tuning with 3:2 5ths) because of the way the piano settle. This hypothesis is all possible and we will try to verify it in march.

Have a good day, all !

Isaac



Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/24/10 07:07 AM


Jake,

Your way to put Chas and my intentions into words is correct, right from the start when you write:

..."CHas is a theoretical variation on theoretical ET and focus, to me, seems to be on harmonic partials. He's not arguing for using fixed freqs in an actual tuning."...

Likewise, in writing:..."his temperament bears the same relation to a tuning as theoretical ET bears to a tuning..."

And..."conventional ET based on 12 repeating steps encourages inharmonicity, but if you use 24 steps, which sharps the notes just slightly from conventional ET, IH tends to naturally get reduced, and many partials beat in a sweet way. The math then demonstrates why the beating happens."...

..."But the math was arrived at from experience--it essentially explains why some partials match up and how some beat in a pleasing way if you use a different multiple for creating the theoretical intervals. (And then go in and tune the damned thing--but he can't say that in a math paper...)"...

For your ways and your open minded (and mind opening) approach, I appreciate very much your valuable contribute. Thank you for your analysis and your elaborations (not last, for all those question marks!).

Jeff, you write:

..."I am not talking about how a tuning sounds. I am talking about the validity of tuning theories."...

I kindly ask you to acknowledge some of my research's targets:

- how and why a tuning can sound better
- how Temperamental Theory and models can be improved
- how and why improved aural piano tuning practice can be related to modern theory

To me, it seems that you would prefere to talk about the non-validity of tuning theories.

Generally speacking, being prejudiced against theories and/or models can make impossible to share interest and efforts for further investigations (on theoretical and practical aspects), as it can make impossible to share even the practical evidencies that have led to the elaboration of one precise model, in this case Chas Temperamental model.

In my opinion, today Pianoteq may represent a great help for deepening some temperament and aural tuning issues, including your favorite questioning about iH.

You may then put your urgencies aside for a little while and, if you like, elaborate towards the application of Modern ETs models. How about recording and share some of your practical checks and tests?

Isaac, thanks a lot for the amount of energy and elaborations you are devoting. I hope to be able to contribute on Pianoteq settings and evidencies too. What can I do?

Regards, a.c.

.

Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/24/10 07:37 AM

Originally Posted By: alfredo capurso
.....

To me, it seems that you would prefere to talk about the non-validity of tuning theories.

.....


Only when the theories are invalid.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/25/10 03:40 AM


Jeff, it was about three months ago when I addressed you to some simple reading:

http://en.wikipedia.org/wiki/Theory

...“Theories are abstract and conceptual, and to this end they are never considered right or wrong.

Instead, they are supported or challenged by observations in the world. They are 'rigorously tentative', meaning that they are proposed as true but expected to satisfy careful examination to account for the possibility of faulty inference or incorrect observation... 

...Sometimes two theories have exactly the same explanatory power because they make the same predictions. A pair of such theories is called indistinguishable, and the choice between them reduces to convenience or philosophical preference...

...The form of theories is studied formally in mathematical logic, especially in model theory...

...Theories used in applications are abstractions of observed phenomena and the resulting theorems provide solutions to real-world problems. Obvious examples include arithmetic (abstracting concepts of number),geometry (concepts of space), and probability (concepts of randomness and likelihood)...

...In science, generally, theories are constructed from elementary theorems that consist in empirical data about observable phenomena. A scientific theory is used as a plausible general principle or body of principles offered to explain a phenomenon...

...A scientific theory is a deductive theory, in that, its content is based on some formal system of logic and that some of its elementary theorems are taken as axioms. In a deductive theory, any sentence which is a logical consequence of one or more of the axioms is also a sentence of that theory.

...Theories are intended to be an accurate, predictive description of the natural world.

Theories as models
Main article: Scientific model

Theories are constructed to explain, predict, and master phenomena (e.g., inanimate things, events, or behavior of animals). A scientific theory can be thought of as a model of reality, and its statements as axioms of some axiomatic system. The aim of this construction is to create a formal system for which reality is the only model. The world is an interpretation (or model) of such scientific theories, only insofar as the sciences are true.

Theories in physics
In physics the term theory is generally used for a mathematical framework—derived from a small set of basic postulates (usually symmetries—like equality of locations in space or in time, or identity of electrons, etc.)—which is capable of producing experimental predictions for a given category of physical systems. A good example is classical electromagnetism, which encompasses results derived from gauge symmetry(sometimes called gauge invariance) in a form of a few equations called Maxwell's equations.

Intertheoretic reduction and elimination
Main article: intertheoretic reduction

If there is a new theory which is better at explaining and predicting phenomena than an older theory (i.e. it has more explanatory power), we are justified in believing that the newer theory describes reality more correctly. This is called an intertheoretic reduction because the terms of the old theory can be reduced to the terms of the new one.

For instance, our historical understanding about "sound," "light" and "heat" have today been reduced to "wave compressions and rarefactions," "electromagnetic waves," and "molecular kinetic energy," respectively. These terms which are identified with each other are called intertheoretic identities. When an old theory and a new one are parallel in this way, we can conclude that we are describing the same reality, only more completely.

In cases where a new theory uses new terms which do not reduce to terms of an older one, but rather replace them entirely because they are actually a misrepresentation it is called an intertheoretic elimination. For instance, the obsolete scientific theory that put forward an understanding of heat transfer in terms of the movement of caloric fluid was eliminated when a theory of heat as energy replaced it."

May I ask you now not to be misleading? Or else, would you start one more Topic on your personal outlooks? You know, I'd rather think of you as a reliable poster.

(O): Keep on tuning the way you do, you can be happy. Keep on wondering, you can still be happy.

a.c.

.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/25/10 09:40 AM

Alfredo:

As a young man I played trombone in circus bands. Whenever the magician wanted to hide what he was really doing he used smoke and mirrors. That is what your diversions on just what a theory is and how your tuning sounds are. They are just diversions from what I am saying, which is what you want to hide.

Your mathematical explanation of how you tune does not work due to iH. We both know it but you try to hide it.

But there is very good news. Many great tuners have been unable to explain how they tune, mathematically or otherwise. You may be one of them.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/26/10 07:58 AM


(O). Many of us might be unable to explain anything, some of us are able to doubt and share.

I've found interesting this short reading, style and format too.

http://books.google.com/books?id=4Vjsjvq...;q=&f=false

It is a 1835 Essay on Temperament, you may like it too.

a.c.

.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 02/26/10 08:53 AM

Thanks, Alfredo:

I am not sure when I will get a chance to read though it. I like the idea that it was written by the head assistant on the nautical almanac establishment. From a quick glance, it is written much like the many navigation treatises I have read. I will probably enjoy it for that reason if for no other.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 02/26/10 09:42 AM

Seems to be a defense of straight ET, but I'll have to read more. Love the opening of chapter one:

"Sound is an affection of the mind"
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/01/10 05:31 PM


Hello.

Yes Jake, I liked that too.

By reading also Claude Montal's work (Paris, 1836)

http://books.google.fr/books?id=PIw8AAAA...;q=&f=false

kindly linked for us by a French colleague, again we can conferm our understanding about why, when we say "temperament", we still think about a suffered "compromise".

Also in Wikipedia,

http://en.wikipedia.org/wiki/Musical_tuning#Tuning_systems

"Systems for the twelve-note chromatic scale" (scroll down)

We still read: “It is impossible to tune the twelve-note chromatic scale so that all intervals are "perfect"; many different methods with their own various compromises have thus been put forward.”

Claude Montal writes (page 41): "L'octave seule doit etre rigoureusement juste...".

More recently, Serge Cordier would have written the equivalent of: "La quinte seule doit etre rigoureusement juste".

Six years later Bernhard Stopper would have written: "La douzième seule doit etre rigoureusement juste".

Today Chas temperamental theory does not favor any interval and does not limit the temperament's module to 13 (pure octaves), 8 (pure 5ths) or 20 (pure 12ths) notes.

Simply out of consciousness, Chas can be acknoledged as a geometric entity where all intervals are in reciprocal function, a self-bearing beats-architecture.

The "pure" concept is so renewed and the approach to the sound scale is shifted from a static ratio, like the one for any “beatless” interval, to a dynamic beat-ratio for an infinite set, stable and yet evolvable.

Then, our practical tempering does not need to be that kind of compromise, it can be the weaving of an ideal web.

Regards, Alfredo.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/01/10 07:38 PM

Reading further in the Woolhouse book, I see that he starts off by explaining an ideal ET, but then elides towards a well tempered tuning, with even a chart listing the best keys. Still haven't finished, however.

Odd to see how the various intervals have been favored.

A bit off-subject, but while we're discussing older theory: Here's a link to Barbour's Tuning and Temperament at the Internet Archive (registration may be required to download the pdf). Looking over the table of contents, I see that he doesn't even use the term "well tempered," instead devoting a chapter to "irregular systems":

http://www.archive.org/details/turningandtemper027139mbp

(Whoever originally uploaded it didn't proofread.)
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 03/05/10 06:21 AM


To listen to correct use of HT on modeled historical pianos (forte and such).

Some of the recordings are convincing, despite some predictability in tone.


http://www.pianoteq.com/discover_pianoteq3?type=pianoforte

Thanks for your comments.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 03/05/10 06:43 AM


Generally speaking, I see tuning a piano like this :

On one side you have the piano harmony and resonance.

On the other side you have the need to obtain a congruent system to play in all keys.

(ther is a 3d aspect which is the room acoustics, but I will lay it aside)

If you tune the piano and the tempering method used is very strong, acoustically speaking, it may fight or modify somehow the harmony of the instrument (find it was the case with the Cordier tuning, where the relation between intervals is more heard than the piano resonance itself, probably the same occur when I listen to a Stopper tuning.

It is the same with a standard tuning which is highly stretched , at the edge of the octave beat, the stretching method is to me more "in front" than the natural harmony, that may be help the tone to be more crisp but it fight the quietness of listening.

The same happens with Chas, but by chance the resonance point and the congruence of intervals seem to match more in that case, and the crispness of tone, be it due to the Chas or to the extra tension given to the tuning pin and small wire segment , is felt as natural and "just" (musicians opinion, my brother wife , harpist even told me "at last a piano that sound tuned!")

We have no idea on how other instrumentalist perceive the pianos justness, they seem to accept what they find and try to match it.

I guess that some of the "mystery" of CHAS lies in the wy the 4th and the 5ths are reconciled thru the double octave.

I've find that the RBI intervals differs in beat rate depending of the instrument iH, as on other tuning methods, so it is not a method that use a "standard" beat rates set"

What I find funny is that the Chas is said to provide a better progression "at the expense of the octave justness". in fact I find that the octave is enhanced by the tuning, at last at the piano. it is probably slightly less stretched in the mediums but the progressiveness is then nicely going up and down. the double octave is at 0.98 cts higher (plus the ih correction automatically used when tuning).

The drawback is that resonance is very present, as if the sustain pedal was used more. the harmony is then sounding slightly closer, or smoother, the correct "charging" of the pin-block may well be necessary to keep the correct enlightening of the melody (but may be not, I will experiment with close unisons whenever possible)




















Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 03/06/10 05:50 AM

The Pianoteq developper, Philippe Guillaumme (whe is/was a piano technician) made a CHas tuning file that takes in account the piano model ih .

Here is a real application of the tuning formula in a virtual piano :

http://www.forum-pianoteq.com/uploads.php?file=CP33%2005.03.2010%202%20CHASIH%20demo.mp3

I need no more to be happy (and the Pianoteq software is doing VERY good on that !)- you have a trial version that is complete if you wish ... go to the Pianoteq forum or ask me if you want the CHas tuning file for Pianoteq.


Same music but with standard tuning , for comparaison purpose

http://www.forum-pianoteq.com/uploads.php?file=CP33%2005.03.2010%201.mp3

Best regards.



Posted by: Phil D

Re: HISTORICAL ET AND MODERN ETs - 03/06/10 11:57 AM

Thanks for these mp3s Isaac. The CHAS tuning really seems to make the chords 'breathe' so much better. I'm sold on this technique. I think I will attempt to tune it when I next have some time. See what it can do for the old Erard!
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/06/10 12:44 PM

That sound is very, very good. The treble 12ths are wider, however, than what Alfredo specifies in his tuning sequence, using a 3:1 check.(Sorry, Philippe. Just being specific about the details of the tuning.)

(By the way, as Olek says: PianoTeq has a demo available for the standard edition with some notes silenced. But there is not a demo for the pro version, which lets you tune each note individually and adjust the amplitude of each partial in each note, etc.

I recently found, in any case, that the ability to adjust each partial's amplitude makes the program very good for listening to beats while pitching each note or the unisons. You can mute all of the partials you don't want to hear, so that you can listen to just the 3rd and 1st partial while tuning 12ths, say.)
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 03/06/10 03:14 PM

Euh Jake, I apologize, because as adepts of the Chas ET concept, we should not have contradiction publicly (all those may stay confined to the ashram !)

But to me the 12ths in the high treble are tempered , I can hear it , but you gave me doubt so I measured with Tunelab.

Put the display at zero move for instance at G7 (Tunelab is tuned to the G7 frequency)
Play C 6 - the display goes right , showing a 3d partial of C6 being higher than the actual pitch of G7

measure the offset by tapping on the display with the mouse till it is stopped.

I measured 2.71 cts offset form a pure triple of the fundamental frequency . (it is well tempered, in that case)
I wonder how do you test the 12th, if you hear the M6 faster than the 17 th that mean that the interval is shorter than pure.
If you find the 3d partial of C6 higher than the fundamental of G7 that is, a tempered 12th.

Which notes did you find over "pure "twelve ?

Anyway, iH plays also a role, and modify the way the notes are pitched. G7 with a high iH, may tone higher than its fundamental frequency. fundamental of C6 may be lower than 1/3 the frequency of G7 , that is normal, to me, the 3d partial is what provide the beat with the 12th so its frequency is what counts)

In the recording I dont feel the high treble as asking for more stretch, to me that is one of the main advantage of the Chas ratio, as it bring a high coherence. When we stretch "artificially" just to please the ear, we cut in the resonance, as adding stretch octave after octave finally provide a high treble that have lesser sympathetic resonances.

Whenever it is possible to have a natural stretch all along (and I wonder if it is even possible out of the Chas ratio) the instrument get sonorous but stay smooth.

I also have find that in the basses the 5ths are yet tempered (the same than in the medium, while in a more classical tuning, the fifths get very large in the bass and even invert sometime.

I am unsure that the formula applied get exactly to the result from aurally tuning Chas, but the main things are really there, I verified the beat rates, the intervals, on a midi keyboard, and they have, to me the same relations than with an aural tuning.

May be you expect the fundamental frequencies to be less than 1/3 ratio, it may be the case where the ih is lower.

Despite the limitations, (a few notes missing, no direct tuning) I enjoy much the demo of Pianoteq -i am not equiped enough with a decent midi keyboard, but I have read the users comment, saying the software acts more as a musical instrument because of real time computation of tone (compared with sample based setups) I suppose that in the future modeling will be the tendency, for digital instruments. The possibilities are amazing (as on Pianoteq the strike point changing, the hammer voicing changing the length of strings , and now , allowing us to test different tunings... etc..).

I also appreciate the interest of Philippe Guillaume for the Chas concept, and his work to put in reality something that we could not do only with pianos...
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 03/07/10 04:13 AM


Here is a real application of the CHAS tuning formula :

http://www.forum-pianoteq.com/uploads.php?file=CP33%2005.03.2010%202%20CHASIH%20demo.mp3

Here is the same piece with a standard tuning (ET both)

http://www.forum-pianoteq.com/uploads.php?file=CP33%2005.03.2010%201.mp3

Best regards.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/07/10 07:55 PM


Thanks Isaac, what has been recorded makes an undeniable difference.

Philippe and Jake, Pianoteq is highly performing indeed and I'm very, very happy. Thank you.

Best regards, a.c.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/08/10 01:09 AM

Originally Posted By: Kamin
Euh Jake, I apologize, because as adepts of the Chas ET concept, we should not have contradiction publicly (all those may stay confined to the ashram !)

But to me the 12ths in the high treble are tempered , I can hear it , but you gave me doubt so I measured with Tunelab.

Put the display at zero move for instance at G7 (Tunelab is tuned to the G7 frequency)
Play C 6 - the display goes right , showing a 3d partial of C6 being higher than the actual pitch of G7

measure the offset by tapping on the display with the mouse till it is stopped.

I measured 2.71 cts offset form a pure triple of the fundamental frequency . (it is well tempered, in that case)
I wonder how do you test the 12th, if you hear the M6 faster than the 17 th that mean that the interval is shorter than pure.
If you find the 3d partial of C6 higher than the fundamental of G7 that is, a tempered 12th.

Which notes did you find over "pure "twelve ?


I, too, like the recording, but: I was just doing the 3:1 check that Alfredo says to use in his tuning sequence. The 12ths are wide when I examine them in Pianoteq. Are we perhaps discovering a conflict: Pianoteq shows 12ths as wide on 3:1, but TuneLab shows them as narrow? We need to know. (We aren't contradicting each other. We're trying to get all of these things right.)
Posted by: Bernhard Stopper

Re: HISTORICAL ET AND MODERN ETs - 03/08/10 03:32 AM

Originally Posted By: Jake Jackson


I, too, like the recording, but: I was just doing the 3:1 check that Alfredo says to use in his tuning sequence. The 12ths are wide when I examine them in Pianoteq. Are we perhaps discovering a conflict: Pianoteq shows 12ths as wide on 3:1, but TuneLab shows them as narrow? We need to know. (We aren't contradicting each other. We're trying to get all of these things right.)


Maybe the Chas tuning was autosettling into a Stopper tuning in pianoteq, who knows? (for the dumb people out there, this is a joke, haha!)

Where´s the problem Jake? If the piano synth sounds good and the duodecimes (twelfths) are on the wide side of a third-partial-of-the-lower-note vs fundamental-of-the-upper-note (or simply said a 3/1) partial match, it is apparently more a Stopper tuning equivalent than a Chas tuning. The only persons who may be concerned about this are Capurso and Kamin (and eventually me of course if my tuning is going to be marketed under Chas name).





Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/08/10 05:34 AM


Stopper, I politely ask you to keep your market anxiety out of this Topic.

You could contribute, for instance, by describing your only-pure model more in depth (?), by explaining how a beatless 3:1 ratio can be congruent (how can it make sense) with beats simmetries (?), and by sharing your aural tuning sequence for a pure 3:1 ET (?).

a.c.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/08/10 12:31 PM

The problem was...I wasn't just trying to get a sound that I liked--I was trying to be very precise in following CHas.

(Remember that I said that the 12ths were wide--so it's actually neither a Stopper, which specifies just 5thd, nor a CHas, assuming the wide reading is correct. The intervals in the midrange are CHas (I think?), however, so it's more of a stretched CHas.)

But I must say I need more information. It may already be somewhere in this nine page thread. Sorry if I missed it, but two questions that reveal the sorry state of my understanding:

1. To have slightly wide octaves and slightly narrow 12ths, on what partials does one listen for the beats? 4:2 for the octave and 3:1 for the 12ths?

2. When speaking of wide octaves, does this mean just using a 4:2 check on the octaves, which will produce a wider octave than a 2:1 check, or slightly widening the octave past that? In other words, is just getting the upper partials nonbeating the goal, which will widen the octave, or is one making those upper partials beat slightly, so that the octave is widened still more?
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 03/08/10 12:40 PM

Jake:

If you are trying to get wide double octaves and narrow 12ths, just tune 4:2 octaves. Because of iH, tuning stacked 4:2 octaves will always produce a double octave that is wide of 4:1. Whether the single octaves, double octaves or 12ths will sound like they beat depends on the listener.

If you are trying to understand Alfredo's tuning instructions, I cannot help you. I have not been able to reconcile the different things he has said.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 03/08/10 04:05 PM

Jake,

about the 12th, I recorded today a twelve with a pure 3:1 ratio.
I mean : 440 hz (A-49) and 1320 Hz : E6

That twelve had 5 beats at the 3:1 level , coming form the 3d partial of A440 that was at 1325 Hz (measured with Tunelab)

It was on that piano, I admit it is a highly inharmonic one

To tune that 12th so it have no beta at all, the E6 may be tuned at 1325 Hz.
That is what tuners call a "pure" interval (which by evidence is all but "pure" but that is another story).

Frankly I did not get yet all the theoretical explanations, from Alfredo paper, (but I work on that) I was lucky enough to see him doing, to listen and to analyze that with what I know about tuning - as usual those kind of things take time aint as discovering something and understanding immediately what happens.

Jake you misunderstood about the octave (while the octaves are always wide at some point in a piano, if minimally the 2d partial of the bottom note IS the pitch of the fundamental of the upper , this is what Philippe call "iH correction", if not the octave sound false, and too small.

The equivalence of beats in Chas is between the 12th and the DOUBLE octave (2 octaves stacked)

This lend to octaves that are wide but it is not as say Jeff 4:2 + 4:2, the bottom octave can be short of 4:2 , it depends of the level of iH at that part of the piano (and the level of iH of that particular piano). There is always a tendency to oversimplify those concepts, practically many things are intricate, many technical gesture have to be learned, and appropriated, a good job is the result of many details added.


ALfredo tunes by listening directly at the slow and lower level of beat rate : octaves at 2:1 , doubles at 4:1 12ths at 3:1 ; 5ths at 3:2 not using the checks that compare 2 fast beating intervals, as the M6 M17th to check the 12th size.

I tuned the last piano using those checks (after having followed the same method Alfredo uses) , and seem to me they are suitable for that and that the result is similar.

Simply it may be easier to tune directly and compare the beat progression of intervals that are next each other, than to use totally different intervals, that add complexity for the listening (but in the end the evenness of tone is helping, all intervals may be progressive so one can use whatever interval he prefers.

Coming back to the theory, I simply noticed that the method works perfectly, and that a "hot spot" is there, efficient and audible.
In the end the harmony is raised, the piano sound a tad larger, that have always be my intention to tune in the harmonic spectra of any piano, taking care that the notes spectra add each other nicely en raise the resonance of the instrument.

One of the main problem for tuners is to tune the high treble so it does not sound too low, nor too much stretched. Most of the time the top end of the piano follow a kind of added stretch that is not really lining with the notes under. The same occur in the basses. Enlarging the mediums helps to get there more in line, but only the Chas method allow to get some crispness in the treble (due to the good coupling of many intervals with the top note)without accentuating the stretch curve (it accentuate , but naturally because of the ih raising much in the treble).

Voila, thats all I can say at the moment. There is even more in that, I feel so, but I cant say much more.

I had yet today a pianist that call me saying he like the way the piano plays now , I appreciate it; not easy to do new things...

On the records made with Pianoteq, what I hear is may be not noticed by anyone, but I know what I am looking for.


The Chas tuning is highly balanced in a stable equilibrated way. Other ways to balance a tuning are available, providing harmony, but very often the zone where the notes are all perfectly in tune in the main harmonic modes is not so large, 4- 5 octaves span may be, then the piano may have registers, and the tuner have to even/regulate those registers so they are appropriate to the acoustic of the place.
I am yet to listen Chas when used in concert, and with orchestra, in a room , I go for it. To me if the justness seem to be raised in the ear of musicians most probably it will be good to play with orchestra also.

The effect is so particular that I cant predict what it will give in that situation.

Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/08/10 05:18 PM

Yes, I see now. But where I still get lost: given that the double octaves and 12ths should beat equally, how much should they beat?

Am I seeking a compromise to adjust for iH, or is there instead an intentional slight roll that I want to install? What should I do, in other words, if the piano has very low iH, so that the double octave beat and the 12ths beat are almost indetectable? Should I slightly repitch both to create a more perceptible, slow rolling that is identical on both the double octave and the 12ths?
Posted by: Inlanding

Re: HISTORICAL ET AND MODERN ETs - 03/08/10 05:35 PM

Hi Jake,
It might depend on how the other notes relate to each other down the register so as to stay consistent with the amount of stretch. You have also to consider how the "whole piano" sounds. That is one of the advantages of checking double octaves, etc.

I tuned a few pianos on Saturday and experimented with a compromise between a double octave and an octave and a 5th. The wider the octaves become up the register relative to the tempered section, the less narrow the 5ths become, working their way to near pure.

Frankly, when you get either correct, the instrument will sound good. It then becomes more qualitative and a matter of taste as to how much to stretch.

Without really good unions anyway, all the octave stretching and temperament choices begin to lose their value.

If you have time, post a few samples of your tunings.

Glen
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 03/08/10 05:58 PM

Originally Posted By: Jake Jackson
Yes, I see now. But where I still get lost: given that the double octaves and 12ths should beat equally, how much should they beat?

Am I seeking a compromise to adjust for iH, or is there instead an intentional slight roll that I want to install? What should I do, in other words, if the piano has very low iH, so that the double octave beat and the 12ths beat are almost indetectable? Should I slightly repitch both to create a more perceptible, slow rolling that is identical on both the double octave and the 12ths?



Jake this is a very good question ! on pianos with high iH all mean to absorb that iH and find something harmonious are good. But if the piano have low iH , to have the same beat value in an octave it may be less stretched than usually.

I did not have that situation yet, so I cant say. As the idea is to have an equilibrium between the double octave, the 12
th, that relation induce also a symmetric relation
2 octaves lower.

I tend to thing that the global stretch may be lowered then.

There is a roll, but it is so slow it couple before finishing its cycle. anyway it is not noticed as a roll, just as the beginning of one. It may be ascertain by checks using other intervals, as the M3 and the double octave, or the M3 and the octave, and comparing the beat speed. But with differences as small as 0.3 bps it is very easy to miss, and easier to go for a kind of tone , or a behavior of the interval, and stick to it.

Anyway, the difficult part is to begin, after that the good spot is in the ear and in the piano resonance. (that part is less reproduced with Pianoteq , what I hear is some resonance, but not as much reinforcement as at the piano- but it is still partly there so it may be possible to tune it.

You may try to learn to recognize a "pure 5th" or a "pure 12t" from a larger one and a tempered one. Musically, the output is different, even if the beats may be difficult to perceive at first, the color of the interval change.




Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 03/09/10 07:24 AM

Jake:

With a 12th and 15ths having a common note on top, the algebraic difference of their beatrates will always be equal to the beatrate of the implied fourth on the bottom regardless of how the top note is tuned. So if you want them to be equal beating, and the fourth beats 1 bps wide of just, the 12th must beat 1/2 bps narrow and the 15th must beat 1/2 bps wide. 1/2 - (-1/2) = 1.

When tuning equal beating 12ths and 15ths, fourths beat about 1 bps in the middle of the piano, a little faster in the treble and a little slower in the bass. So the 12ths and 15ths may beat up to 1 bps in the treble, and probably slower than can be noticed in the bass.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/09/10 10:27 AM

(Glancing at the thread title and seeing "Historical ET and Modern ETs," I worry that I'm narrowing the focus too much, here. I'll continue over on the CHas pretuning thread.)
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/13/10 07:41 AM

Hello, just a personal comment about a fresh acknowledgement.

A young piano tuner and PW poster from Finland, Patrick (pppat), writes:

..."there is something esthetical about the mathematically symmetrical tuning (ET), but there is no question that the color palette of EBVT III makes the (sensible) pianist play the instrument in a different way."...

To me, this is quite something: for the first time a positive comment is spent about the mathematical symmetries of Modern ETs.

What may any young tuner share next?

1 – The first “conventional” ET, 12th root of two, has evolved into “variants”

2 – These ET “variants” have now been described both mathematically and geometrically, they represent Modern ETs

3 – Modern ET theory is finally practicable

4 - Modern ETs beats-symmetries can increase the performance of any piano

About any tuner, I hope his/her understanding about Modern ETs beat-symmetries go from their aesthetic beauty deep down to their astonishing practical effects. Then, he/she will be able to recognize past and present hybrid tunings with a high degree of specific knowledge and professional consciousness.

Regards, a.c.

.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 03/13/10 08:31 AM

You know, When I have read those kind of comments for the first time, I have find them somehow presumptuous,and I recall I have stated that.

Now that I have tried n and hopefully understand (at last partly) the composition of that tuning, I may say that I understand what Alfredo is trying to state ).

The result of that evening of beats, symmetry and higher resonance, gives the tuner a different ear when he listen to a more conventional ET, and it provide him a reference model to compare with. That is very strange as a sensation, but the level of harmony is then apprehended when listening to more classical tunings.

THen , in some cases the same kind of effect can be perceived sometime only in a portion of the scale. SOmetime it is even larger than the ratio, (un focusing) and in other situations the compactness of the tuning is what jump to the ear.

I believe that it may change the way we listen, eventually the way we tune, indeed and certainly the way we "stretch" a tuning if done in our usual way.

To me, at the same time the Chas is at the best place for resonance and harmony, while being "at the edge", meaning that a step above and the piano will not tone well.

So knowing that kind of limit in spread is a very useful thing, to me , as the tuning itself is simply "normal" the ability of the tuner to have a good tone and stability, and to understand how the piano settle, is only what will make the difference, part experience, part good sensations, part listening, but justness is well taken in account by the ratio itself, that is a quiet comfort sensation, which is appreciable.


I have seen private witnesses and acknowledgments coming from other tuners and they seem to say all the same thing.

I know some good tuners, and it is really strange, but all of them have doubts : do I have well stretched that tuning ? Is the justness well reconciled ? Many of them are unsure of the real justness of the instruments, and that seem to be confirmed by the orchestra instrumentalists that say that the piano is "in tune enough" for them.

We dont imagine how much some of us can be wanderers even after 30 years of career and more ! I'd appreciate comments from other tuners on that aspect (but seem to me that having strong affirmations is also a natural tendency in that trade, and that questioning itself is not much in the trend, nor agreable)


The theory is that as long as the tuning come by the Chas ratio, it may settle in there, for some reason

This may be somewhat difficult to test and prove, but possible, if someone have an idea of a battery of to test it would be welcome
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/13/10 11:37 AM

One thing that I find striking is that EBVT and CHas, although obviously very, very different in intention, both seek equal beating on the narrowed 12ths and widened double octaves. They are seeking similar resonances. (But of course EBVT brings out the key color changes, while CHas instead seeks the ET goal while trying to keep the resonances.)
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/14/10 02:22 PM

Originally Posted By: Kamin

Here is a real application of the [CHAS] tuning formula in a virtual piano :

http://www.forum-pianoteq.com/uploads.php?file=CP33%2005.03.2010%202%20CHASIH%20demo.mp3

[...]

Same music but with standard tuning , for comparaison purpose

http://www.forum-pianoteq.com/uploads.php?file=CP33%2005.03.2010%201.mp3



Isaac, Alfredo:

Very good example - the difference is highly noticeable. The CHAS tuning sounds uniform, yet open.

What would be the "standard tuning" of the file that CHAS is compared to?
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/14/10 03:21 PM

Originally Posted By: UnrightTooner
Jake:

If you are trying to get wide double octaves and narrow 12ths, just tune 4:2 octaves. Because of iH, tuning stacked 4:2 octaves will always produce a double octave that is wide of 4:1. Whether the single octaves, double octaves or 12ths will sound like they beat depends on the listener.


Jeff,

What would pure 12ths in the mid-range break down to octave-wise, in your experience? 6:3's, or somewhat narrower?

This as a practical question, given different inharmonicity and scaling problems. I can do the math theoretically (as I know you can), but what's your 'hands-on' experience?
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/14/10 03:28 PM

Originally Posted By: Kamin

ALfredo tunes by listening directly at the slow and lower level of beat rate : octaves at 2:1 , doubles at 4:1 12ths at 3:1 ; 5ths at 3:2 not using the checks that compare 2 fast beating intervals, as the M6 M17th to check the 12th size.


Isaac,

could you give a more specific explanation? 2:1 octaves and 3:2 fifths sounds good in theory. Did you invent a new instrument or something? :-D
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 03/14/10 03:37 PM

Pat, in mine (experience) , less than 6:3 , a very quiet octave in fact .
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/17/10 07:46 PM

Originally Posted By: alfredo capurso
Hello, just a personal comment about a fresh acknowledgement.

A young piano tuner and PW poster from Finland, Patrick (pppat), writes:

..."there is something esthetical about the mathematically symmetrical tuning (ET), but there is no question that the color palette of EBVT III makes the (sensible) pianist play the instrument in a different way."...

To me, this is quite something: for the first time a positive comment is spent about the mathematical symmetries of Modern ETs.

What may any young tuner share next?

1 – The first “conventional” ET, 12th root of two, has evolved into “variants”

2 – These ET “variants” have now been described both mathematically and geometrically, they represent Modern ETs

3 – Modern ET theory is finally practicable

4 - Modern ETs beats-symmetries can increase the performance of any piano


Thanks for the quote, Alfredo, and I do agree on what you wrote here.

I'm also been following your work (mainly due to Isaac's kind updating), and I really like your concept. I will try it out.

Which brings me to a thought. Would it be a good idea to summon this method in a separate thread? The preparatory setting, the idea of stretch and so on. These threads have had a rather vivid posting rate, and the basic information gets somewhat hidden in here.

Just a thought. Being a math person myself I find the principles for your way of tuning interesting, I would certainly try it if I got the reference litterature in a more compact form.

By the way, I think this forum is great for the curious ones. Always something new to try, new challenges, helpful hints, and so on. It's really good to have this community-style exchanging of ideas going on!
Posted by: Phil D

Re: HISTORICAL ET AND MODERN ETs - 03/17/10 07:55 PM

Quote:

Which brings me to a thought. Would it be a good idea to summon this method in a separate thread? The preparatory setting, the idea of stretch and so on. These threads have had a rather vivid posting rate, and the basic information gets somewhat hidden in here.


Yeah, all the good information is so difficult to find amongst all the nitpicking and defending! A summary of techniques would be so very useful, if you have the time or the inclination!

Alfredo, you did mention wanting somebody with the english skills to help you write something about this technique. Perhaps I can be this person, if you would like to work together on producing a usable tuning sequence etc.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/18/10 05:04 PM


..."Perhaps I can be this person, if you would like to work together..."...

Yes N a M, what a nice offer, thank you, I'm looking forward. I'll be back home in a week's time, otherwise I'd be willing to start tonight, were the circumstances appropiate.

..."It's really good to have this community-style exchanging of ideas going on!"...

It is my pleasure too, glad that you are curious, Pat.

Regards, a.c.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/19/10 12:07 PM

Not a Mongoose:

Did you see the CHas Preparatory Tuning thread? I created a preliminary list of the major qualities of CHas there, and Alfredo made corrections. It might serve as a point of departure. These is a sequence of steps in that thread, too. Not a conventional (Anglo-American?) sequence, exactly, since Alfredo doesn't set a one octave bearing, but it may let you construct something closer to a conventional sequence.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/19/10 03:28 PM

Just a passing note. I just read that A.J. Ellis, whose essays on pitch and tuning are often cited here, was one of the sources for Shaw's Dr. Higgins in "Pygmalion" and thus for "My Fair Lady." Henry Sweet, who studied with Ellis, appears to have been the main source, however.

Had no idea.
Posted by: BDB

Re: HISTORICAL ET AND MODERN ETs - 03/19/10 04:03 PM

You should read the introduction to Pygmalion for the exact details. For that matter, it is worth reading the entire play, including the epilog.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/23/10 07:50 AM

Bill, thank you for your explanation. I'm replying here since we talk about ET, music and theory, though I do not consider my self a musicologist.

You say:...“Yes, Alfredo, it means that he (Rameau) changed his mind about what he was interested in. The temperament he used was a modified meantone and it was VERY unequal and that was typical of his time.”...

We may as well say that Rameau changed not only his “interest”, he changed his entire approach to intervals and temperament issues.

...“Just like Bach, he decided at one point that he wanted a temperament that was more accessible to all keys.”...

You call that “accessibility” which to me sounds indefinite, I'd call it “in tune”, i.e. the sense of the intervals proportions that we can share. In other words, they were looking forward to getting reed of any “wolf”, they were simply asking for maximum euphonicity.

...“The theory of ET had always been there, since the time of Pythagoras and even before that among the ancient Chinese way before the common era.”...

This may be a simplification. The “idea” of equal size semitones is very ancient, but the practice for progressive intervals was not. Not even today, and you yourself seem to confirm. And more: the octaves then were theorized “pure”. It was only last century when some models opened to stretched theoretical octaves. Have you noticed?

...“But did you also read that just because he (Rameau) thought about ET did not mean he could tune it and he could not. Rameau was known for many temperaments, including some quasi ETs but not ET itself. He did not discover a way to tune ET accurately.”...

I'm not surprised. The temperament was based on one octave module, then theoretical octaves were “pure”, the 2:1 octave's ratio was favoured, not having been mixed with all the others, so the first ET theory was not practicable. In fact, I still don't know about which ET you talk about. And I find strange how your theoretical interest and understanding can suddenly drop, strange how you do not seem to notice the route towards the harmonic resonances of the sound whole, and strange how you do not seem to bother about a significant difference between the first ET and modern approaches.

...“It would be quite highly manipulative in my view, to take that one phrase that you found to suggest that 11 years after he wrote about the effects of interval sizes on emotions, he took a tranquilizer and tuned his pianos in ET after that.”...

It looks like the issue is bounced back (ok), but to me your quotation sounded exploitable. Anyway, why do you talk about tranquillizers? Interval size is one matter, cacophony is a different matter. Wouldn't one need a tranquillizer when surrounded by “wolfs”?

...“What I was actually looking for was a list of descriptions of the effects of various key signatures that composers themselves wrote. They are in Owen Jorgensen's publications somewhere but I thought I might find them on the web and they may be but I cam across that phrase by Rameau.”...

Today you could get more theoretical knowledge available, beyond “a phrase” you could come across.

...“It described quite well what I was referring to in the interpretation of the Schubert Impromptu. You can hear Rubinstein play it and if you like that, fine but I for one, have heard it performed in an amazing way that I will never forget.”...

Fair enough. That phrase was exploitable and you've heard an amazing version of Schubert Impromptu that you'll never forget. But in any case, what has this got to do with colour and emotions.

...“The fact that Rameau later attempted to explore ET was not pertinent although I did consider adding that I thought his change of mind was an interesting twist. That interesting twist does not change the fact that interval sizes do affect the emotions.”...

You say Rameau's “twist”, I'd say acknowledgement. Sincerely, I think that a massive quantity of clichés are being loaded onto a tuning technique, as if the technical result itself – (O) an enjoyable tuning - was not enough. In my opinion, any arbitrary out-of-tune interval can only hurt our “ear” and our emotions. How about a professional dancer wearing an non-equal costume, the one I like, skin-contact silk and jute, would that help his/her emotions?

...“Patrick may also be able to come up with some other examples as he learns to play according to temperament and show us how ET affects his mood in one way but the EBVT affects it differently.”...

May I ask you which ET? Rameau's ET? A Modern ET? Again it gets turbid and I feel confused, you talk about ET, but you continuously notice reverse well, then you would expect Patrick to tune what you call true ET, but you do not acknowledge modern ETs, maths having little to do with music (?). Is there a point I'm missing?

Regards, a.c.

.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/08/10 07:43 AM


Bill, in Chas thread you wrote:..."However, knowing about other means of identification is useful and constructive, the same as knowing another language very thoroughly is. It is an expansion of the mind. When we do not limit ourselves to just one way of thinking, that we understand what other people say, in their own way, we become a more enlightened person."...

Leave my own way aside, when we talk about ET we are talking about "nature's way" and its ordered proportions. This can help to understand why a geometric progression is (aurally) so strongly appealing.

..."That is why I did not choose to argue with you on the other thread when I gave my opinion. Yes, I do have my own opinion about what well temperament can provide. No, I do not choose to tune any pianos in the CHAS method because I feel that it is virtually the same concept that I would have if I were to tune a piano in ET but I choose not to do that."...

The point is that Chas, Cordier's ET, Stopper's ET must not be confused with 12th root of two ET, i.e. the first model based on natural proportions. Then, whether you call Chas ET model "Chas" or "what Bill Bremmer feels being virtually the same concept that he would have if he were to tune a piano in ET", does not really matter.

And after all, the simple acknowledgment of modern variants of ET would merely prove your enlightenment. You could now start referring to your own opinions and ET in very precise terms, so avoiding confusion amongst your/our colleagues.

BTW, is saying "method for tempering" equal to saying "temperamental theory", in North American English?

Regards, a.c.

Edit: Recently I read: "some temperaments are more equal than others", quite funny, (O) very true.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 04/08/10 08:26 AM

Originally Posted By: alfredo capurso
.....

The point is that Chas, Cordier's ET, Stopper's ET must not be confused with 12th root of two ET, i.e. the first model based on natural proportions.
.....


Well, the pythagorean tuning is also based on natural proportions. It could be argued that the 12th root of 2 is not based on natural proportions because it is based on an irrational number (it cannot be described by a ratio made of whole numbers).

But the point I really want to make is that the 12th root of 2 ET is different than the others that are mentioned because it cannot be tuned aurally on a real piano. It defines pitches without regard to inharmonicity. And that is also the problem with the published CHAS theory. Although there is an aural sequence for tuning CHAS, which takes into account inharmonicity, the CHAS theory does not. If we divide “marrow from bone” CHAS theory is very similar to 12th root of 2 theory because it is based on a fixed ratio, but CHAS tuning is not. They are two different things just as 12th root of 2 theory is different from tuning ET with aurally pure octaves.

And please do not resume that deceptive "shell game" about what a theory is and what a model is.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/08/10 04:22 PM


Jeff sorry, on "deceptive games" I cannot help you.

The article linked below may better explain what I mean when I talk about nature's proportions and logarithmic scales:

Mario Livio: "The golden number: nature seems to have a sense of proportion":

http://findarticles.com/p/articles/mi_m1134/is_2_112/ai_98254967/?tag=content;col1

Together with this article there is plenty of literature in the web on the same issue.

Regards, a.c.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 04/08/10 04:29 PM

I believe that whatever the iH is we tune in it because it is the source for the real tone we hear.

It may not have to do much with the model itself. Instruments with inharmonic tones have been tuned to pure 5ths Cordier. Indeed the speed of 3ds may have raised a lot, but if the idea is to obtain relations between beats, iH is not playing a so large role in the effect, not more than with a standard tuning.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 04/09/10 07:08 AM

When you talk about proportions, such as semitone ratios, inharmonicity cannot be ignored in a meaningful discussion.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 04/09/10 07:26 AM

Frankly, I suggest that no. Inharmonicityy play a role in the particular tone of the instrument ,and also in its ability to be tuned more or less open (hence based on a 4:2 on beat octave)

It may play a role in a discussion, but if you try to tune with pure double or triple frequencies (in Hz) you get nowhere.


The piano have its tone, and that is what is tuned, that is what I mean. Ih is giving us problems because its uneven progressivness is in the way on pianos with less than good scales. The stretching of the intervals above the basic ih correction give us some "room" to reconciliate these, that is one of the main reason why it is used, to me.

Ih will adbsorb some of the beating and create others.

We need to "decompress" the piano, to open the tone, so we are not annoyed by iH.

But it can be also a bad habit !

If you are interested in iH and its relation to tuning, do you know what the are the iH level of grands or verticals of differnt brands , and how they change the way you tune them ?




Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 04/09/10 08:12 AM

Originally Posted By: Kamin
.....

If you are interested in iH and its relation to tuning, do you know what the are the iH level of grands or verticals of differnt brands , and how they change the way you tune them ?


Yes I do. I have a collection of measured iH curves and a database application to see the effects of different tuning schemes. Aurally I notice the difference in stretch when comparing 12ths to 4:2 octaves and 4:1 double octaves depending on the size of the piano. But starting in the direction of finding the best stretch for a given piano has led me in a different direction when actually tuning.

I am tuning more and more by playing three notes at a time and striving for the best sound or resonance. This also gives quite a bit of stretch. After tuning the temperament, with the color of the 4ths and 5ths I want, I then tune octaves by including the fifth down from the top note. When I can then tune 12ths, I again include the 5th from the top note. There are plenty of other checks, of course.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/21/10 05:32 PM


Jeff,

You write:..."After tuning the temperament, with the color of the 4ths and 5ths I want, I then tune octaves by including the fifth down from the top note. When I can then tune 12ths, I again include the 5th from the top note."...

This sounds interesting. Could you let us listen to a recording of your tuning (slow playing of chromatic intervals)?

Have you tried Chas Preparatory Tuning?

Regards, a.c.

.
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 04/21/10 07:51 PM

Yes Jeff, I agree with Alfredo - I think this is interesting, too. Any new field reports from your experiment with three notes?
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/22/10 04:00 AM


Hi Patrick,

have you already posted about your EBVT+pure 12ths variant tuning, after some days? Were 12ths still pure?

Would you post a recording of your chromatic intervals too, played in slow sequence, say 4 seconds each, same touch/intensity?

Regards, a.c.

.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 04/22/10 07:17 AM

Alfredo & Pat:

I am continuing to use this technique and like it more and more, but it demands a very equal temperament otherwise there is no “best” pitch for the note being tuned. But then when everything is right, well, then everything is right! (Sometimes I think that it is not that my glass half empty, it is that I don’t have a glass at all.)

I have no plans on trying the CHAS tuning, preparatory or otherwise, or any other tuning with a four letter abbreviation. wink And sorry, I do not have any recording equipment and probably would not bother if I did.

It is not difficult to make the tool to reach a 12th and then you can find out for yourself what you hear. I think there is much to be said for playing more than two notes at a time when tuning.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/26/10 05:20 PM


Jeff, you write:

..."I am continuing to use this technique and like it more and more, but it demands a very equal temperament otherwise there is no “best” pitch for the note being tuned."...

Well, why don't you tell us more about your technique?

..."But then when everything is right, well, then everything is right! (Sometimes I think that it is not that my glass half empty, it is that I don’t have a glass at all.)"...

When can we (aural tuners) say "everything is right"? What do you mean?

..."I have no plans on trying the CHAS tuning, preparatory or otherwise, or any other tuning with a four letter abbreviation."...

This is too bad, tough you'll certainly have your reasons.

..."And sorry, I do not have any recording equipment and probably would not bother if I did."...

Why would you not bother? You see, at some point pro aural tuners check their overall tunings and then, with actual results, we can contribute. More than words and more words, for sharing what we are talking about, it could be enough listening to a sequence of chromatic 5ths, 6ths and 10ths, 12ths, 15ths, 17ths and 19ths from C2 to C7 played slowly (4 regular secs each) and with the same energy (read touch).

Also leaving RBIs progression aside, you surely know, 5ths and 12ths are easly checkable by ear, both musically and beat wise. Tune your piano, play it for one hour, or leave it season for three days and check it again. Then you may appreciate why I talk about a Preparatory Tuning.

Regards, a.c.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 04/27/10 10:33 AM

Alfredo:

There is nothing more that I can explain. A string can be tuned to a beat rate when playing two notes and the beat rate can be compared to other beat rates or to a clock. But when playing three notes there is much more to hear. Could you really explain the difference in taste between yellow and brown mustard? I couldn't. I am moving beyond mere theory, even though it is still fascinating to me, and tuning for the best ….. tone? resonance? fahrvergnügen? So if you are interested, go ahead and try it. I can not explain it further, and am still working on it anyway.

Something I do notice is that the more equal the temperament is, the more stretch you can get away with. And this technique does show up any small errors in the temperament.

As far as preparatory tuning, if the tuning sounds different in a few days, how could someone possibly know how to tune a few days earlier so that it will sound a certain way a few days later? It sounds like snake oil to me. Until a piano is stable the tuning will change in ways that cannot be completely predicted.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/27/10 05:31 PM


..."I can not explain it further, and am still working on it anyway."...

Nevermind, do work on it and let us know your findings.

..."Something I do notice is that the more equal the temperament is, the more stretch you can get away with."...

Sorry, what do you mean?

..."And this technique does show up any small errors in the temperament."...

More than usual?

..."As far as preparatory tuning, if the tuning sounds different in a few days, how could someone possibly know how to tune a few days earlier so that it will sound a certain way a few days later?"...

Exactly, we should avoid that our tuning may sound different in a few days. This is what the Preparatory Tuning is about: taking into account the piano settlings, gaining the tuning form through the piano settlings.

..."It sounds like snake oil to me. Until a piano is stable the tuning will change in ways that cannot be completely predicted.".

You are right, predicting is quite a challenge. Though we know for sure that the piano will settle, therefore our tuning form is bound to be "de-formed".

Then we can guess the tuning "over-form" and let the piano settle on our favorite form.

After all, archers can evaluate winds, speed, distances, although not "completely".

And we tuners do not need to wait for a few days, we can solidly play the piano while we are tuning it. Correct?

Regards, a.c.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 04/29/10 10:41 AM

Alfredo:

So if snake oil doesn’t work you go back to the shell game.

The impossibility of predicting how a piano’s tuning will settle after a few days (and therefore the futility of tuning in a way to produce a later desired tuning) is pointed out as snake oil. Then the “few days later” is changed to typical pin setting technique, a shell game tactic.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/29/10 06:58 PM


Sorry Jeff, I do not share your interests.

a.c.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 04/30/10 07:11 AM

I know.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 05/13/10 02:10 PM


Hello.

Thank you, Kees, for suggesting me to listen to Sweelinck's chromatic fantasia. I went on youtube and I listened to three versions.

I agree with you, those tuning have strong melodic effects. I do not feel like raising an aesthetic issue, so what follows is only some of my personal thinking.

While I can understand the route through many temperaments toward modern ET's, for achieving the playability of all key signatures first and maximum euphonicity later, I cannot be sure those sounds and their harmonic and melodic relations are what the composer really had in his mind (I can not even be sure how correct those MT tuning are).

As I said, I tend to believe we may have a natural harmonic heritage which may be referred to matter and its vibrating modes. Then, I tend to believe that composers manage to transfer on paper their inner singing, and that in those times (1600) they had to get along with what had been achieved, the overall understandings and the available “modernities”.

Today we still understand iH as the reason for stretched tuning curves. My hope is now to share Chas Temperamental Theory, its latest ET modulus and the system's constants, that release the most correct* reason for stretching all intervals.

As I think we may all enjoy scientific progress, I also think we are ready for this to happen. Actually, it is my opinion that, as in many cases, our practice has anticipated theory.

Then it may only be a matter of dismissing wrong teachings and wizard's frocks, and letting emotional and rational get along together.

(*) Referred to the semitonal scale and intermodular octaves.

Sweelinck's chromatic fantasia.
On harpsichord:

http://www.youtube.com/watch?v=bIWYYVoFNd0

on virginals:

http://www.youtube.com/watch?v=Swubdbp4oxk&feature=related

in MT tuning (?):

http://www.youtube.com/watch?v=EHExcd6PYxQ&feature=related

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/03/10 06:02 PM


In another thread, Patrick writes:

..."ET often turns closer to UT at those ends too! In the extremes, it's just what brings out the best resonance - personally I couldn't care less if it works out mathematically."...

..."The only reason I can think of right now is that the symmetry of ET makes it's easier for me to approach it from an analytical viewpoint. Tuning EBVT III, I tend to listen for harmony. That makes it much harder - again, for me."...

Originally Posted By: Emmery,
The practical application of ET removes offensiveness at the slight expense of colour.

Patrick:..."I don't agree on either "offensiveness" or "slight expense". It removes key color totally, turning the tunings it into something very similar to grayscale. Which has a certain beauty to it that I like, too."...

Originally Posted By: Emmery,
The other temperaments including EBVT can gain some colour, but with a proporional loss of freedom in playing in all keys or introducing unwanted dissonance . For EBVT to gain universal acceptance in the public, somehow the public needs to be convinced that freedom to express music in ALL keys with the least offensiveness is less important than the more colourful expression of some music played in specific keys. I doubt this will fly mainstream on home based piano tunings for piano technicians and will probably remain in the confines of some performance halls or exhibitions on alternative temperaments.

Patrick:..."the public doesn't have to sign any UT declarations at all. I don't think they could care less - as long as they are moved by the music coming out of the piano, be it whatever logic behind the tuning. This is often neglected in this forum. We tune for the pianos to be played, not to be calculated."

I still cannot understand this thing about "colour", nor why we should lessen (on purpose) the harmoniousness of any chord. What can the reason or the pleasure be in going from a lambish key to a wolfish one?

Does a pianist or a composer really think in terms of variable harmoniousness? And if he/she really did, could their personal preferences ever be said objective, ever be shareable?

How is it possible to refer to "colour" as to the feeling we get from a chord that could sound better in tune?

Can a musician ever be vexed when he/she finds that all key-signatures sound absolutelly beautyfull? When all key-signatures, like in my experience, can readly and generously give back all their harmonic potential?

I don't know about you (All), when I tune I do not think "grey" at all, actually when a chord, any chord is in tune I can hear an astonishing amount of partials coming out, which in my feeling make up the whole available colours. Then, by adding more sounds, I can play with colours. And it will be playing in the warmest place, safe as beauty, immaculate as a shore-line can be.


Regards, a.c.


CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
Posted by: Cinnamonbear

Re: HISTORICAL ET AND MODERN ETs - 07/03/10 11:53 PM

Originally Posted By: alfredo capurso

[...] What can the reason or the pleasure be in going from a lambish key to a wolfish one? [...]


EBVT III is much, much, much more subtle than what you are trying to imply here.

Originally Posted By: alfredo capurso

[...] How is it possible to refer to "colour" as to the feeling we get from a chord that could sound better in tune? [...]


My experience playing it on my own piano, and listening to the recordings of Grandpianoman, Patrick Wingren, and others who posted recordings, is that EBVT III is perfectly in tune. I've tried to describe it to people by calling it "magnified clarity" or "magnified purity."

Quoted from another thread [bolded italics added for emphasis]:

Originally Posted By: LisztAddict
I am not a pro tuner, but I hope it's okay for me to make one post in here. I use Tunelab and today I got an EBVT file from Kees for my piano. When I loaded the file up and looked at the tuning curve, it's no longer a curve. I said to myself "wow, that looks interesting". Not sure what to expect but I gave it a try. Some notes stay the same as before, a few I had to pull up or drop down a bit. I think the most I had to change with any one note was just about 3 cents. The end result really amazed me. I could not believe that only changing a few notes just a tiny bit could make such a big difference. Anyway, I am very happy with whatever math Kees did to the tuning file I sent him.

Thanks Kees!!! smile


LisztAddict is a very experienced and sensitive pianist. He liked it! That should tell you something about EBVT III.

--Andy
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/04/10 04:41 AM


Thank you, Cinnamonbear.

I wrote:

"I still cannot understand this thing about "colour", nor why we should lessen (on purpose) the harmoniousness of any chord. What can the reason or the pleasure be in going from a lambish key to a wolfish one?"

I'm referring to Unequal Temperaments (UT) and conceptual (subtle?) reasons for featuring them. As for the rest, how EBVT sounds and why, I have my opinion, and I can understand when you say "EBVT III is perfectly in tune". But this is not the point nor the thread, I would like to discuss about this (subtle?) "colour" thing.

Last posted:

"Does a pianist or a composer really think in terms of variable harmoniousness? And if he/she really did, could their personal preferences ever be said objective, ever be shareable?

How is it possible to refer to "colour" as to the feeling we get from a chord that could sound better in tune?

Can a musician ever be vexed when he/she finds that all key-signatures sound absolutelly beautyfull? When all key-signatures, like in my experience, can readly and generously give back all their harmonic potential?

I don't know about you (All), when I tune I do not think "grey" at all, actually when a chord, any chord is in tune I can hear an astonishing amount of partials coming out, which in my feeling make up the whole available colours. Then, by adding more sounds, I can play with colours. And it will be playing in the warmest place, safe as beauty, immaculate as a shore-line can be."


Regards, a.c.


CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/04/10 10:52 AM

Originally Posted By: alfredo capurso

I still cannot understand this thing about "colour", nor why we should lessen (on purpose) the harmoniousness of any chord. What can the reason or the pleasure be in going from a lambish key to a wolfish one?
.
Alfredo - "Well-tempered Clavier", and the way Bach writes, should give a good example of reason and pleasure for using differently colored keys.

Originally Posted By: alfredo capurso

Does a pianist or a composer really think in terms of variable harmoniousness? And if he/she really did, could their personal preferences ever be said objective, ever be shareable?

All the composers I've worked with - including myself smile - enjoy the power of intonation. Since we can't do that on the fly on the piano, UT is still (to me) a better choice than ET to carry something of the vocal, strings and wind/brass sound to the piano.

As I write this once more, I notice that I really do look at tuning from a musical angle all the time. Maybe this is a gap that can never bridged (between technical execution and musically desired result), but I hope it could - In playing, as well as in tuning.

Originally Posted By: alfredo capurso

How is it possible to refer to "colour" as to the feeling we get from a chord that could sound better in tune?

"Better in tune" - would that be ET? I doubt so. All the intervals in ET are compromised, so let's hope that ET is not the single, ultimate "in tune" sound.

Originally Posted By: alfredo capurso


I don't know about you (All), when I tune I do not think "grey" at all, actually when a chord, any chord is in tune I can hear an astonishing amount of partials coming out, which in my feeling make up the whole available colours. Then, by adding more sounds, I can play with colours. And it will be playing in the warmest place, safe as beauty, immaculate as a shore-line can be.

Yes, and I admit that the analogy of gray-scale vs colors has its shortcomings. Color inside keys, yes. Color between keys, no. I wrote about that in the other thread, where you and Bernhard also participated.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/04/10 01:56 PM


Originally Posted By: alfredo capurso
I still cannot understand this thing about "colour", nor why we should lessen (on purpose) the harmoniousness of any chord. What can the reason or the pleasure be in going from a lambish key to a wolfish one?

Patrick, you reply:..."Alfredo - "Well-tempered Clavier", and the way Bach writes, should give a good example of reason and pleasure for using differently colored keys."...

This is an old, debatable issue. I have heard Bach being played with all sorts of tunings. Have you heard Bach played on Chas? You may then understand me talking about reason and pleasure. But, what is your reason? What is your pleasure? What do you like about going from a lambish key to a wolfish one? Can you explain?

Originally Posted By: alfredo capurso
Does a pianist or a composer really think in terms of variable harmoniousness? And if he/she really did, could their personal preferences ever be said objective, ever be shareable?

P:..."All the composers I've worked with - including myself smile - enjoy the power of intonation. Since we can't do that on the fly on the piano, UT is still (to me) a better choice than ET to carry something of the vocal, strings and wind/brass sound to the piano.
As I write this once more, I notice that I really do look at tuning from a musical angle all the time. Maybe this is a gap that can never bridged (between technical execution and musically desired result), but I hope it could - In playing, as well as in tuning."...

I hope you look at "in tune" from a musical angle and I should feel no gap. Do you mean ensamble "real time intonation"? If that is bad with a fixed modern ET, which is the most euphonious solution, it is worse (logically) with a fixed UT, plus the vocal UT and the strings UT (all hypothetical), what is that you like? Or perhaps you mean: a fixed UT reminds me of the power(?) of intonation. Then you find again that your piano has not that power "on the fly"...is this what you like?

Originally Posted By: alfredo capurso
How is it possible to refer to "colour" as to the feeling we get from a chord that could sound better in tune?

P:..."Better in tune" - would that be ET? I doubt so. All the intervals in ET are compromised, so let's hope that ET is not the single, ultimate "in tune" sound."...

ET/compromise may be referred to the historical ET, in Chas ET all intervals are ideally weaven together. As a musician, I should hope that you retain the meaning of "a chord that could sound better in tune".

Originally Posted By: alfredo capurso
I don't know about you (All), when I tune I do not think "grey" at all, actually when a chord, any chord is in tune I can hear an astonishing amount of partials coming out, which in my feeling make up the whole available colours. Then, by adding more sounds, I can play with colours. And it will be playing in the warmest place, safe as beauty, immaculate as a shore-line can be.

P:..."Yes, and I admit that the analogy of gray-scale vs colors has its shortcomings. Color inside keys, yes. Color between keys, no."...

Thanks, I shall reword my question: How is it possible to refer to "colour" as to the feeling we get from a sequence of chords that could sound better in tune?
And the other question: Can a musician ever be vexed when he/she finds that all key-signatures sound absolutelly beautyfull? When all key-signatures, like in my experience, can readly and generously give back all their harmonic potential?


Regards, a.c.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/06/10 01:43 PM


Hello. I think Bernhard Stopper's description of its own tuning may be usefull eventually.

"I suppose that you can agree that musical intonation preference for melodic perception is proven to be more pythagorean like, especially for the major thirds. I think this is status quo of teaching at music universities, as a lecturer for composition you have probably knowledge about this.

What is the reason for this? In believe that our brain´s neural network has been highly optimized over evolution to reduce redundancy. If we assume that this neural network ignores the fifth partial for musical processing, we can have an explanation why we prefer melodically a more pythagorean third over a harmonically pure third in the musical perception.

In my tuning theory, another musical preception preference has an important role:
It has been found, that pure octaves don´t satisfy musical perception either.

If we look closer to the pythagorean major third with it´s ratio of 81/64*, we can split this ratio down to 3^4/2^6, that means musically four pure duodecimes (twelfths) upwards and six pure octaves downwards, which yields our pythagorean third.
*(we can leave inharmonicity by side at this moment, in real word piano tunings it´s just a problem of affine transforms.)

If we replace those six pure octaves (as they don´t satisfy melodical/musical perception) with octaves that satisfy this perception (in my tuning that means stretching every octave with a nineteenth of the pythagorean comma), the pythagorean thirds are getting transformed (or corrected) by six acoustic satisfying octaves. These thirds are then slightly greater than in standard ET, but not as extreme as in pythagorean tuning. They are more comfortable melodically than pure thirds and harmonically more comfortable than the pythagorean thirds, (even more comfortable than the thirds in the outer keys of unequal temperaments). Additionally, they have a distinctive musical size which can be explained by and are coherent with a redundancy-optimized neural network. This distinct size can also be trained way easier by soloists compared to up to twelve different sizes in unequal temperaments.

Not to speak about the effect of the specific symmetry in the ET form on pure duodecimes (twelfths), which makes the impression of dissapearing of the beats of the major thirds in chords.

So equal temperament in this special case (based on pure duodecimes aka StopperStimmung) is tonal for me while unequal temperaments (including EBVT´s and standard ET) are atonal.

And i prefer a tonal tuning. (How close we are with this statement :-) .

Let me also mention that my tuning was not developped through an abstract mathematical model. The math is just applied to try to explain what made me (and many many others) so inspired about the musicality of this tuning. Bernhard Stopper".

Bernhard, some time ago you were about to post your aural tuning sequence. Have I missed it?

Regards, a.c.
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/06/10 05:15 PM

Originally Posted By: alfredo capurso

Patrick, you reply:..."Alfredo - "Well-tempered Clavier", and the way Bach writes, should give a good example of reason and pleasure for using differently colored keys."...

This is an old, debatable issue. I have heard Bach being played with all sorts of tunings. Have you heard Bach played on Chas? You may then understand me talking about reason and pleasure. But, what is your reason? What is your pleasure? What do you like about going from a lambish key to a wolfish one? Can you explain?

No, I haven't heard Bach on CHAS (except for Isaac's Bach/Siloti, which I think sounded really good). But as far as the Well-tempered Clavier, It is really evident that close keys in a WT/UT results in music that are different from the remote keys. You don't really have to listen to any other thing than the springiness of the prelude in C# major and compare it to the calm C major prelude to see what I mean. These characteristics of the keys get lost in ET, no matter which version of ET.

Originally Posted By: alfredo capurso

P:..."All the composers I've worked with - including myself smile - enjoy the power of intonation. Since we can't do that on the fly on the piano, UT is still (to me) a better choice than ET to carry something of the vocal, strings and wind/brass sound to the piano.
As I write this once more, I notice that I really do look at tuning from a musical angle all the time. Maybe this is a gap that can never bridged (between technical execution and musically desired result), but I hope it could - In playing, as well as in tuning."...

I hope you look at "in tune" from a musical angle and I should feel no gap. Do you mean ensamble "real time intonation"? If that is bad with a fixed modern ET, which is the most euphonious solution, it is worse (logically) with a fixed UT, plus the vocal UT and the strings UT (all hypothetical), what is that you like? Or perhaps you mean: a fixed UT reminds me of the power(?) of intonation. Then you find again that your piano has not that power "on the fly"...is this what you like?


A fixed modern ET might be the most euphonious solution to you and others, but not to many non-piano musicians. At least in my experience of working with strings, choirs, wind/brass etc. by themselves, the intonation is not ET. Why would it be? I'd love to have the luxury of setting a new tonal center on the fly and deal with the intervals the way they sound best, but this is an impossibility with the piano. So yes, these nuances - the power of intonation - gives a sound that reminds me of a good UT… a temperament where interval sizes (most prominently = the major 3rds) vary from one key to another.


Originally Posted By: alfredo capurso

P:..."Better in tune" - would that be ET? I doubt so. All the intervals in ET are compromised, so let's hope that ET is not the single, ultimate "in tune" sound."...

As a musician, I should hope that you retain the meaning of "a chord that could sound better in tune".

Yes this I do, and it happens almost every time i strike chords in an ET tuning smile

Originally Posted By: alfredo capurso

Thanks, I shall reword my question: How is it possible to refer to "colour" as to the feeling we get from a sequence of chords that could sound better in tune?

Same problem here. You ask me somehing giving facts that I disagree with - how could I answer anything such? Ask a decent question that, at least slightly, leaves the door open for your ideals not being universial, then we could talk about that.

Originally Posted By: alfredo capurso

And the other question: Can a musician ever be vexed when he/she finds that all key-signatures sound absolutelly beautyfull? When all key-signatures, like in my experience, can readly and generously give back all their harmonic potential?


But of course! I know quite a few musicians that wouldn't touch ET with a ten foot pole, when it comes to interpret music written for "colored keys" (like, for example, the WTC)


Regards, a.c.
[/quote]
Posted by: Bernhard Stopper

Re: HISTORICAL ET AND MODERN ETs - 07/07/10 05:23 AM

Originally Posted By: pppat
music written for "colored keys" (like, for example, the WTC)



"WTC WAS WRITTEN FOR ET"

As i know that you know there exist also this other opinion, i don´t tell you what i call you here grin

ET was a revolution at Bach´s time and Bach composed WTC to praise this revolutionary achievement by demonstrating how all keys work WELL with this temperament. (Not to speak of the fact that there was no EBVT in sight for him!)

Bernhard Stopper
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/07/10 08:15 AM

Originally Posted By: Bernhard Stopper
Originally Posted By: pppat
music written for "colored keys" (like, for example, the WTC)



"WTC WAS WRITTEN FOR ET"

As i know that you know there exist also this other opinion, i don´t tell you what i call you here grin


You are free to call me what you want, Bernhard, as long as you have the backup for it wink

Neidhart's thesis that WTC was written for ET doesn't really have that much backup anymore, so it might be wise to drop it. However theoretical one might get, there is always the music itself. Bach composes his WTC in a tension/release fashion between the keys, and I'm sad that you miss that.


Originally Posted By: Bernhard Stopper

ET was a revolution at Bach´s time and Bach composed WTC to praise this revolutionary achievement by demonstrating how all keys work WELL with this temperament. (Not to speak of the fact that there was no EBVT in sight for him!)


ET was known long before Bach, and rejected as unmusical. Probably because the listener's ears weren't accustomed to the strange sound (all intervals compromised, and duplicated 12 times) we have gotten used to.

I once more refer to the C major prelude and the C# major prelude. In ET, the character of the two preludes transposed to the vice versa key is the same. In a WT/UT, there is a real strength to the compositions that separates them, not only in key or tempo, but in tension.

You say your StopperStimmung is derived from aural tuning practice into theory. That I like! Now, how come (regarding Bach's tuning) you want to force a theory on music that clearly speaks in a language distant to that theory? This makes no sense to me.
Posted by: Bernhard Stopper

Re: HISTORICAL ET AND MODERN ETs - 07/07/10 10:45 AM

Originally Posted By: pppat

Neidhart's thesis that WTC was written for ET doesn't really have that much backup anymore, so it might be wise to drop it.


Sorry i don´t follow you with this. Drop it. I don´t, as i see no evidence for me to do so. I try to explain again why.

Originally Posted By: pppat

However theoretical one might get, there is always the music itself. Bach composes his WTC in a tension/release fashion between the keys, and I'm sad that you miss that.


I simply prefer a clear and beautiful sounding tuning in every key. A slightly stretched tuning the way i am doing does provide that. Remember Glenn Gould recorded WTC in ET (an intuitively stretched ET, done by an extraordinary good tuner.)
And i don´t miss any tension/release fashion at all in Glenn Gould`s recordings.

Originally Posted By: pppat

ET was known long before Bach,


Yes, by chinese musicians, but it was not widely known in europe unless Werckmeister introduced it to a broader public here.

Originally Posted By: pppat

and rejected as unmusical.


No, it was highly appreciated when it came up. Again: Bach wrote his WTC to praise the revolutional achievement of it. Bach called his work "Well-tempered clavier" because it was sounding well and musical in all keys.

Originally Posted By: pppat

....strange sound (all intervals compromised, and duplicated 12 times)....


Remember what i was saying about the musicality of solo intonation, they were measured to be closer to pythagorean intervals than to be pure intervals. Solo intonation is what we hear with the inner ear. If we replace every octave part in pythagorean intervals by an acoustical satisfying octave, we are spot on the ET form i am using, this isn´t compromising at all, it is transforming pythagorean intervals by acoustic satisfying octaves. You are welcome to recognize the relevance concerning melodic musicality of this principle here.

Originally Posted By: pppat

I once more refer to the C major prelude and the C# major prelude. In ET, the character of the two preludes transposed to the vice versa key is the same.
In a WT/UT, there is a real strength to the compositions that separates them, not only in key or tempo, but in tension.


The characters are different and remain different, even with a beautiful sounding and well done (stretched accordingly, systematically or by intuition) ET. Unlike in UT, BOTH preludes sound beautiful and musical in ET. I always will prefer melodical musicality and beauty by purity in all keys which is both possible with a musical ET form over stretch/tension from UT, which is probably the only goal to win with UT.

Originally Posted By: pppat

You say your StopperStimmung is derived from aural tuning practice into theory. That I like! Now, how come (regarding Bach's tuning) you want to force a theory on music that clearly speaks in a language distant to that theory? This makes no sense to me.


I see no contradiction at all. ET´s of that time were probably performed with an intuitive amount of stretch to satisfy musicality. I assume that this was done very close to what i am doing and what Bach (and every other musical individual including you) preferred/is preferring with his inner ear on melodical (musical) perception.

Remember how many times in the EBVT III thread here and the AB comparison test in the pianist forum thread, where people who were open minded expected that the better sounding record must be EBVT, and later it turned out that their preference was for ET instead. You are ignoring your own caused facts here, if you keep on claiming that ET is unmusical, i suppose just because you want to be ET to be unmusical.

I apologize if i may not respond, my time is actually very limited.

Bernhard Stopper



Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 07/07/10 12:34 PM

Originally Posted By: Bernhard Stopper

I see no contradiction at all. ET´s of that time were probably performed with an intuitive amount of stretch to satisfy musicality. I assume that this was done very close to what i am doing and what Bach (and every other musical individual including you) preferred/is preferring with his inner ear on melodical (musical) perception.

ET was not used in Bach's time. Harpsichords and baroque organs do not tolerate it. Very low inharmonicity of the hpschd translates in almost no room to stretch the octave.

Your knowledge of Bach seems to be based on 19th century biographies reflecting more the authors preconceptions than reality. Of course he didn't use ET. No self-respecting early music performer uses ET anymore these days.

On the piano, for which Bach did not write since it did not exist, you can of course do as you please. I prefer UT but ET sounds fine too. As the purpose of playing Bach on the piano is to make it sound good it may be more important to let the piano sound good than to be historical. Of course "good" is a matter of taste.

Kees
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/07/10 02:03 PM

Originally Posted By: Bernhard Stopper
Originally Posted By: pppat

Neidhart's thesis that WTC was written for ET doesn't really have that much backup anymore, so it might be wise to drop it.


Sorry i don´t follow you with this. Drop it. I don´t, as i see no evidence for me to do so.[...]


Originally Posted By: DoelKees

ET was not used in Bach's time. Harpsichords and baroque organs do not tolerate it. Very low inharmonicity of the hpschd translates in almost no room to stretch the octave.

Your [@Berhnard] knowledge of Bach seems to be based on 19th century biographies reflecting more the authors preconceptions than reality. Of course he didn't use ET. No self-respecting early music performer uses ET anymore these days.


Bernhard, this is exactly why I thought it would be a good thing to drop this theory. I do not know of one single acclaimed music scholar/researcher/theorist today that would claim that Bach used ET. This unfortunate theory somehow gained ground during the advocating of ET, but it is gone by now. Really.

Originally Posted By: Bernhard Stopper

Originally Posted By: pppat

I once more refer to the C major prelude and the C# major prelude. In ET, the character of the two preludes transposed to the vice versa key is the same.
In a WT/UT, there is a real strength to the compositions that separates them, not only in key or tempo, but in tension.


The characters are different and remain different, even with a beautiful sounding and well done (stretched accordingly, systematically or by intuition) ET. Unlike in UT, BOTH preludes sound beautiful and musical in ET. I always will prefer melodical musicality and beauty by purity in all keys which is both possible with a musical ET form over stretch/tension from UT, which is probably the only goal to win with UT.


No, no… The music remains different, but the advantage of the key colors are gone. I really can't find a way to be more clear about this than I have in my earlier postings, and if you can't see/hear/feel this major (sic!) difference, I am truly sorry.

Originally Posted By: Bernhard Stopper

Remember how many times in the EBVT III thread here and the AB comparison test in the pianist forum thread, where people who were open minded expected that the better sounding record must be EBVT, and later it turned out that their preference was for ET instead. You are ignoring your own caused facts here, if you keep on claiming that ET is unmusical, i suppose just because you want to be ET to be unmusical.

My memory might fail me, but I don't think that I've said that I find ET unmusical? What I'm talking about here is the musical strength of color in the keys.
And to be very clear, I do NOT make any claims that EBVT automatically produce a better sounding recording. I find the AB tests fascinating in that sense, because they give feedback without predjudice smile

I see all of this as a great research, where you, me and others are most needed.

What have been been completely demolished through the AB tests, though, are the claims that remote keys in EBVT are offensive to the ear. If so, there should have been no hesitation on deciding which Clair de Lune (Db flat) was ET and which was EBVT.

So, honestly all - you can't have it both ways. Some argue that EBVT is simultaneously a) offensive in remote keys, b) a quasi-ET that is too close to a truly super-duper perfect ET (which we all of course tune wink ) to be of any worth. Make up your mind, or keep silent, guys!

(disclaimer: this was not in any way directed towards you personally, Bernhard, I just tried to economize my posts a bit grin )

Originally Posted By: Bernhard Stopper

I apologize if i may not respond, my time is actually very limited.


Thank you for the concern, but there is no need to apologize - we are in no hurry!
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/07/10 05:02 PM


Patrick, you write:

...“No, I haven't heard Bach on CHAS (except for Isaac's Bach/Siloti, which I think sounded really good). But as far as the Well-tempered Clavier, It is really evident that close keys in a WT/UT results in music that are different from the remote keys. You don't really have to listen to any other thing than the springiness of the prelude in C# major and compare it to the calm C major prelude to see what I mean. These characteristics of the keys get lost in ET, no matter which version of ET.”...

You say...WT/UT results in music that are different from the remote keys? I would not say “music” but ambient atmospheres, and in modern ET's atmospheres (and emotions) do change within the highest degree of euphonicity. Then, leaving Bach's intentions aside, we could learn from Beethoven and understand, once for all, that the same key-signature can open to any “calmness” and any “springiness”. Is this what you mean when you say “colour”? Really, I do not get your point.

http://www.youtube.com/watch?v=yR5AVUiNI-0&feature=related

http://www.youtube.com/watch?v=9nBSGi86r-c&feature=related

...“A fixed modern ET might be the most euphonious solution to you and others, but not to many non-piano musicians. At least in my experience of working with strings, choirs, wind/brass etc. by themselves, the intonation is not ET. Why would it be?”...

Any theoretical ET, once put into practice, will soon result in a modern quasi-ET (due to ordinary decay). And let's put our discussion into context, you are looking for conceptual contents for featuring UT's but, do you really think that “...others...strings, choirs, wind/brass etc.” have EBVT in their mind? Out of an ideological effort, you seem to refuse modern ET's validity in terms of tuning reference. Anyone would still be able to play with ETD few cents deviations, they would simply be what they are, singular deviations from modern ET. 

You ask why should others go for modern ET intonation. That is simply because modern ET sounds absolutely euphonious in all keys. If you ask how can it be so, for what I can explain, it is because our physiology is in line with nature's logarithmic geometry and proportions. And I still do not see how we could agree on a "subjective" template, more than on a "natural" template. 

...“I'd love to have the luxury of setting a new tonal center on the fly and deal with the intervals the way they sound best, but this is an impossibility with the piano. So yes, these nuances - the power of intonation - gives a sound that reminds me of a good UT… a temperament where interval sizes (most prominently = the major 3rds) vary from one key to another.”...

Intervals sizes could, should and would variate on the bases of your taste, like intervals sizes could, should and would variate for anyone, on the bases of their "in tune" taste. Can you imagine? That would not even be brown, as Stopper mentioned, it would be black like hell. 

Originally Posted By: alfredo capurso
As a musician, I should hope that you retain the meaning of "a chord that could sound better in tune".

You reply: “Yes this I do, and it happens almost every time i strike chords in an ET tuning.”...

I was not really looking for this kind of answer, since you (admittedly) can not talk about Chas. I was trying to understand: what is the pleasure in going from a dullish to a wolfish key? On this, can you sing? If you can sing, would you say you are “in tune”?

Originally Posted By: alfredo capurso
Thanks, I shall reword my question: How is it possible to refer to "colour" as to the feeling we get from a sequence of chords that could sound better in tune?

You reply: “Same problem here. You ask me somehing giving facts that I disagree with - how could I answer anything such? Ask a decent question that, at least slightly, leaves the door open for your ideals not being universial, then we could talk about that.”...

Actually, I'm saying that some chords may sound well tuned, others may not, and you seem to agree. Anyway, the issue is “color”. My points are: 1. it will not be alternating dullish and wolfish chords the way we can add “color”, nor enhance cadences, unless we admit cacophony. 2. Anyone may prefer its own (color) template, but that would be like hell (referred to ensamble / orchestra). 3. You seem to talk about "color", meaning either your own “in tune” preference or your own “practical tuning” preference. 4. My ideal (Chas) is not universal in that it is just mine, but in that it can be explained as “proportions (read harmony) in nature”. 

Originally Posted By: alfredo capurso
And the other question: Can a musician ever be vexed when he/she finds that all key-signatures sound absolutelly beautyfull? When all key-signatures, like in my experience, can readly and generously give back all their harmonic potential?

...“But of course! I know quite a few musicians that wouldn't touch ET with a ten foot pole, when it comes to interpret music written for "colored keys" (like, for example, the WTC).”...

Your conclusions about WTC and colored keys have the value of an arbitrary inference and I would really drop this kind of proof. Anyway, you may tell those musicians that now they could enjoy modern ET, not the age-old compromise but a tangible ideal. And I say this out of my pro experiences and only after having made sure that Chas model is shareable, both in scientific and practical terms.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/08/10 11:03 AM


Originally Posted By: Bernhard Stopper
"I see no contradiction at all. ET´s of that time were probably performed with an intuitive amount of stretch to satisfy musicality. I assume that this was done very close to what i am doing and what Bach (and every other musical individual including you) preferred/is preferring with his inner ear on melodical (musical) perception."

Kees, you reply:..."ET was not used in Bach's time."...

J.S.Bach died in 1750. The first, historical ET (12th root of two) had been formalised about 50 years earlyer. If I were you, Kees, I would explain that statement of yours, possibly in another thread. In any case, Stopper said: "ET´s of that time were probably performed with an intuitive amount of stretch to satisfy musicality." Indeed, even in those times, they had to stretch octaves so, what is relevant here, 12th root of two was simply inadeguate. The other two wrong axioms, pure octaves and a 12 semitones module will have been misleading for any temperament.

..."Harpsichords and baroque organs do not tolerate it. Very low inharmonicity of the hpschd translates in almost no room to stretch the octave."...

I haven't tuned baroque organs yet, but I have tuned Chas ET on harpsychords a good number of times (for concerts), never have I had troubles. You say "...almost no room to stretch octaves", yet it is possible.

..."Of course he (Bach) didn't use ET. No self-respecting early music performer uses ET anymore these days."...

Any reliable poster would not confuse his/her own ideas with real facts. For what I can say, many early music (concert) performers enjoy the use of modern ET.

..."As the purpose of playing Bach on the piano is to make it sound good it may be more important to let the piano sound good than to be historical."...

Playing Bach on the piano may be explainable with more than one purpose, but if the purpose was to make Bach and the piano sound good (professionally) there is no doubt, you have to be able to tune.

..."Of course "good" is a matter of taste."...

Nonsense. You can sing on your own, no matter how "out of tune" you are. But if you sing (and/or play) with others, you have to "sound good". If you are not in tune, many musicians could/would tell you.

a.c.
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 07/08/10 11:53 AM

Originally Posted By: alfredo capurso

..."Of course "good" is a matter of taste."...

Nonsense. You can sing on your own, no matter how "out of tune" you are. But if you sing (and/or play) with others, you have to "sound good". If you are not in tune, many musicians could/would tell you.

You forgot to mention Chas.

Kees
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 07/08/10 12:13 PM

Originally Posted By: DoelKees
Originally Posted By: alfredo capurso

..."Of course "good" is a matter of taste."...

Nonsense. You can sing on your own, no matter how "out of tune" you are. But if you sing (and/or play) with others, you have to "sound good". If you are not in tune, many musicians could/would tell you.

You forgot to mention Chas.

Kees


Everyone likes a little ***, but nobody likes a smart ***.
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/09/10 06:23 PM

Originally Posted By: Alfredo Capurso

[Kees]..."Of course he (Bach) didn't use ET. No self-respecting early music performer uses ET anymore these days."...

Any reliable poster would not confuse his/her own ideas with real facts. For what I can say, many early music (concert) performers enjoy the use of modern ET.


Well, Alfredo, maybe where you live. I haven't heard an ET-tuned harpsichord in any high-level early music concert for many, many years.

And, oh, I really think you should stop dissecting paragraphs, (and even sentences!) to make your case. Soon you will be down to single words, and then you can debate almost anything. It won't be in context, though, and that makes your counter-arguments pretty much worthless.

Respect us other posters when you quote, please.
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/09/10 06:35 PM

Originally Posted By: Alfredo Capurso

Originally Posted By: alfredo capurso
And the other question: Can a musician ever be vexed when he/she finds that all key-signatures sound absolutelly beautyfull? When all key-signatures, like in my experience, can readly and generously give back all their harmonic potential?

...“But of course! I know quite a few musicians that wouldn't touch ET with a ten foot pole, when it comes to interpret music written for "colored keys" (like, for example, the WTC).”...

Your conclusions about WTC and colored keys have the value of an arbitrary inference and I would really drop this kind of proof. Anyway, you may tell those musicians that now they could enjoy modern ET, not the age-old compromise but a tangible ideal. And I say this out of my pro experiences and only after having made sure that Chas model is shareable, both in scientific and practical terms.

I do not speak of proof, I just made an observation.

I have a big problem with you referring to ET as 12th root of 2 as the old way, and CHAS as the revelation. I do not know of any decent tuner that has ever tuned a theoretical ET. On the other hand, I know of many who have tuned a temperament octave between 4:2 and 6:3, and expanded this temperament along the principles of equal-beating 12ths and 15ths. This I think would be quite the same as your CHAS, and I think it is implemented every day, all around the world. Without the need for exclusiveness.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/10/10 09:55 AM


Patrick, you write:

...“And, oh, I really think you should stop dissecting paragraphs, (and even sentences!) to make your case. Soon you will be down to single words, and then you can debate almost anything. It won't be in context, though, and that makes your counter-arguments pretty much worthless.
Respect us other posters when you quote, please.”...

Patrick, you could have replied my previous post, you could have explained more in depth what you really mean when you talk about color, enhancement, emotions, ET's etc., but you prefer to post about an issue that I cannot take seriously.

You had written: “I know quite a few musicians that wouldn't touch ET with a ten foot pole, when it comes to interpret music written for "colored keys" (like, for example, the WTC).”.

My reply: “Your conclusions about WTC and colored keys have the value of an arbitrary inference and I would really drop this kind of proof.”

Now you write:... “I do not speak of proof, I just made an observation.”...

Let's see your “observation”. For what I understand, you offer a fact ( “I know quite a few musicians that wouldn't touch ET...”), and you give for granted that some music was written for "colored keys", which is debatable, and you give for sure that WTC was written for "colored keys", which again is debatable.

For what I understand, by mentioning the musicians you know, you intended to prove what you could not prove nor support with arguments, namely 1. some music was written for "colored keys", 2. WTC was written for "colored keys", 3. we need “colored keys” for expressing “calm” or “springiness” or what ever emotion. So Patrick, you may start respecting yourself, yours was not an observation.

You also write:..."I have a big problem with you referring to ET as 12th root of 2 as the old way, and CHAS as the revelation. I do not know of any decent tuner that has ever tuned a theoretical ET. On the other hand, I know of many who have tuned a temperament octave between 4:2 and 6:3, and expanded this temperament along the principles of equal-beating 12ths and 15ths. This I think would be quite the same as your CHAS, and I think it is implemented every day, all around the world. Without the need for exclusiveness."

Your post may prove your ignorance about practical tuning and theory, which might not be bad “in se”, but you could read Chas threads and deduce what is “implemented every day”. In fact, theoretical and practical aspects have long been discussed, so today it is difficult (for me) to justify your ignorance.

What may really represent a revelation, what would be offensive here is your attempt to banalize Chas temperamental theory and tuning issues. This would be bad in that you'd try to impoverish my solid sharing. And it would be worse in that it would show (to me) how your own education is not favoring your intellectual attitude. This tendency of yours, together with your (usual) arrogance and (unusual) impudence, would leave no room for more words.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 07/10/10 01:40 PM

Here is a list of organs and carillons in the Netherlands that are tuned unequally.

Not to argue any specific point, but I thought it's interesting.

Kees
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/11/10 07:58 AM


Hello. Thank you, Kees, for the link above.

About colour, cadence enhancement, moods, emotions, ET's etc.

Géza Anda plays LUDWIG VAN BEETHOVEN (1770–1827): 33 Variations in C major on a Waltz by Anton Diabelli, op.120
33 Variationen C-Dur über einen Walzer von Anton Diabelli
33 Variations en ut majeur sur un thème de valse d’Anton Diabelli.

Thema and Variations 1/10:

http://www.youtube.com/watch?v=C_RMhv10y3o&feature=related

11/19:

http://www.youtube.com/watch?v=VOuWBwMD8uA&feature=related

20/29:

http://www.youtube.com/watch?v=PhB2sIZ-QKA&feature=related

30/33:

http://www.youtube.com/watch?v=-aTFkqHWjlo&feature=related

Joseph Kerman's comment:..."It is above all a work of the most violent jolts and contrasts, starting with Variation 1, an imposing, somewhat menacing march placed right after Diabelli’s speedy waltz. Later moments are sublime, tender, noble, uncanny, boisterous, raucous – clusters of variations of every kind, it seems, of every mood, character, tempo, velocity and texture."...

Who is Joseph Kerman?

http://music.berkeley.edu/people/profile.php?person=27

I found Kerman's comment (and the variations list) here:

http://www.onyxclassics.com/pressroom/ONYX4035.pdf

Out of my own interest for "colored keys" I found some "in favour" literature (Willis G. Miller):

http://www.millersrus.com/dissertation/#

My actual question:

Do you think Beethoven could ever be in need for "colored keys" (for the time being, read "non-equal temperaments")?

Regards, a.c.
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 07/11/10 12:26 PM

a.c. writes:
>>Do you think Beethoven could ever be in need for "colored keys" (for the time being, read "non-equal temperaments")?

Greetings,
Yes, I do. There are several reasons, but the overriding one is that even today, an A-B comparison of Beethoven's keyboard works in ET and WT causes an overwhelming response in favor of the WT.(I have done this numerous times in front of audiences of piano technicians as well as musicians).
If one were to analyze LVB's choices of keys in which to compose his sonatas, it is found that the progression of use follows the same progression of dissonance in the thirds of any of the various forms of WT, i.e., C is the most common, F# the least, with all other keys used in direct proportion to their distance from C, (except for the favoritism LVB shows for Eb, which has its own possible explanation of utility).
Beethoven was adamant that his keyboard works be played in the key he composed them. The necessity to keep the harmonic balances as intended would be a more than plausible explanation for this. It is a simple matter, once one understands the organization of tempering in a WT, to 'parse' Beethoven's works and observe that only in the original key does one find coherent progressions of dissonance leading to resolutions in more consonant triads. If one were to change the key by a half-step, these coherent increases in dissonance disappear.

The following is from the technicians list, where I and another debated Lvb's choice of keys. Enid Katahn, a pianist, gives the musical reasons why a WT is important for Beethoven's sonatas, using op. 90. as an example.


inre the choice of keys in a conventional WT, a previous tech writes:
>There are some pieces where you could argue that a reverse of that system would be better; for example, Beethoven's op. 90. The opening in
Em(relative of G major) which is filled with tension might benefit from a
reverse WT.

To which Enid repsonds;
"Not true. Just because a key is more dissonant than Cmaj. doesn't
neccessarily mean it isn't peaceful. There is a difference between dissonance
as harshness and dissonance as emotionality, or expressiveness". In this
piece, Beethoven was looking for keys with more expression. As he goes
through, there are places where he creates a lot more contrast than he would
have in a more consonant key, such as C major."

Several examples:

bar 9: Beginning in a Gmaj, this passage moves downward, finally passing
through Cmaj before ending on a B triad. So, LVB places the most consonant
chord on the keyboard immediately before one of the most highly tempered. On
a WT , this juxtaposition creates a great harmonic contrast. The
pianist/historian's perspective on this is " This extreme contrast may be
read as LvB's way of letting us know that there is something going on under
the surface and it is not all as peaceful as you might think". (If LVB did
write this piece for his sponsor Baron Lichnowsky and his wife , it could be
making a musical referrence to the stormy marriage that they hid below the
verneer of civility in public. Beethoven is known for this sort of
stuff..Call the musicologists!!.)

However, what if Beethoven had written Op. 90 in C?
"If op. 90 had been composed in the "more consonant" key of C, Bar 9 would
have moved from from G to C, causing a change in how the passage works,
especially the last two chords. In the original key, the final modulation
from C to B creates a particularly strong musical resolution of this passage,
a resolution suggesting something mysterious. Had the sonata been in C, the
move from F to E would not be as dramatic. Instead, the passage would end
with two chords more similar to one another instead of its original very
"expressive" chord played against a background of maximum consonance."

In view of the above, when David writes "to argue that WT has more color
and therefore is more interesting, musical, dynamic,
multi-dimensional,<snip>is a waste of time". , I must disagree for the
following reason, among others:
In WT this modulation changes not only the pitch of the interval, but
also the beating, or "color', whereas in ET, only the pitch changes. Since
more happens when you drop 100 cents while changing from a 7 cent to a 19
cent third than when you simply drop everything 100 cents and the ratios stay
the same, I consider the WT to be more "multi-dimensional" and dynamic than
ET. The WT modulation is certainly more complex, even in the simplest
physical terms.
I would suggest that harmonic contrast, used in the above example, works
to enhance the expressive intentions of this music. (this is in the opening
bars, where we normally expect to find the musical expectations and hints of
things to come to be laid out). The choice of key determines the degrees of
contrast in the passages and I don't think Beethoven left those to anything
arbitrary.


Example 2: second mvt. going into bar 32,
The original choice for this passage in C#minor, a very colorful,
expressive key in WT. Enid writes:
" had Beethoven written op 90 in C, this would place this passage in Am,
which defeats the whole purpose. Am is a pleasant, peaceful sound, all the
way through, but this passage is supposed to be full of emotion". Played in
the key of Am on a Young temperament, the passage sounded lifeless to the
several listeners present.

Example 3: The passage beginning at 115.
Here, Beethoven goes from one extreme of consonance to the other, and does
it in a very refined fashion. Starting in C, he moves through Cm, C#min,
C#, Emaj, E7, then crashing B's resolving to E. In a WT, these modulations
create a steady rise in the amount of tension leading up to the climatic B,
from which, in the final move to E, creates a strong resolution. A
masterful example of using progressively increasing tempering as the passage
develops, arriving at a point of maximum "expression" (B) just before the
final resolution (to E). The emotionality or expression of the piece is
heightened by this coherent, organized increase.
However,if the sonata were in C, this progression would have begun in Ab! Hardly a consonant pleasant beginning, and a place from which it will be difficult to increase tension. That is a very intense key to begin a passage such as this! Where is there to go??
Had Op.90 been composed in the "more consonant" Key of C, the movement
would travel through: Ab, Abm , Am, A, C C7 G then ending on C. So, the passage
would have had the softening of the tempering going against the rise of
musical tension plus that odd return to consonance in the middle A to C move.
Also, the climatic, expressive chord would not be the original's heavily
tempered B, but rather, a usually dulcet G. This would be an odd use of
temperament and wouldn't be supportive of the musical direction the passage
exhibits.
All in all, Mrs. Katahn feels like Beethoven knew exactly what he was
doing. The "color" effects created in a WT consistantly work with the
musical direction of his music. This is to be expected, since,as she points
out, composers didn't just start with the first note and go through to the
end, but rather, they had distinct musical moments that they would go about
linking together, figuring out how to get from here to there,etc. In
anything but ET, the choice of key is a fundamental component of how the
harmony functionswith the musical direction.
Hope that helps
Regards,
Posted by: Gadzar

Re: HISTORICAL ET AND MODERN ETs - 07/13/10 01:34 AM

I'm impressed!

I guess musicians, and specially composers of piano music, are better placed than we piano technicians to talk about temperaments.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/13/10 12:06 PM


Thank you, ED Foote, for your feedback.

I was asking: Do you think Beethoven could ever be in need for "colored keys" (for the time being, read "non-equal temperaments")?

You write:..."Yes, I do. There are several reasons, but the overriding one is that even today, an A-B comparison of Beethoven's keyboard works in ET and WT causes an overwhelming response in favor of the WT.(I have done this numerous times in front of audiences of piano technicians as well as musicians)."...

I'm sure what you report can happen indeed but, in my experience, it may depend on the ET and WT that were/are compared.

We needed to stretch 12th root of two octaves but we had no indications about how octaves should be stretched, nor about how/why 4ths, 5ths, 12ths and 15ths could effect the tuning of modern ET's.

This is why I would not be surprised to hear a stretched (attempt) version of our historical ET that sounds worse than a (stretched) non-ET. Today, though, you could compare any WT with an advanced, modern ET model and perhaps update your preferences. BTW, did you get to know that our historical ET (12th root of two) has evolved into advanced ET models?

By mentioning Beethoven (and links above) I meant to ask:

For what concerns music, may not Beethoven Variations prove that it is up to the composer to manage emotions, moods, tensions Vs release, dark Vs bright atmospheres etc., on the basis of their own creativity, their imagination and intentions, even playing in the same one key? Even if they were deaf?

Today I would also ask: which (stretched) WT would Beethoven have had in its ears? Would Beethoven have based his musical energy and modulations on close to C and remote “colored” keys issue?

I would also ask: What makes up for a “mild WT” today? Just any temperament that, by design, deviates a few cents from ETD's variants of the first ET? Few cents, otherwise it gets too wolfish, few cents, otherwise it would be called ET?

I ask all this because my urge for singing “in tune” and for composing (small c) came much earlier than any temperamental issue. My "in tune" urge was already there when I was five. So I would never rely on a particular temperament for my inspiration, I could not care less. At the opposite, if I had had precise sounds in my ears, different from what a semitonal scale can sound like, I would have created my own temperament. And this is actually happening today with microtonal scales. But perhaps I'm wrong, perhaps Composers would check their piano and semitonal temperament first, and only then would they compose and play.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
.
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 07/13/10 01:42 PM

Greetings,
I wrote:
"even today, an A-B comparison of Beethoven's keyboard works in ET and WT causes an overwhelming response in favor of the WT.(I have done this numerous times in front of audiences of piano technicians as well as musicians)."...

Al responds:
>>I'm sure what you report can happen indeed but, in my experience, it may depend on the ET and WT that were/are compared.

I don't know that it matters too much, any of the plausible tunings of 1800, (Young, Kirnberger/Prinz, Prelleur,) have blown the finest ET's available out of the water! For modern ears, the Coleman 11 is still enough to make the profound difference.

A.C.
"We needed to stretch 12th root of two octaves but we had no indications about how octaves should be stretched, nor about how/why 4ths, 5ths, 12ths and 15ths could effect the tuning of modern ET's."

I have found that the amount of stretch is a moot point when an ET runs into a WT. ET sounds like a constant buzzing after the ear has been introduced to a WT that varies the tempering from say, a 6 cent C-E to a 21 cent F#-A#. I have stretched and compressed octaves on tunings, Stretching for concerto work, compressing in the Nashville recording studios, (for the bass players and producers listening to the congruence between the bass and piano). The high stretch is also favored by jazz players trying to cut through an overly energetic combo. I hate the sound, hearing it as unrelenting tension, and coupled with the lack of variety between the consonance and dissonance of a WT, it gets to be exhausting.

>> Today, though, you could compare any WT with an advanced, modern ET model and perhaps update your preferences.

Been there, done that. ET, regardless of stretch, is still a hyper-active intonation, and lacks the ability to affect our autonomic systems, (sympathetic and parasympathetic). The psycho-emotive effects of consonance/dissonance have been scientifically shown to be real, subliminal, and consistent. Stripping them out of music that was composed to utilize them compromises the emotional impact.

A.C.
I meant to ask:
For what concerns music, may not Beethoven Variations prove that it is up to the composer to manage emotions, moods, tensions Vs release, dark Vs bright atmospheres etc., on the basis of their own creativity, their imagination and intentions, even playing in the same one key? Even if they were deaf?"

I'm not sure they prove anything, but if you plot the key usage in the Variations, you will find a pattern. This same pattern shows up in the micro as well as macro view of music, i.e. Mozart's use of the keys, as well as Schubert and Brahms, display the same pattern. Chopin, interestingly enough, shows the exact same pattern but in reverse!

A.C.
"Today I would also ask: which (stretched) WT would Beethoven have had in its ears? Would Beethoven have based his musical energy and modulations on close to C and remote “colored” keys issue?"

I believe that his modulations were to create the coherent rise and fall of tension in his compositions, and the use of the resources of a WT, regardless of stretch, was a consistent and ever present factor. I would suggest you look at his sonata in F#, (can't remember the number). It is a singular piece in his work, and only makes real sense if you play it on a keyboard with a WT in place. You can't get pure fifths any other way.

A.C.
"I would also ask: What makes up for a “mild WT” today? Just any temperament that, by design, deviates a few cents from ETD's variants of the first ET? Few cents, otherwise it gets too wolfish, few cents, otherwise it would be called ET?

I would consider any tuning that deviates, in the historical pattern, from ET by less than two cents to be mild. However, even three cents can create a C-E that is only tempered 7 cents by raising the C and lowering the E. Also, if you lower the F# and raise the A# by three cents, you are very near the full syntonic comma, so it takes little to create huge differences from ET.

A.C.
"I ask all this because my urge for singing “in tune” and for composing (small c) came much earlier than any temperamental issue. My "in tune" urge was already there when I was five."

Did you naturally sing a 14 cent wide third? If so, you are unique in my experience. I have only heard that amount of stretch in unaccompanied voice when the singer is strongly leading to something else, otherwise, most voices I have heard naturally gravitate towards Just. As one singer told me, "Everything changes as soon as the piano begins to play".
I see nothing natural about out of tune singing, and a tempered third is, technically, "out of tune". (assuming by 'in tune' we mean no dissonance).

A.C.
" perhaps Composers would check their piano and semitonal temperament first, and only then would they compose and play."

I think it more plausible that composers of the time were aware of the resources available in the various keys, and selected them for particular musical purposes. We don't hear funeral dirges in the simple keys, nor lullabies in the remote ones. When the musical tension builds, we find a common reliance on modulation from consonance to dissonance,and we never hear a resolution occurring by moving to a more highly tempered key that what leads up to it. This is not coincidence, since the practice was nearly universal between 1700 and 1850, with echos following even after that.
All in all, if one were to play all the piano literature composed between Bach and Brahms on a well-tempered piano, there would be far less total dissonance than if it were played on one that had all thirds tempered 13.7 cents. What I think is important is that we get away from the idea that consonance is good and dissonance is bad. As Plutarch said centuries ago, "Music, to create harmony, must investigate discord".

Regards,
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/14/10 07:29 AM


Hello Ed,

I'm again leaving for some days, so excuse the "quantity" of my replies. I'm very glad for getting to know your outlook on this subject, actually I went to your site...and I'll be happy to read the whole content.

Me:>>I'm sure what you report can happen indeed but, in my experience, it may depend on the ET and WT that were/are compared.

ED:..."I don't know that it matters too much, any of the plausible tunings of 1800, (Young, Kirnberger/Prinz, Prelleur,) have blown the finest ET's available out of the water! For modern ears, the Coleman 11 is still enough to make the profound difference."...

Sorry for my ignorance, what does "blown the finest ET's available out of the water", I do not know this idiom. Then, which "finest" ET are you referring to? Aural or ETD? One stretched-octaves version of 12th root of two or a modern ET? I think that would matter a lot, actually it may be foundamental.

ED:..."ET sounds like a constant buzzing after the ear has been introduced to a WT that varies the tempering from say, a 6 cent C-E to a 21 cent F#-A#. I have stretched and compressed octaves on tunings, Stretching for concerto work, compressing in the Nashville recording studios, (for the bass players and producers listening to the congruence between the bass and piano). The high stretch is also favored by jazz players trying to cut through an overly energetic combo. I hate the sound, hearing it as unrelenting tension, and coupled with the lack of variety between the consonance and dissonance of a WT, it gets to be exhausting."...

My first guitar would variate 3rds very much, though I cannot say how many cents. That I could not stand, I wanted all chords to sound in tune. In the ET I tune, 3rds like F#4-A#4 are so tense that I would never ask for more tension. You say "I hate the sound, hearing it as unrelenting tension, and coupled with the lack of variety between the consonance and dissonance of a WT, it gets to be exhausting."

Yes, perhaps we go for different settings. What for me gets exhausting in non-equals is this hearing a quite nice interval but, soon after, having to reduce my openness, my acceptance when, playing another interval, the wolf shows out. It is all this ear-adjustment that tires me, that would put me off and distract me every time.

I'll be back. Regards, a.c.
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 07/14/10 10:51 AM

Alfredo writes:
" what does "blown the finest ET's available out of the water", I do not know this idiom.

It means no comparison. At one class, in a room of 20 techs, comparing the Coleman 11 to an ET, 2 preferred ET. In numerous comparisons, even after playing in all the keys of a WT, the overwhelming preference has been for the WT piano. I have compared them to my own ET, as well as several other ET's created by very fine technicians. One time, in Texas, the ET piano was tuned by Tom Seay, and it was as fine a tuning as I have ever heard. The audience still heard the WT as more pleasing. It is not the execution of the ET that causes its shortcomings, but rather, the selection!
All the stretch in the world does not create the variety of the keys.

"Then, which "finest" ET are you referring to? Aural or ETD? One stretched-octaves version of 12th root of two or a modern ET? I think that would matter a lot, actually it may be foundamental."

I don't think so, but perhaps we should give ET a definition we can use for comparison. Let us consider that a piano tuned in ET will have an equal amount of tempering in all like intervals, i.e. all thirds are tempered the same. Which casts an inquisitive light on the following two statements:

"My first guitar would variate 3rds very much, though I cannot say how many cents. That I could not stand, I wanted all chords to sound in tune."

By the above definition, if the thirds vary, it is not ET.


"In the ET I tune, 3rds like F#4-A#4 are so tense that I would never ask for more tension."

By the definition above, why would one third be more tense than another? The F#-A# third is tempered the same as the G-B, otherwise,the tempering is not equal! As was stated earlier, we hear logarithmically, so the tempering of the F#-A# should be heard no more "tensely" that any other. Even though the G-B third will beat faster than the F#-A#, it is not heard as more highly tempered because it is occurring at a higher set of frequencies. The human perception of tempering is not pitch dependent.

If one hears a particular key as being more tense on an ET, I submit that it is conditioning,based on an individual's ability to recognize keys by pitch, which brings the whole musicological/historical precedent into consideration.
Consider that if we always were slapped every time we saw the color red. it would be normal for us to wince at ever stop light. If we always heard the key of F# used for high tension composition,(which is not far from the truth in classical music), the pitch-cognizant listener will automatically ascribe tension to the key, regardless of how it is tuned. Pavlov was right!
Looking over piano literature as a whole, we see very clear trends in how keys were used by composers. The most expressive parts of the sonatas are most often placed in the most remote keys, and rarely are those remote keys used to resolve a composition. Why? Listen to LVB's "Waldstein". The second mvt. was written to replace the original, (which became "Andante Favorite"). It begins in F, goes through a step by step journey into highly dissonant chords, and slowly returns to a place that creates an incredible resolution in C for the final mvt. I suggest that any musical listener,if deprived of hearing the final mvt.after this section, will feel like they have been left hanging. However, when that bass note C hits, there is a strongly visceral relaxation that takes place. The effect of tempering is totally syncronized with the composition. This is not by random choice of key!
I suggest that trying for resolution by going from any given key to a more highly tempered key is so extremely rare because it does not allow the listener to feel the relaxation, on the subliminal level, that the composer is attempting to create.
We are calmed by consonance, and stimulated by dissonance. Thus, the use of UT's allow the ebb and flow of tension is a critically important factor in getting the most impact from the music.

Sonatas are harmonic journeys, they build tension and then resolve it. This creates the emotional response. When the tempering is employed to heighten this effect, (by resolving to less tempered sounds,which is a near constant in classical music), the emotional impact is stronger because our bodies are being manipulated in the same direction that our conscious minds are. This sounds like hocus-pocus, but is easily demonstrated.
If we truly want the most out of the music we love, we have to try all plausible alternatives, and the use of WT's in the 1800's is more than plausible.
Best regards,
Posted by: Inlanding

Re: HISTORICAL ET AND MODERN ETs - 07/14/10 11:07 AM

Very excellent post, Ed.

Thanks

Glen
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/14/10 11:50 AM

Hi all, have been away for a few days, just catching up on the forum now.

Alfredo:

Originally Posted By: Alfredo Capurso
Let's see your “observation”. For what I understand, you offer a fact ( “I know quite a few musicians that wouldn't touch ET...”), and you give for granted that some music was written for "colored keys", which is debatable, and you give for sure that WTC was written for "colored keys", which again is debatable.

For what I understand, by mentioning the musicians you know, you intended to prove what you could not prove nor support with arguments, namely 1. some music was written for "colored keys", 2. WTC was written for "colored keys", 3. we need “colored keys” for expressing “calm” or “springiness” or what ever emotion. So Patrick, you may start respecting yourself, yours was not an observation.


WHAT? You asked:

Originally Posted By: Alfredo Capurso
Can a musician ever be vexed when he/she finds that all key-signatures sound absolutelly beautyfull? When all key-signatures, like in my experience, can readly and generously give back all their harmonic potential?


... and I replied:

Originally Posted By: pppat
But of course! I know quite a few musicians that wouldn't touch ET with a ten foot pole, when it comes to interpret music written for "colored keys" (like, for example, the WTC)


... and you start talking about proof? I don't get it. Still don't.

Originally Posted By: Alfredo Capurso
Your post may prove your ignorance about practical tuning and theory, which might not be bad “in se”, but you could read Chas threads and deduce what is “implemented every day”. In fact, theoretical and practical aspects have long been discussed, so today it is difficult (for me) to justify your ignorance.

What may really represent a revelation, what would be offensive here is your attempt to banalize Chas temperamental theory and tuning issues. This would be bad in that you'd try to impoverish my solid sharing. And it would be worse in that it would show (to me) how your own education is not favoring your intellectual attitude. This tendency of yours, together with your (usual) arrogance and (unusual) impudence, would leave no room for more words.


Well, there are quite a lot of very good tuners and math persons on this forum who can't understand what you're trying to say in your paper, nor in the elaborations in the CHAS threads, so I don't feel left out in the cold here.

You can call me, or others ignorant (which you have done quite some times now), but if you see all the cars on the highway driving in the wrong direction you'd really be wise to start asking yourself if you drive on the wrong side of the road...

If mostly everybody else that discuss with you sooner or later are considered arrogant and ignorant, that should be a sign that something is not quite right - either with your CHAS, your polemic skills, or both.
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/14/10 12:43 PM

Ed,

I really like your extensive postings of Mrs. Katahn's comments. I haven't found a really suitable punch line for what a WT does to harmony yet, but I've been speaking quite a bit of its affect on the harmonic progression of a musical piece. It is good to see these analytical quotes underlining the same phenomenon.

Originally Posted By: Ed Foote

A.C.
>> Today, though, you could compare any WT with an advanced, modern ET model and perhaps update your preferences.

Been there, done that. ET, regardless of stretch, is still a hyper-active intonation, and lacks the ability to affect our autonomic systems, (sympathetic and parasympathetic). The psycho-emotive effects of consonance/dissonance have been scientifically shown to be real, subliminal, and consistent. Stripping them out of music that was composed to utilize them compromises the emotional impact.


I like that description, hyper-active intonation smile ET as a temperament doesn't really stimulate the listener or the musician in more than one single way, a little bit like driving a car in 2nd gear all the time.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/15/10 08:12 PM


Hello.

ED, those days are really busy for me but I shall reply properly on what you have said, thank you. Amongst your own arguments there is one that sounds nicely and unusually "dissonant", it is this one:..."What I think is important is that we get away from the idea that consonance is good and dissonance is bad. As Plutarch said centuries ago, "Music, to create harmony, must investigate discord"...

This is where we may agree on, as you mentioned (by chance?) one of Chas theory's pillars. This is why you do not find any "pure" interval in Chas ET model. That is how you could stop this maso-romantic game, this going through alternate pain and pleasure, wolfish and justish chords, remote and close keys-signature. Today we can explain (and go for) a consistent and solid "in tune" choir. Which non-equal/WT can you detect?

Mozart - The Magic Flute - end of opera (duet and chorus)
http://www.youtube.com/watch?v=bFdB8Zz8VOo

The Swingle Singers - Badinerie (Johann Sebastian Bach)
http://www.youtube.com/watch?v=jHcNHL8AyfU&feature=related

Bach aria 4° corda Swingle Singers
http://www.youtube.com/watch?v=4xQdboqVOzA&NR=1

Patrick, you write:

..."Well, there are quite a lot of very good tuners and math persons on this forum who can't understand what you're trying to say in your paper, nor in the elaborations in the CHAS threads, so I don't feel left out in the cold here."...

Despite what you can read in Chas threads, I'll never leave you out in the cold.

..."You can call me, or others ignorant (which you have done quite some times now), but if you see all the cars on the highway driving in the wrong direction you'd really be wise to start asking yourself if you drive on the wrong side of the road..."...

This is what I wrote: "Your post may prove your ignorance about practical tuning and theory, which might not be bad “in se”, but you could read Chas threads and deduce what is “implemented every day”. In fact, theoretical and practical aspects have long been discussed, so today it is difficult (for me) to justify your ignorance.

What may really represent a revelation, what would be offensive here is your attempt to banalize Chas temperamental theory and tuning issues. This would be bad in that you'd try to impoverish my solid sharing. And it would be worse in that it would show (to me) how your own education is not favoring your intellectual attitude."

That means that I'd find difficult to justify your ignorance, and that I'm puzzled about the effects of your education on your intellectual attitudes, since I wonder whether you intented to be offensive or what.

..."If mostly everybody else that discuss with you sooner or later are considered arrogant and ignorant, that should be a sign that something is not quite right - either with your CHAS, your polemic skills, or both."...

Patrick, I think it is the first time ever that I admit ignorance, wanting to go for the "easyest" option. This could prove you how polemics do not interest me. Yet I'd like you to check yourself (you'd want to be reliable) and list (for me too) all these "mostly everybody else...".

Thanks and regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/15/10 08:47 PM

Originally Posted By: Alfredo Capurso

[@Ed Foote] Today we can explain (and go for) a consistent and solid "in tune" choir. Which non-equal/WT can you detect?

Mozart - The Magic Flute - end of opera (duet and chorus)
http://www.youtube.com/watch?v=bFdB8Zz8VOo

The Swingle Singers - Badinerie (Johann Sebastian Bach)
http://www.youtube.com/watch?v=jHcNHL8AyfU&feature=related



Non of these are ET, nor ar they any fixed intonation at all. It's just good (and occasionally not so good) intonation executed on non-fixed instruments.

Originally Posted By: Alfredo Capurso
Yet I'd like you to check yourself (you'd want to be reliable) and list (for me too) all these "mostly everybody else...".


Sure, I can do that - although I don't think it would be too hard for you to realize that yourself. You'd just have to think about who have discussed things with you during the time you've been on this forum, and then think about who is still doing so.

If I list them, I'd like to do that in a PM, for one reason only: I do not want to drag them back into a discussion they have chosen not to participate in. Your call.
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 07/16/10 01:08 AM

Alfredo writes:
"That is how you could stop this maso-romantic game, this going through alternate pain and pleasure, wolfish and justish chords, remote and close keys-signature. Today we can explain (and go for) a consistent and solid "in tune" choir. "

Ayyyeee! I haven't been clear enough. Music is an emotional event for me. I like the pain and pleasure in the wolfish and just chords. I don't want to listen with my head, I want to have my breathing changed, and the variety of tempering will do that more strongly than its lack. We know that our bodies react to dissonance, and Beethoven seems to have known it, too.
I want my castles made of natural, inconsistent, field stone, not symmetrical brick. I want to feel the irregularities of wood instead of the perfectly consistent plastic surface. I crave food that is sweet and sour, I like music to be soft and loud, fast and slow, harmony, pure and ragged. I like thirds that are near pure, and I like them even more after glancing off the comma. It is exciting to me to hear a composer gradually taking the ear into very expressive territory without ever making such a big leap that it breaks the spell, and then reminding us how good harmony sounds when it resolves in more pure intervals. I like that stuff, and the composers seem to know how to use it.
So, I don't see the palette formed by a well temperament to be a liability, but rather, an asset. There are places for an edgy dissonant third and curiously, composers rarely put them in the wrong place.
The rise and fall of dissonance from tempering in Classical piano music seems, to me, to be intentionally used by the composers. We can argue the degree of historical plausibility all day long, but that lacks the realness of listening. Since the difference is a sensual one, not an intellectual one, assuming a historical imperative based on research instead of what the music sounds like is, imho, folly.
I try to focus not only on what the music sounds like,( occupational hazard for a professional tuner), but rather, what it feels like. These are not the same thing. (more later, I guess).
Regards,
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/16/10 06:44 AM


Originally Posted By: Alfredo Capurso
[@Ed Foote] Today we can explain (and go for) a consistent and solid "in tune" choir. Which non-equal/WT can you detect?

Mozart - The Magic Flute - end of opera (duet and chorus)
http://www.youtube.com/watch?v=bFdB8Zz8VOo

The Swingle Singers - Badinerie (Johann Sebastian Bach)
http://www.youtube.com/watch?v=jHcNHL8AyfU&feature=related

Patrick, you say: "Non of these are ET, nor ar they any fixed intonation at all. It's just good (and occasionally not so good) intonation executed on non-fixed instruments."...

I ask then: what makes intonation good? What makes intonation "not so good"? Although those are voices, they can not sing "just" intervals (just like we cannot tune just intervals on a piano). So I ask: how do they temper themselves? I used to sing with my sister, we both knew who and when was "occasionally not so good". I'm sure singers themselves could say when they themselves sound not so good. Do they refer to a compromise or to an ideal? Which non-equal or WT could they refer to, all together and in real time? How do they stretch intervals and manage to make me feel (quite) good?

Children's choir Kolibri - Mass in G major, BWV 236 - 4: Domine Deus, Johann Sebastian Bach
http://www.youtube.com/watch?v=bokZHuCWNP4

AI Josh Groban children choir frm Africa - You Raise Me Up
http://www.youtube.com/watch?v=0OOhd6R2EiY

Originally Posted By: Alfredo Capurso
Yet I'd like you to check yourself (you'd want to be reliable) and list (for me too) all these "mostly everybody else...".

..."Sure, I can do that - although I don't think it would be too hard for you to realize that yourself. You'd just have to think about who have discussed things with you during the time you've been on this forum, and then think about who is still doing so."...

Let me know what you realize. For what I can say and expect, in Chas threads posters come and go freely, anytime.

..."If I list them, I'd like to do that in a PM, for one reason only: I do not want to drag them back into a discussion they have chosen not to participate in."...

Cam'on Patrick, be reliable and tell me/us who you have in mind. After all it was you involving others in public. And you were not playing a ghost game, were you? wink

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 07/16/10 08:48 AM

Originally Posted By: Alfredo Capurso
Patrick, you say: "Non of these are ET, nor ar they any fixed intonation at all. It's just good (and occasionally not so good) intonation executed on non-fixed instruments."...

I ask then: what makes intonation good? What makes intonation "not so good"? Although those are voices, they can not sing "just" intervals (just like we cannot tune just intervals on a piano). So I ask: how do they temper themselves? I used to sing with my sister, we both knew who and when was "occasionally not so good". I'm sure singers themselves could say when they themselves sound not so good. Do they refer to a compromise or to an ideal? Which non-equal or WT could they refer to, all together and in real time? How do they stretch intervals and manage to make me feel (quite) good?


If we are talking about a cappella singing, the singers are of course intonating by ear only, not out of any given theoretical model. In my view, intonation on the fly is superior to what we are dedicated to: the tempering of an instrument with fixed pitch. Then again, it's much harder to execute nicely.

Then, if a piano is tuned in ET, singers intonate to ET. If a piano is tuned in a WT, singers intonate into that WT. This happens on the fly, by ear, and is much easier than we often think in this forum. It can be a bit trickier with strings, because a physical, kinetic aspect comes into play - the feel of the fingerboard. Good players usually adjust fast, though.

If there is any doubt about the power of on the fly intonation by ear, you can make the following test (which I've used a lot of times, in both choir and theory classes). What you need is a group of singers, large enough for them to be able to use staggered breath efficiently, produce a continous long tone without breaks.

Play a C major chord, and let them sing C4 and hold that note. Then play different chords that includes C4 (F major, Gb7#11, Ab maj7, Cadd9/E, Eb6, Dm7b5, Db maj7, aso)
, and make that C4 the top note of the chord, including it on the piano too. The choir will sing your ET C4.

Now, do the exact same test, but this time leave out the top note (C4) on the piano. What you will hear is a C4 that constantly varies in pitch, seemingly effortlessly! By ear, the singers raise and lower the pitch to the place where it just "sounds right".

Let me recapitulate: even if the piano is tuned in ET, if the singers are free to intonate to it, not restricted by the same tone played on the piano, they will make more natural choices. This is where we are hopelessly stuck with our fixed pitch on the piano. I've said it before, and here it is again: To me, a WT/UT is a way of bringing some of that liveness into the piano. It is not as effective as free intonation on the fly, but it is - again, to me - much more natural than ET.

But, just as Ed says, unequal tunings have been used to the composers advantage in writing music for the piano. Hence, this shortcoming of fixed intonation has actually been utilized in favor of the composer, for bringing different emotions into the harmonic progressions. No theories claiming otherwise, however vigurously researched, will stand a chance to the proof of the music itself.

Originally Posted By: Alfredo Capurso

..."Sure, I can do that - although I don't think it would be too hard for you to realize that yourself. You'd just have to think about who have discussed things with you during the time you've been on this forum, and then think about who is still doing so."...

Let me know what you realize. For what I can say and expect, in Chas threads posters come and go freely, anytime.

..."If I list them, I'd like to do that in a PM, for one reason only: I do not want to drag them back into a discussion they have chosen not to participate in."...

Cam'on Patrick, be reliable and tell me/us who you have in mind. After all it was you involving others in public. And you were not playing a ghost game, were you?


No, I stand by this decision, out of respect to others. If that means that you find me less reliable, then so be it. Still, I can PM you if you don't figure it out yourself.
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 07/16/10 09:18 AM

12 tone keyboard instruments are the only instruments which require temperament. All other instruments and voices adjust intonation as the music progresses.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/16/10 11:08 AM


Hello Bill,

you say: "12 tone keyboard instruments are the only instruments which require temperament. All other instruments and voices adjust intonation as the music progresses."

Is that what you hear?

Leonid Kogan Paganini with guitarre
http://www.youtube.com/watch?v=kpXlCheiXY8&feature=related

Kogan Paganini
http://www.youtube.com/watch?v=Ovnky2hwgWM

Regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/17/10 08:39 PM


..."12 tone keyboard instruments are the only instruments which require temperament. All other instruments and voices adjust intonation as the music progresses."

Hello. I'd say "...All other instruments and voices adjust intonation as their music-understanding progresses".

For a violinist, in my idea for any musician (on a instrument or voice), intonation may be a gift that he/she would (re)gain in the shortest lapse of time, even with a good teacher, if the teacher could share that talent.

In my idea, any instrumental-voice will be tempered, because "just-related" frequencies all together would not sound good. And it will not be adjustable because every musician ends up singing that gift. This is why, hopefully, they can be and they are musicians.

1.UTO UGHI LE QUATTRO STAGIONI DI VIVALDI S. SABINA DI ROMA
http://www.youtube.com/watch?v=uhhLXQok82A

7 years old violinist No.2 (mendelssohn violin concerto)
http://www.youtube.com/watch?v=GrMwMQt7MXM&feature=related


What do you think? Regards, a.c.



Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 07/18/10 09:51 AM

Originally Posted By: alfredo capurso

Hello Bill,

you say: "12 tone keyboard instruments are the only instruments which require temperament. All other instruments and voices adjust intonation as the music progresses."

Is that what you hear?

Leonid Kogan Paganini with guitarre
http://www.youtube.com/watch?v=kpXlCheiXY8&feature=related

Kogan Paganini
http://www.youtube.com/watch?v=Ovnky2hwgWM

Regards, a.c.
.


The violonist adjust his "stretch" to the guitare which have none. As usual thats the non fixed tone instrument that adapt his justness to the one of the fixed tone.

I find the result sounding flat and not very harmonious, may be the guitare would have benefit of enlarging the tuning ...

Best wishes !
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 07/18/10 09:58 AM

Originally Posted By: alfredo capurso


Hello. I'd say "...All other instruments and voices adjust intonation as their music-understanding progresses".

For a violinist, in my idea for any musician (on a instrument or voice), intonation may be a gift that he/she would (re)gain in the shortest lapse of time, even with a good teacher, if the teacher could share that talent.

In my idea, any instrumental-voice will be tempered, because "just-related" frequencies all together would not sound good. And it will not be adjustable because every musician ends up singing that gift. This is why, hopefully, they can be and they are musicians.

1.UTO UGHI LE QUATTRO STAGIONI DI VIVALDI S. SABINA DI ROMA
http://www.youtube.com/watch?v=uhhLXQok82A




What do you think? Regards, a.c.





a little before 4:00 they lower their intonation (first violin and solist) while when they play tutti, the treble raise and raise, naturally. (as often ) I get no clue about pythagorean justness by listening there, only that they seem to temper more at some moment.

may be simply it is hot and all strings go flat, hence the pitch lower ...


Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 07/18/10 10:42 AM

I dont find the Swingle singers are singing particularely just

while they are enjoyeable of course, they have a somehow "loose" intonation, purposely or not.

It is anyway as difficult to sing just than to play just at the violin !
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 07/18/10 10:48 AM

Originally Posted By: alfredo capurso



Children's choir Kolibri - Mass in G major, BWV 236 - 4: Domine Deus, Johann Sebastian Bach
http://www.youtube.com/watch?v=bokZHuCWNP4
f


The piano is " dans les choux !" (in the backyard, with the tomatoes and potatoes ! ) the violinist is able to adapt while playing a little lower when in the treble, but the choir is higher, naturally.

The piano would have benefit of a more open tuning (some came to mind !)

Best regards
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 07/18/10 10:56 AM


AI Josh Groban children choir frm Africa - You Raise Me Up
http://www.youtube.com/watch?v=0OOhd6R2EiY

You call that a singer ? sheep sing better ! beeehhh !
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/18/10 08:40 PM


Isaac, what a pleasure. I was half way with this post...

Alfredo writes:
"That is how you could stop this maso-romantic game, this going through alternate pain and pleasure, wolfish and justish chords, remote and close keys-signature. Today we can explain (and go for) a consistent and solid "in tune" choir. "

ED:..."Ayyyeee! I haven't been clear enough. Music is an emotional event for me. I like the pain and pleasure in the wolfish and just chords. I don't want to listen with my head, I want to have my breathing changed, and the variety of tempering will do that more strongly than its lack. We know that our bodies react to dissonance, and Beethoven seems to have known it, too.
I want my castles made of natural, inconsistent, field stone, not symmetrical brick. I want to feel the irregularities of wood instead of the perfectly consistent plastic surface. I crave food that is sweet and sour, I like music to be soft and loud, fast and slow, harmony, pure and ragged. I like thirds that are near pure, and I like them even more after glancing off the comma. It is exciting to me to hear a composer gradually taking the ear into very expressive territory without ever making such a big leap that it breaks the spell, and then reminding us how good harmony sounds when it resolves in more pure intervals. I like that stuff, and the composers seem to know how to use it.
So, I don't see the palette formed by a well temperament to be a liability, but rather, an asset. There are places for an edgy dissonant third and curiously, composers rarely put them in the wrong place.
The rise and fall of dissonance from tempering in Classical piano music seems, to me, to be intentionally used by the composers. We can argue the degree of historical plausibility all day long, but that lacks the realness of listening. Since the difference is a sensual one, not an intellectual one, assuming a historical imperative based on research instead of what the music sounds like is, imho, folly. I try to focus not only on what the music sounds like,( occupational hazard for a professional tuner), but rather, what it feels like. These are not the same thing."...


Me too, I'd say "Music is an emotional event for me". Since my head is not involved, I cannot think in terms of (due) pain and pleasure. My emotions flow and do not call for a rational explaination, unless my ear is disturbed. My ear has to do with my brain but not with my rational. My emotions can flow untill my ear recognizes a friendly, warm, euphonious environment.

When my ear detects a wolfish sound, I feel like my castle is not safe anymore, like if those beautyful, ever different field stones (read partials) that could decorate my castle in an orderly way, are now deforming into a mess. It is not a question of symmetry nor dissonance. Actually a "dissonance" is nice as long as it makes sense. It is an "out of tune" dissonance that I find unpleasent, just like an "out of tune" consonance.

You write:..."We know that our bodies react to dissonance, and Beethoven seems to have known it, too."..

I'd mention Beethoven's own words (or music) only (please). Our body reacts to dissonance, my body reacts even more to unjustifiable, over-dissonances. Yes, sweet and sour can be nice, not for the sake of it though, i.e. not as a theoretical/conceptual reason. Take any usual tuning, depending on the chords sequence, we can play "sweet and sour" and still sound quite in tune. Isn't this banal?

You write:..."I want to feel the irregularities of wood instead of the perfectly consistent plastic surface"...

Have you read about one actual non-equal Vs ET compareson? Even "educated", lined up listeners could confuse the two. Which "plastic" are you talking about? Is yours a bizarre (or exploitable) issue?

You write:..."It is exciting to me to hear a composer gradually taking the ear into very expressive territory without ever making such a big leap that it breaks the spell, and then reminding us how good harmony sounds when it resolves in more pure intervals. I like that stuff, and the composers seem to know how to use it."...

For what I can say, the scale and chords geometry itself can variate from "tense" intervals to "calm" ones, and the temperaments (historical) main issue was the wolf, i.e. where could we relegate the wolf, how could we circumscribe the (today-solved) problem.

You write:..."So, I don't see the palette formed by a well temperament to be a liability, but rather, an asset. There are places for an edgy dissonant third and curiously, composers rarely put them in the wrong place."...

I'd say: Composers may rarely (?) refer to them. Do you really think composers wait for you/us to give them a temperament?

..."The rise and fall of dissonance from tempering in Classical piano music seems, to me, to be intentionally used by the composers."...

Yes, dissonance and consonance, on the bases of the harmonic structure, not on dayly "out of tune" gimmicks.

..."Since the difference is a sensual one, not an intellectual one, assuming a historical imperative based on research instead of what the music sounds like is, imho, folly."...

So, why do you bother whether it should be WT or ET? I did bother, I needed to bother firstly as a musician, secondly as a pro tuner.

..."I try to focus not only on what the music sounds like, (occupational hazard for a professional tuner), but rather, what it feels like. These are not the same thing."...

Yes, you could work on that and line up your feelings.

Regards, a.c.
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 07/18/10 10:38 PM

Alfredo writes:
.
>>When my ear detects a wolfish sound, I feel like my castle is not safe anymore, like if those beautyful, ever different field stones (read partials) that could decorate my castle in an orderly way, are now deforming into a mess.>

If the point and intention of listening to music is to feel "safe", then we are talking at cross-purposes. Perhaps meantone, with its perfectly safe thirds, would do this, but would it not get boring? Life is messy.

a.c. >>Actually a "dissonance" is nice as long as it makes sense. It is an "out of tune" dissonance that I find unpleasent, just like an "out of tune" consonance.<

We got a semantics problem. Maybe some definitions are in order? Let's consider Just to be consonant. Everything else is simply degrees away from it. Let's consider "out of tune" as anything that calls attention to itself rather than the music. There is no point to go assigning values of good and evil, since taste is subjective.
With that, we can ask the question, where does your limit of tolerance occur? Consonance is nice, but we can't live there, so how far from consonant is too far. It seems to be a 13.7 cent third. This is an odd size, resulting from physical limits of our hands and fingers colliding with the physics of vibrating strings. Why would that resulting compromise be of particular harmonic interest? It is certainly not consonant, since it beats like crazy.

A.c. asks: Have you read about one actual non-equal Vs ET compareson? Even "educated", lined up listeners could confuse the two.<

I have presented exactly this program at 7 National conventions of the PTG,the CAPT, as well as numerous other events for non-technicals. We listen, very carefully, to both tunings. This is after I have taken the entire audience on a tour through the keys of the WT. We listen to what Brahms wrote in Eb,other pieces in Ab, Bm,G, you name it. I point out the variety of thirds, and what they sound like as 17ths. And we compare the same piece on both pianos, and there is NEVER any confusion as to which is which.
ET has a profoundly different sound that, once recognized, is usually easily identified. There are passages in the middle keys, which are tempered so close to ET that it could be confusing to those that don't have pitch recognition, but there are big differences in how the WT keys feel, and the skill to sense them is not hard to develop, even for modern ears. It just requires a willingness to listen from another perspective.
As a sidebar, the effect on the artists that play is profound. Most of them have never touched a WT, and they all, every one, loved it.


>>Which "plastic" are you talking about? Is yours a bizarre (or exploitable) issue?<<

I don't know about "bizarre. Plastic was a figure of speech. It refers to a man-made chemical artifact (polymers and such) as a metaphor for the artificial intonation that results from dividing an octave up into 12 steps, destroying consonance everywhere for the sake of control.
Exploit that, if you must, but I really don't understand the question.

In response to me saying, "It is exciting to me to hear a composer gradually taking the ear into very expressive territory without ever making such a big leap that it breaks the spell,

A.C. writes:
For what I can say, the scale and chords geometry itself can variate from "tense" intervals to "calm" ones,

That may be enough for some. The intellectual processing of the music may be creating as much emotional involvement as a particular person seeks. However,our autonomic nervous systems are not being stimulated the same way as if given varying doses of dissonance. Variety has its effect in all senses. The rubato is a prime example. Crescendos, likewise. Why not harmonic variety? Almost all other instruments provide it.
The musical complexity, both physically and in composition, is greater with a non equal temperament, since there is more than one change when there is a modulation. In any ET, the only thing to change when modulating is the pitch center. In a WT, there is the change of pitch center, and, if desired, the change of tension due to tempering. This change can be higher, or lower, or it can be missing in action, all dependent on the composers intentions. How can the options be anything but a feature? One has to really love the sound of a 14 cent third to give that all up.

>> and the temperaments (historical) main issue was the wolf, <<

I think there was too much interest in temperament, long after the wolf had been spread out to dry, to dismiss intentional placing of the tempering according to key signature, as virtually all WT's do. It was done too consistently to ignore.

a.c.
>> Do you really think composers wait for you/us to give them a temperament?<<

No, I don't. I think they simply used the intonation they inherited. Giving something up in the most used keys to make the remote ones usable would have been a very natural progression from thinking in restricted meantone sense.
What is implausible is that the complete Classical era would have suddenly happened because equal temperament made it so, and no composer said anything about it. Modern composers don't specify ET,(Gershwin? Rachman,etc), why would we expect differently 200 years ago? They worked with the status quo,and in Beethoven's time, I don't think ET was the norm.

a.c. <<So, why do you bother whether it should be WT or ET? I did bother, I needed to bother firstly as a musician, secondly as a pro tuner.>>

I bother 'cause I love music, and I want as intense an experience as possible. After becoming familiar with alternatives, ET has come to sound boring and aesthetically bankrupt for music composed prior to 1900. It places terrible tempering in places it has no business being, and gentrifies wildly dissonant passages. It averages everything out in a bland sameness, like tapioca. The music deserves more, and so do we.
Regards,
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/19/10 10:36 AM

Hello.

ED writes:..."If the point and intention of listening to music is to feel "safe", then we are talking at cross-purposes. Perhaps meantone, with its perfectly safe thirds, would do this, but would it not get boring? Life is messy."...

"Safe" was a figure of speech, as a metaphor for a natural (referred to nature's geometry), home-ish (referred to my own geometry), possibly euphonious environment (referred to a warm, reliable, shareable scale-geometry). As a metaphor for explaining when can my emotions flow. Nothing to do with Meantone pure thirds, actually nothing to do with pure fifths or octaves either, since they would give rise to messy tunings (I should not tell you).

To be able to tell how your life is messy, I should know you better, see your house, check your habits...but would not "ever-messy" get boring too? And ever-sweet'n sour? Ever intense? No, I do not think that can be a way. If anything, music composition is "order", and not for the sake of it but to make music shareable. Infact, the common line seems to be "share order", not mess as an order, you may just go out and check. In nature we find both, mess and order, and this helps me understand your craves, be them your own craves. I'd rather go for my own mess and would not expect to share it.

So, the porpuse of this writing is to understand what is behind the preference for WT and I thank you ED. It seems that we (ear-equipped people) can say when intervals and chords sound good or if they can sound better, and even agree on that. But it seems also that "sounds good" is a matter of personal taste. In any case, it seems that we should not have all chords sound ever "in tune", otherwise it gets boring. It seems that a fixed mess can contrast boredom, but wasn't life messy enough?

ET is mentioned as normally tuneable, commonly down to perfection, and ET's regularity with its rule applied to perfection makes it boring. It seems that music can be much more emotional if we deviate few cents, if we go through pain-and-pleasure, and it seems that we can be told the (ever?) fixed and correct amount of pain and the (ever?) correct amount of pleasure, so that we can finally enjoy music (ever?) in the proper, intented way. Am I with you?

a.c. >>Actually a "dissonance" is nice as long as it makes sense. It is an "out of tune" dissonance that I find unpleasent, just like an "out of tune" consonance.<

ED:..."We got a semantics problem. Maybe some definitions are in order? Let's consider Just to be consonant. Everything else is simply degrees away from it. Let's consider "out of tune" as anything that calls attention to itself rather than the music. There is no point to go assigning values of good and evil, since taste is subjective."...

Say that what you say is true, how can you ensure my "emotional" then? And why do you go for fixed good and evil?

..."With that, we can ask the question, where does your limit of tolerance occur? Consonance is nice, but we can't live there, so how far from consonant is too far."...

In my case, also dissonance (read dissonant chords) can be nice, and beat-proportions (read nature's geometry) drive my ear and tell me where I am.

..."It seems to be a 13.7 cent third. This is an odd size, resulting from physical limits of our hands and fingers colliding with the physics of vibrating strings. Why would that resulting compromise be of particular harmonic interest? It is certainly not consonant, since it beats like crazy."...

I shall tell you about Chas. It cannot be called a compromise, as it can stretch all intervals into a self-referencial beat-geometry. Chas describes a self-contained beat structure which can be modelled into an ET form to perfectly fit our 12 semitones scale.

A.c. asks: Have you read about one actual non-equal Vs ET compareson? Even "educated", lined up listeners could confuse the two.<

..."I have presented exactly this program at 7 National conventions of the PTG,the CAPT, as well as numerous other events for non-technicals. We listen, very carefully, to both tunings. This is after I have taken the entire audience on a tour through the keys of the WT. We listen to what Brahms wrote in Eb,other pieces in Ab, Bm,G, you name it. I point out the variety of thirds, and what they sound like as 17ths. And we compare the same piece on both pianos, and there is NEVER any confusion as to which is which.
ET has a profoundly different sound that, once recognized, is usually easily identified. There are passages in the middle keys, which are tempered so close to ET that it could be confusing to those that don't have pitch recognition, but there are big differences in how the WT keys feel, and the skill to sense them is not hard to develop, even for modern ears. It just requires a willingness to listen from another perspective.
As a sidebar, the effect on the artists that play is profound. Most of them have never touched a WT, and they all, every one, loved it."...

Ok, I'll avoid telling you how Chas ET is successful. That would not be an argument.

>>Which "plastic" are you talking about? Is yours a bizarre (or exploitable) issue?<<

..."I don't know about "bizarre. Plastic was a figure of speech. It refers to a man-made chemical artifact (polymers and such) as a metaphor for the artificial intonation that results from dividing an octave up into 12 steps, destroying consonance everywhere for the sake of control.
Exploit that, if you must, but I really don't understand the question."...

Can you actually devide an octave up into 12 steps, down to absolute and steady perfection? You seem to anticipate what nobody can achieve, i.e. a perfect and steady ET. And a perfect WT, can you tune it on 88 keys? To me, that sounds a bit like a pretext, like debatable, aleatory concepts for approximate, aleatory deviations from sound tunings.

..."In response to me saying, "It is exciting to me to hear a composer gradually taking the ear into very expressive territory without ever making such a big leap that it breaks the spell,

A.C. writes:
For what I can say, the scale and chords geometry itself can variate from "tense" intervals to "calm" ones,

..."That may be enough for some. The intellectual processing of the music may be creating as much emotional involvement as a particular person seeks. However,our autonomic nervous systems are not being stimulated the same way as if given varying doses of dissonance. Variety has its effect in all senses. The rubato is a prime example. Crescendos, likewise. Why not harmonic variety? Almost all other instruments provide it."...

The variety you talk about is our drama and we get that in any case, no need to theorize it.

..."The musical complexity, both physically and in composition, is greater with a non equal temperament, since there is more than one change when there is a modulation. In any ET, the only thing to change when modulating is the pitch center. In a WT, there is the change of pitch center, and, if desired, the change of tension due to tempering. This change can be higher, or lower, or it can be missing in action, all dependent on the composers intentions. How can the options be anything but a feature? One has to really love the sound of a 14 cent third to give that all up."...

About these concepts, I think I've said enough. And I tend to think that any composer, if anything, would go for his/her own urge for an original temperament, they would not wait for our artistic, fixed non-equal temperament.

>> and the temperaments (historical) main issue was the wolf, <<

..."I think there was too much interest in temperament, long after the wolf had been spread out to dry, to dismiss intentional placing of the tempering according to key signature, as virtually all WT's do. It was done too consistently to ignore."...

I think there were too many difficulties in ET temperament, long after the wolf had been theoretically spread out to dry, to dismiss intentional placing of the tempering according to key signature, as virtually all ET's and WT's end up doing. It was done too consistently to ignore, but this tragic "consistency" can not make an argument.

a.c.
>> Do you really think composers wait for you/us to give them a temperament?<<

..."No, I don't. I think they simply used the intonation they inherited. Giving something up in the most used keys to make the remote ones usable would have been a very natural progression from thinking in restricted meantone sense.
What is implausible is that the complete Classical era would have suddenly happened because equal temperament made it so, and no composer said anything about it. Modern composers don't specify ET,(Gershwin? Rachman,etc), why would we expect differently 200 years ago? They worked with the status quo,and in Beethoven's time, I don't think ET was the norm."...

For what I can read, ET is not the norm, not even today. This is why I'm trying to share Chas.

a.c. <<So, why do you bother whether it should be WT or ET? I did bother, I needed to bother firstly as a musician, secondly as a pro tuner.>>

..."I bother 'cause I love music, and I want as intense an experience as possible. After becoming familiar with alternatives, ET has come to sound boring and aesthetically bankrupt for music composed prior to 1900. It places terrible tempering in places it has no business being, and gentrifies wildly dissonant passages. It averages everything out in a bland sameness, like tapioca. The music deserves more, and so do we."...

I agree, we deserve good tunings and I cannot really say how horrible your ET experience might have been. May a good tuning free your mind of pain and pleasure routines and unconvenient prejudices, may you acknowledge that 12 root of two ET has evolved.

Best regards, a.c.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 07/22/10 07:34 AM

Hi Alfredo :

here is may be what you are trying to understand :


http://www.youtube.com/watch?v=gU8uREFN3CU&feature=related

http://www.youtube.com/user/PersianTunedPiano#p/u/1/XB8oD5lUFIU

Personally I like that very much, and I understand it is a contextual thing.

Now the way the piano is tuned allow most probably for one and only one mode.

... confusing the discusssion a bit more !!!
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 07/22/10 04:27 PM

Originally Posted By: Kamin

[Persian piano tuning]
Now the way the piano is tuned allow most probably for one and only one mode.

It's possible to tune the piano so all the Persian "modes" except one (which is often omitted anyways) can be played, but each in one specific "key" only.

A common technique, also used on santur, is to tune a different key (scale) on say C2-C4 and C4-C6. So if you need microtones not available in C4-C6 you "steal" them from C2-C4.

In this tuning some notes need to be raised 40cents so often the whole piano is tuned 40 cent flat. Not a problem in Persian music.

For just one mode you sometimes can get away with instead of raising e.g. Eb by 40cent just lower E by 60 cent. Often you don't need the Eb and E at all, or you can steal them from the lower octave if needed.

Kees
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 07/24/10 04:11 AM

Kees that is interesting, get me bluffed ! you know about those different modes apparently.

Where can I find some information on that ?

What is the name (Persian modes ?)

I was expecting the fact that only one key (or very little) was available then.

In any case I like that music, that is refreshing , sound "authentic" .
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 07/24/10 12:48 PM

Kamin, I have a website on it: Persian music
which has some information on Persian music theory. It is of course a large subject.

Kees
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 11/16/10 07:39 PM

Hello.

Just for sharing two good news. On the academic front, an article on Chas has recently been written by Prof. Nicola Chiriano and published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) of the University "Bocconi" - Milano. Here it is, in the original version (Italian):

http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pia...

After Babel, it is now being translated in English.

On the practical side (for VT (ETD) users), in C.A.P.T. piano forum, Ernest Unrau (RPT - Canada) has released an updated tuning simulation.

To All, best regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Discussion (PW):

http://www.pianoworld.com/forum/ubbthreads.php/topics/1194874/1.html

Approach, method and sequence (PW):

http://www.pianoworld.com/forum/ubbthreads.php/topics/1383831/1.html
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/19/11 07:50 PM


Hello,

I read with interest about color and I'm also concerned about "in tune" and "resonance".

I'd like to share a live recording of Chas ET tuning:

http://myfreefilehosting.com/f/07c3ca3905_6.32MB

Your comments are welcome.

The article on Chas, recently written by Prof. Nicola Chiriano and published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) of the University "Bocconi" (Milano), is here (Italian):

http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte

Best regards, a.
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 03/19/11 09:25 PM

Hello Alfredo,

Thank you for posting that recording. The Fazioli is truly one of the very finest pianos in the world. There is only one in my clientele but I love to tune it. It has the cleanest, purest sound of all the pianos I tune.

Your recording sounds perfect. There is certainly nothing wrong with it at all. It meets the highest expectations as far as I am concerned that any professional sounding recording should have. When the music modulates, it is as smooth as silk. Obviously, this is the way you prefer it to sound and your clients have come to expect it from you.

If I were to go to that same place, tune the same piano and have the same artist perform that music but this time in the EBVT III, there may be many people who could not distinguish the difference one from the other even though we both know that there would be deliberate and carefully constructed differences.

I can easily accept that you, personally, would dislike the EBVT III tuning. You would hear subtle and sometimes not so subtle texture differences during the modulations. The ending chords would be calmer than in your recording and there would be increased tension in other parts. To me and the people who like the EBVT III, that is the very difference which they have grown to like and appreciate for what it offers to the music.

You certainly have the advantage in that your style of ET tuning is the epitome of standard practice. However, it is not a question of ET being "right" and anything else being "wrong". It is not a question either about any non-equal temperament being "out of tune" and only ET is "in tune". They are all "out of tune" one way or another. One cannot even say that ET is the "least" out of tune temperament although some may well perceive it that way. It is all out of tune to the same slight degree. There is no harmony that is either more consonant nor dissonant than the other. Some people say that is the advantage of ET whil others say that it is a disadvantage.

Whether one prefers strictly ET or definitely does not like ET is a matter of personal preference. People should be allowed to have their preferences and not be told that one is "right" and the other is "wrong" even if we each may find our own personal justifications for our preferences.

Soon, there will be made available on Patrick's thread some more comparison recordings. Opinions both ways will be invited. What will not be welcome are rude and condescending remarks that come from no foundation or that stand alone as the listener's opinion.
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 03/19/11 11:06 PM

Originally Posted By: alfredo capurso
The article on Chas, recently written by Prof. Nicola Chiriano and published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) of the University "Bocconi" (Milano), is here (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte
Best regards, a.

I wish my Italian was better, because the translation that Google gives me of even the first sentence is quite nonsensical:

"In 1691 the German organist Andreas Werckmeister found an ingenious way to tune the instruments in a way closer than ever to an equal temperament."

Kees
Posted by: Gadzar

Re: HISTORICAL ET AND MODERN ETs - 03/19/11 11:32 PM

Mr. Capurso,

Superb tuning. thumb
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 03/20/11 12:00 AM

Originally Posted By: DoelKees
Originally Posted By: alfredo capurso
The article on Chas, recently written by Prof. Nicola Chiriano and published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) of the University "Bocconi" (Milano), is here (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte
Best regards, a.

I wish my Italian was better, because the translation that Google gives me of even the first sentence is quite nonsensical:

"In 1691 the German organist Andreas Werckmeister found an ingenious way to tune the instruments in a way closer than ever to an equal temperament."

Kees


Kees,

I was able to have Google translate the entire document with a couple of clicks. Not every phrase is translated with complete grammatical accuracy but you will still understand the text.

I'll do you, Alfredo and everyone a favor by posting this Boxnet link to the document as I stored it in my documents file:

http://www.box.net/shared/p544e4hz6o

Just for everyone's information, as I read the document, the word "mesotoniche" is not translated but it is obvious to me that it is what we call "meantone". In the math equations, the word for "Pythagorean" appears as "Pitagoriche". I will not comment on the article at this time as I am still studying it.
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 03/20/11 12:09 AM

Thanks Bill, but I still get the same erroneous first sentence from your link.

Kees
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 03/20/11 12:17 AM

Hmm, I think you may find the entire document to fit that description.
Posted by: Cinnamonbear

Re: HISTORICAL ET AND MODERN ETs - 03/20/11 02:15 AM

That was gorgeous, Alfredo! Thank you for posting this recording. What a beautiful sound, and the performance was stellar!
Posted by: Grandpianoman

Re: HISTORICAL ET AND MODERN ETs - 03/20/11 02:39 AM

Hello Alfredo,

Thanks for posting that...lovely sound and performance.........unisons are so clean too...hopefully, I can get that kind of stability in the future.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/21/11 01:10 AM

Alfredo,

The link to your recording has already expired. Please post it again.

EDIT: The download is fine now.

Lovely tuning and playing, Alfredo. Thanks for posting this.
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 03/22/11 12:58 AM

Sounds good, but the last CE would sound a lot better when it was more in tune as in an UT.

Kees
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/22/11 07:18 AM


Hello,

thank you All for your feedbacks, I can only be happy if that recording sounds nice to you too.

Thank you, Bill, for your comment.

…"Whether one prefers strictly ET or definitely does not like ET is a matter of personal preference. People should be allowed to have their preferences and not be told that one is "right" and the other is "wrong" even if we each may find our own personal justifications for our preferences."…

Definitely you are right, but I still wonder how that "one" will define his/her preferences. Think of an orchestra or a choir, I still believe that, when it is the case, we all can recognize an higher degree of harmony, we could say if someone is singing out of tune. Why? My answer is that we can share a sense of proportion, energy and fusion, all being part of our inner and outer nature.

As I could say, in my opinion EBVT may sound better than many ET attempts, the latter sometime resulting in a...UT stronger (as you say) than many others. But then I'm still afraid we talk about two (or more?) different ETs. I think you talk - in abstract - about an ETD stretched variant of 12 root of 2, which in practice can only result in a UT (or worse) precisely for two reasons: firstly, because it is based on some iH approximate models (ask Robert Scott for his latest parameters - and remember Stopper's?...proper consideration of inharmonicity...); secondly, because - in my experience - there is no model, there is no tuning-form that we can aim at directly. It's like when we want to through something in a bin while moving in a car...we'll have to anticipate our through. Always.

Today, my wish is to share the correct ET geometry (for our semitonal scale) and to suggest the correct practice (preparatory curves). Perhaps too much of a change, both in theory and in actual tuning, but for achieving any form we'll have to lay down a ready-to-appear tuning.

To make it short, I would certainly expect people have their preferences, as long as they/we all know what we are talking about. And when I think of theory and practice, I'd say: in practice we can only - if not for one second - experience UTs. Nature itself is dynamic and...very shy.

Best regards, a.c.


Chas tuning mp3 - live recording on Fazioli
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Tuning mp3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Article by Prof. Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte

Discussion (PW):
http://www.pianoworld.com/forum/ubbthreads.php/topics/1194874/1.html

Approach, method and sequence (PW):
http://www.pianoworld.com/forum/ubbthreads.php/topics/1383831/1.html
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 03/22/11 09:46 AM

Alfredo,

I appreciate both yours and Bernhard's perspectives. Mine is based (very briefly) on the idea of the Cycle of Fifths having prime importance to harmony. This was the obvious reason why people chose something else than ET in the 19th and 19th Centuries, even if they could at least approximate ET. They WANTED to hear a distinction in key signature.

The modern piano is more unforgiving in this aspect, especially when it is required to play music from all eras. In general, a Victorian style Well Temperament restores just a hint of that distinction. In my experience, after nearly 20 years of developing a Victorian style WT, it is as far as one can go with a Cycle of Fifths based temperament and yet have it found to be acceptable to the greatest majority. The limitations are that there still remain a very few who have become accustomed to ET and do not want any distinction in key signature. On the other end, there are those who do not find enough distinction in it.

I hope you will listen to the recordings on the ET vs. EBVT III field test thread and whether or not you decide to reveal your guesses publicly, I am sure that with these examples of very complex music, you will have a great amount of difficulty in distinguishing one from the other.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/22/11 11:16 AM


Thanks Bill.

Would you drive me towards your point? Perhaps:

- We need a Victorian style, so that we can enjoy the "distinction in key signature" and distinguish it from ET.

- We need a Victorian style that we cannot distinguish from ET.

- We ought to somehow honor WTs conceptual expectations, those concerning "distinction in key signature", never mind if - in practice - it sounds like some quasi-ET.

- We can all adopt EBVT and acknowledge that it is exactly "as far as we can go" from ET, and most probably even a pro-tuner "will have a great amount of difficulty in distinguishing one from the other".

Or? a.c.
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/22/11 11:28 PM

Alfredo,

good to see you back here. I have actually missed your philosophical approach and your seamless connection between your passion and human life in general.

May I offer yet another alternative?

- We could benefit from a temperament of the Victorian style tradition because, although it might be hard (and sometimes seemingly impossible) to tell it apart from ET even as an analytical listener, still the music might come out in a different way compared to when it is played on the same instrument in another tuning. EBVT III does influence the performer quite a bit.

....................

During the last year I've tuned only EBVT III for concert performances - solo piano as well as chamber music settings. Even a jazz trio with a pianist I figured would like that sound.

Now, musicians have a totally different approach to piano tuning smile Heck, I myself have it when I switch into concert mode and start playing.

Nobody dwells too much upon stretch, beat rates and other things related to our everyday tuners' life. The pianists care about the sound of the piano as a whole.

During the last two months, two highly famous artists have labeled the Steinway D in our concert hall as being one of the best instruments in our country. The Yamaha U3 in one of our old wooden churches is suddenly also top quality, and the same goes for our C5 and C7 in the small halls at the conservatory.

Bill's tuning temperament make the instruments sound in a way that is highly pleasing to many a musician's ear. In fact, I have heard nothing negative about it this far. I was nervous about going "alternative" at first, but every concert confirms my initial hunch as being right: A small town needs something unique, and right now - starting last year - we are slowly but steadily laying ground for special piano music performances.

-------------------

This as input to your dialogue with Bill. Getting back to the music you posted, it is remarkably good tuning, indeed. I really like the instrument, too, which Fazioli model is it? And who is playing?

If it sounds THAT good on a low quality mp3 (128 kbps), I bet the original recording is pristine.

Alfredo, keep hanging around here a bit more. You are needed here... smile

Posted by: Grandpianoman

Re: HISTORICAL ET AND MODERN ETs - 03/22/11 11:52 PM

Pat, that is exactly the way I felt about EBVTIII when I first heard it on my piano. It's hard to put into words, but the piano seems to have a quality of richness and depth that is somewhat absent from ET. The musician in me likes what I hear. I miss it when it's not there, as in my recent efforts at tuning ET.
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/23/11 12:52 AM

GPM: I understand that completely, because you play - and care for - your piano just the way any true pianist would do smile
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/23/11 08:07 AM

Hello Patrick,

Thank you for your feedback, that is a concert Fazioli 278. I asked for that recording because it was home-standard: one mic. + pc, that was all. And sure, if "simple" equipment is used, the product will be quite "naked", good for basic evaluations.

You write:..., still the music might come out in a different way compared to when it is played on the same instrument in another tuning. EBVT III does influence the performer quite a bit."...

No doubts about that. I think we all do what we do so that the piano sounds in a special, unique way, "a different way compared to…another tuning", hopefully for the joy of the performer. But I don't think that is the point. I think the question is "objective reasons for supremacy", both in theoretical and practical terms. And this is relevant when you want to go from "personal" to "universal".

..."Even a jazz trio with a pianist I figured would like that sound."...

I guess you are right.

..."Bill's tuning temperament make the instruments sound in a way that is highly pleasing to many a musician's ear."...

Bill says that himself and for me that is true enough. But one point is: what is the reason? You mention "alternative", but alternative to what? A poor tuning? A stronger WT? A quasi-ET?

On the other hand, how would you justify Bill's crusade against ET?
Is ET-tuning homogeneous worldwide?
Can "as far as one can go from ET" be objective?
How far can you go from EBVT, in one direction or the other?
How many cents deviation from ET are enough for the next XVT that claims supremacy?

I would not mind being told what is best at a logical and proveable level.

Regards, a.c.

Chas tuning mp3 - live recording on Fazioli
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Tuning mp3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Article by Prof. Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte


Posted by: Inlanding

Re: HISTORICAL ET AND MODERN ETs - 03/23/11 10:42 AM

Alfredo,
A most excellent recording of a superbly tuned piano. Great to see you here again!

Glen
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/23/11 01:15 PM

Now, Alfredo. You I know that I love your work, but I'm not sure that Bill has claimed that EBVT III is the only temperament worth tuning. He's praised CHas and Bernard Stopper's work and my impression is that he likes the well temp that David P. tunes in the videos from Emerson College in England. Aren't they apples and oranges, really, a perfect ET and a well-temp, with entirely different intentions behind them?

You have created a lovely sound. Surely the temperaments that Chopin wrote and played in, insofar as we can guess them, and further explorations of well temperaments can exist side by side with recent developments.
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/23/11 03:20 PM

Originally Posted By: pppat
GPM: I understand that completely, because you play - and care for - your piano just the way any true pianist would do smile


Due to the sensitive nature of this subject (ET/EBVT III) on PW lately, I will hasten to add that this was no judging on my part - just an appreciation of GPM's passion for the instrument and the music produced on it. I love the ambiguity of the verb "play", and there couldn't be a better spot for it than in that sentence smile
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/24/11 10:34 AM


Hello Glen, thanks for your words. How are you doing with your tuning?

Hello Jake, thanks for your comment. There might be something about my English, or perhaps my style, that does'nt help. In which case I apologize. Personally, I'm very much in favor of exploration and development.

…."I'm not sure that Bill has claimed that EBVT III is the only temperament worth tuning."…

Well, how do you translate the "one size fits all" claim? But even this would not be the question. What I would like to argue about is "objective reasons", in concrete and logical terms.

…"He's praised CHas and Bernard Stopper's work"…

And me too, I appreciate Bill's work very much. Beyond that…

…"my impression is that he likes the well temp that David P. tunes in the videos from Emerson College in England."…

I've missed those videos. Are they available?

…"Aren't they apples and oranges, really, a perfect ET and a well-temp, with entirely different intentions behind them?"…

Well, there is a point where any difference is lost and only "intentions" are left. Can we talk about that? So, the questions I've posted (above) are real. Would'nt you expect an answer? For what I read, some people in this forum like talking about ET. Would you say they have acknowledged ET recent developments?

Best regards, a.c.
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 03/24/11 11:18 AM

Alfredo,

I certainly never claimed that the EBVT III is the only temperament worth tuning. Even though I tune it most often, there are several others that I use from time to time: 1/7 Comma Meantone, 1/7 Comma Meantone with one pure fifth, Representative 18th Century Well Temperament (which uses the same sequence as the EBVT except that the four initial RBI's are at 4 beats per second instead of 6; the A#-F fifth also remains pure), 1/9 Comma Meantone, 2.5 and 2.6 cents narrow fifths Meantones, Rameau-Rousseau-Hall 18th Century Modified Meantone and a variation of the latter which has the CE M3 at 1 cent width instead of pure and finally, the Vallotti 18th Century Well Temperament.

Any of the above could be used with any kind of music and thus could be considered "one size fits all". In my writing, I have said that ET is apparently considered to be the only temperament which fits that description by those who advocate it. It was Helmholtz's theory. My take on that is that Herr Helmholtz saw all of the many variations and claims of preference and provided his own solution which has an undeniable logic to it from the point of view of an arbitrator.

For example, if there is a court case where there are 12 people having a claim to a certain sum of money but each presents an unsupportable claim, the judge affords each claimant an equal amount while disregarding the value which each claimant had presented as being rightful to them.

The decision is deemed fair but each claimant is equally dissatisfied as much as they are satisfied. The analogy to music is that the judge (Helmholtz, who was a scientist, not a musician) disregarded the value of the key signature.

Other music theorists indeed thought of ET very long ago, including Werkmeister, Neidhardt, Mersenne, Rameau and Marpurg but none of them ever produced a workable way to tune it. Even if they had, according to historical documents, ET was not what musicians of the 17th, 18th and 19th Century wanted to use, so they didn't. They preferred the distinctions in key color that well temperaments, modified meantones and mild meantones provided to the music that was commonly played at that time over the neutrality afforded by ET.

Only in the 19th Century and beyond did music progress to the point of modulations that were not seen in earlier music. Beethoven was perhaps the first to present these kinds of musical "surprises" after he had lost all ability to hear and therefore his mind became more theoretical. His later compositions were very avant guard for their time.

So, in these late 19th Century and early 20th Century pieces for the piano (which, as we know it) did not develop until the very late 19th Century), there was a natural gravitation towards ET. The assumption today is that the music of Chopin, Debussy, Ravel, Gershwin, Scriabin, Rachmaninoff and any others you may care to think of, all required ET.

This is actively being disproved today by the technicians who provide non-equal temperaments to the artists who have embraced them for what they offer and perform any and all types of music from any and all periods on them. That is not to say that people may still have an opinion about such uses as we have seen here on this forum.

A common phrase in our culture is, "Some like it hot, some like it not."
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/24/11 11:55 AM

Alfredo and all,

Well, as a wiser soul here has said, we all sometimes reveal that we believe our own child to be the most beautiful, but maybe we can continue to explore.

Here's a link to an afternoon video with an 1880's Bechstein that David tuned to his well temperament. You may not like it. That's OK. The pianist, Adolfo Barabino, did not know this piano, which is not perfect:

http://www.youtube.com/user/latribe#p/search/10/ZH2IXOfnBqw

I don't want to seem to promote the thread about these videos, which I started after running across them by accident and then writing David to ask him to join the forum to discuss the temperament, but here's the link:

http://www.pianoworld.com/forum/ubbthreads.php/topics/1590814/1.html

I'd actually like to hear what you hear in some of these pieces, Alfredo, and to hear what David would say about the recordings you've made using CHas. I won't be offended or hurt if you dislike them.

David's focus seems to be on exploring variants of the temperaments in which pieces may have been composed, to try to recreate, possibly, the original experience and just to listen to the results. (The question of what temperament Chopin and others composed and played in is of course impossible to answer, although it apparently wasn't ET. We're left trying out the later meantones and well temperaments and temperaments ordinaire and quasi-ET's and listening to the result. A pleasant guessing game, in a sense, but one that can reveal new beauties in the music, so the matter becomes serious. (Beauty is a serious matter?)

By the way, have you considered doing a video or two? How about the Chopin Nocturne Op 9, no 2? Not as a way to create a competition between CHas and a well temperament, but just to provide a reference point. Or an audio recording of the nocturne? Might be interesting, if any time opens up in the next few weeks. I'l like to hear this piece in EBVT III, too. In the Stopper temperament? Does it seem like a good idea to have a well-known piece recorded in the various temperaments as a reference point for discussions? Not as a way to argue for which is best, but as a way to discuss the exact effect on a single piece, instead of generally discussing the effects of a tuning.

Good to hear from you again. I'm looking forward to hearing more things recorded with CHas. (What has become of Kamin?)
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/24/11 07:52 PM

Originally Posted By: Alfredo
Originally Posted By: pppat
Bill's tuning temperament make the instruments sound in a way that is highly pleasing to many a musician's ear.

Bill says that himself and for me that is true enough. But one point is: what is the reason? You mention "alternative", but alternative to what? A poor tuning? A stronger WT? A quasi-ET?


Alternative to any true ET. No matter which stretch, as long as the ET common denominator is fulfilled: Any 3rd beats faster than all the 3rds below it. Any 6th beats faster than all the 6ths below it.
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 03/24/11 09:35 PM

I don't intend sarcasm by saying this but I think of it as an alternative to the Helmoltz arbitration or an alternative to conventional wisdom.

Alfredo, it is a shame that you could not also be a part of the 2011 PTG convention. Perhaps you could join us next year? Ryan Sowers will be the director and he would be the person to address.
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 03/25/11 12:00 AM

Originally Posted By: alfredo capurso
For what I read, some people in this forum like talking about ET. Would you say they have acknowledged ET recent developments?

Depends what you mean by "recent developments". I am not aware of any "recent developments" since about 1440.

Kees
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 03/26/11 04:14 PM

Hi!

I'm looking forward to the recordings here and Jake, thanks for drawing attention to the other thread mentioning my recordings with Adolfo Barabino and friends. Probably as a result of this, someone wrote to me on YouTube:
Quote:
The Chopin preludes in unequal temperament practically had me in tears. It's incredible, really.


The bottom line on temperament is in my mind that musicians once expected much purer intervals than we now hear at least in the home keys and that they used the others to effect. How much was a matter of fact and degree and I've heard it said that there is a fine line between a good temperament, and being out of tune. Whilst fine for the Harpsichord Kirnberger III is brilliant, on the piano I'm not happy that it's not a step too far, so I use a temperament based on Werkmeister pushed as far as I believe one can go. Temperament should have a musical purpose if it is to be part of the music, and not merely to be nice, like treacle.

It's certainly worth experimenting with the temperaments that go in the Werkmeister direction.

Best wishes

David P
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/27/11 09:31 AM

Alfredo,

I just listened to your recent recording again, and I have the same feeling about it that I had when Isaac (Kamin) posted his CHAS tuning (of bach/siloti, I think). This is the kind of ET I'd like to learn how to tune. Would you teach me how to do it?
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 03/27/11 10:54 AM

Indeed. I will ask Ryan Sowers to work on an invitation for Alfredo Capurso to present the CHAS temperament and tuning at the 2012 convention. If Alfredo is able to accept, I am sure we can find someone to work out the language barrier problems. For all of the difficulty there has been in trying to understand Alfredo's concepts in writing, the recording speaks for itself in the quality of his work.
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 03/27/11 02:42 PM

Dear Alfredo

The Chas tuning that you have recorded on the Fazioli sounds to me like a perfect ET piano to me - very fine. (Have you found yet my recordings at Hammerwood and Emerson and the more recent ones on the Yamaha?)

But what is beginning to be apparent is that performers are able to convey more meaning to their audiences if a good UT is used as is being increasingly understood to have been intended to be in use by composers. The other evening a friend of mine tuned a concert instrument to the UT that I use without telling anyone. Apparently no-one consciously noticed but the pianist wanted to communicate with my friend after the concert, obviously curious, but there wasn't time. We're waiting for the next installment.

I'm hoping that Bill might do the same sometime without telling anyone to see what the effect is.

However, I think we are seeing some diversifications of approach as to whether one uses fixed octaves or one allows the inharmonicity to affect the equal temperament. This is not so much an issue on big instruments. Interestingly in the early days of my tuning, I took no account of inharmonicity at all and tuned to purely equal temperament frequencies and the recordings on
http://www.jungleboffin.com/mp4/jan-zak/
are the result.

So http://www.jungleboffin.com/mp4/jan-zak/liszt.mp3 is ET tuned exactly save from A=880, raised by 1 Hz per octave so A - 440, 881, 1763 and some 18 years later the same piano
http://www.youtube.com/watch?v=buDzqBuwm3I
now in UT but with A 440 882 1765

Since this time I have been experimenting with bass octave harmonic reinforcement of the temperament which I have probably mentioned elsewhere intended to assist the instrument to "lock" and "unlock" in the home and remote keys when the sustaining pedal is used and this may have an effect on the perceived resonance of the instrument and which will change in a key dependent way.

http://www.youtube.com/watch?v=hgA1-I5MfNY is a comparison between the unequal temperament at Hammerwood Park and the same piece played on a Yamaha concert instrument, the recordings equalised to attempt to make the instruments similar except for the temperament.

Of all pieces that I find very annoying to listen to now in ET and quasi ET is the raindrop prelude for the reason that the chords shape shift interestingly but don't in ET, it becoming very tediously boring when one has heard the effect in UT. Here it is in UT:
http://www.youtube.com/watch?v=xsn9g4pS2RA

Best wishes

David P
Posted by: Bill Bremmer RPT

Re: HISTORICAL ET AND MODERN ETs - 03/27/11 06:43 PM

Originally Posted By: Unequally tempered


I'm hoping that Bill might do the same sometime without telling anyone to see what the effect is.

David P


My policy has always been, "Don't ask, don't tell" cool
Posted by: Chris Leslie

Re: HISTORICAL ET AND MODERN ETs - 03/27/11 11:04 PM

David

Do you have any evidence of what temperament prevailed at the time of Chopin writing the Funeral March sonata, and what Chopin liked? I am not convinced that the pure/spicy/pure/spicy etc. effect is what Chopin had in mind. To me, the interpretation and the wonderful old tone of the instrument is the key to the sound and not the temperament. I also think that Chopin's piano music goes down well on modern instrument in ET. Millions of Chopin lovers over the decades cannot be wrong! smile
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 11:19 AM


Sure, Patrick, I'm ready to do that. Compatibly with our commitments, I'll be happy to meet you.

Bill, thank you for your proposal and your efforts. When ever, it will be a honor for me to present Chas theory and practical tuning at the PTG.

David, in general I'm more concerned about colleagues and technical/tuning issues than audiences. About your tunings, I think they are enjoyable. In the "raindrop prelude" of yours (UT), some notes belonging to C# do not meet my urge. But that might be me only. Actually, how do you like the last cadenza?

Did composers have UT/WT in mind? This opens to another question: Which UT/WT, amongst dozens? Perhaps the problem was not "what one or ten composers had in their own mind" but what to do with the commas on fixed keyboards, how to win on "wolves" and gain euphony. Personally, as a musician I've always given maximum "in tune" in all keys for granted.

Best regards,

Alfredo


Chas tuning mp3 - live recording on Fazioli
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Tuning mp3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Article by Prof. Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte

Discussion (PW):
http://www.pianoworld.com/forum/ubbthreads.php/topics/1194874/1.html

Approach, method and sequence (PW):
http://www.pianoworld.com/forum/ubbthreads.php/topics/1383831/1.html
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 12:18 PM

Originally Posted By: Chris Leslie
David

Do you have any evidence of what temperament prevailed at the time of Chopin writing the Funeral March sonata, and what Chopin liked? I am not convinced that the pure/spicy/pure/spicy etc. effect is what Chopin had in mind. To me, the interpretation and the wonderful old tone of the instrument is the key to the sound and not the temperament. I also think that Chopin's piano music goes down well on modern instrument in ET. Millions of Chopin lovers over the decades cannot be wrong! smile


Chris,

I know that you were addressing David, but if I may add something:

We don't know the exact temperament that Chopin composed and played in, but the one thing we do know is that his pianos were not tuned to ET, which did not exist except in theory. We do have some reasons to be sure that A4 was not 440, however, and the temperament was set starting from C instead of from A4. The concert pitch of 440 was set later, and tuning forks from the era tend to be C forks, and varied according to the intended piano and setting: see the article on page 800 of The Athenaeum from June of 1885 (well after Chopin's death) which mentions Broadwood's use of three different pitches for a C fork:

http://books.google.com/books?id=WmNIAAA...ing&f=false

So...Yes, millions of Chopin lovers have in several senses been completely wrong. But does Chopin still sound lovely in ET? Of course. I recently found this video of Ingrid Fliter playing the Db nocturne, and it's undeniably beautiful. I can't help but wonder how it would sound if she had played in a temperament and tuning closer to that which Chopin composed in, however:

http://www.youtube.com/watch?v=xaeiARja7pQ

My hope is that David will one day cross paths with Ms. Fliter and persuade her to sit down at his Bechstein. Any tour dates in England...?

EDIT: She's scheduled to play in London this year from June 6-June 12 at Queen Elizabeth Hall. ( http://www.ingridfliter.com/tours.html ).

David, your mission is clear.
Posted by: Bernhard Stopper

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 12:44 PM

Originally Posted By: Jake Jackson
but the one thing we do know is that his pianos were not tuned to ET, which did not exist except in theory.....

....So...Yes, millions of Chopin lovers have in several senses been completely wrong. But does Chopin still sound lovely in ET?


From where do you "know" this and what makes you so sure about?
Already Werckmeister switched to ET in his late writings. He was indeed using ET then, not only theoretically.

Chopin was a friend of Liszt, for example. My teacher´s (Else Herold) teacher (Emil Sauer) was a pupil of Liszt. Sauer did his last recordings around 1942. So this is all not that long ago! That those ingenious pianists did not notice, that the tunings changed notably somewhere on the time axis, is not very plausible to me.
Posted by: pppat

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 12:48 PM

Quote:
Sure, Patrick, I'm ready to do that. Compatibly with our commitments, I'll be happy to meet you.


That sounds really good, Alfredo! I would probably have a chance to come to Sicily pretty soon. I'll PM you about specifics.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 01:41 PM

Hi, Bernhard,

I'm aware that Werckmeister developed and promoted ET in his last two books. I wasn't aware that people were using ET, however, or that Werckmeister was tuning harpsichords or organs to it.

I would like to read more about tuning practices in the 18th and 19th century, but I have found few sources. (About actual tunings as opposed to theory.) In Germany, the situation may be very different. In England, Ellis wrote in the 2nd edition of his translation that Broadwood tuners were not tuning to ET. His charts of tunings such as Broadwood's Best include the deviations from ET (which he saw as ideal). Am I missing other sources that show ET to have been used?

One thing, however, about Chopin: He reportedly valued Bach higher than any other predecessor, so I would strongly suspect that he used a similar tuning even if ET was popular.

However, what to me is more persuasive are the late 18th and early 19th century discussions and prescriptions for Well temperaments. If an acceptable ET could be tuned, was in fairly wide use, and was acceptable, why is the focus so often on Well temperaments or temperaments ordinaire?

But there's no sense in getting into this entire argument in the abstract. Are there German (in English translation) or other texts that you can point me to? I only know what I've read and heard, and I'm limited to English and French.

I would much rather pursue the subject in a logical way than by abstract argument. As best I can tell, based on what I've read, I think it can be said with some certainty that we do know that Chopin didn't compose on a piano tuned to ET. But I'm rational and ready to read and learn more.
Posted by: Chris Leslie

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 04:06 PM

Jake, I am aware that Chopin was not composing and playing on pianos in ET, or at A440, but my question is really if Chopin was fussy at all about a particular temperament. Just because some of us are titillated and see musical advantage in this artefact of keyboard design where is the justification that Chopin was. Is it likely that the various pianos that Chopin encountered were tuned unequally and with any temperament resulting from the desires and skills of tuners, musicians and on the locations. Given the historical evidence I think that Chopin would likely have been tolerant of a narrow range of temperaments, spanning near equal when it ever happened, in much the same way that must of us do today.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 06:03 PM

Maybe it's the uncertainty that fuels so much speculation and so many arguments. If only we could know...

By the way, did you like that Ingrid Fliter video of the nocturne? I do wish there was a way to hear her play in a well temperament. Too bad about those pesky kidnapping laws.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 06:15 PM

Hello Jake.

You write:..."We don't know the exact temperament that Chopin composed and played in, but the one thing we do know is that his pianos were not tuned to ET, which did not exist except in theory."...

I suggest to distinguish theory from practice.

Theory: I guess you talk about 12th root of two ET. That model has never been tuned, simply because (if we think of real sounds, from real string) pure octaves (like any other pure interval) can only exist in theory. And I challenge anyone to prove otherwise. So we might agree on one fact: pure octaves (but not only that) made the first ET model lame.

Bill writes:..."For example, if there is a court case where there are 12 people having a claim to a certain sum of money but each presents an unsupportable claim, the judge affords each claimant an equal amount while disregarding the value which each claimant had presented as being rightful to them. The decision is deemed fair but each claimant is equally dissatisfied as much as they are satisfied. The analogy to music is that the judge (Helmholtz, who was a scientist, not a musician) disregarded the value of the key signature."...

I do not mind Bill's analogy. The judge, we could say, was the thirteenth note, ie the octave. The "pure" octave was there above the claimants and produced an unsatisfactory decision.

Now, to me it is quite evident that the first ET model was not "ready" to be sold as a tuneable temperament. And we might as well justify all the critics in past literature.

Practice: we tuners know that any "good" tuning will not last long...maybe one concert? This makes me believe that many composers of the past - when pianos were not so solid - must have been able to compose and play in many "temperaments"...many quasi-UTS, quasi-WTs, to some extent quasi-ETs like the many we still hear today. But they all would go - until proven otherwise - for ultimate euphony and resonance, which after all is what we expect from an orchestra.

Regards, a.c.


Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 06:31 PM

Hi!

There's a lot to answer here and I'm not going to have time, so please forgive me.

I started from the premise that as a child I was told that there were differences between keys. But I could not hear them so I assumed that I was a bad musician. When building an organ in my teens, as a member of BIOS (British Institute of Organ Studies), I was introduced to the unequal temperament experiments and ultimately the now out of print book by Padgham which examines a number of diverse temperaments. I started with Werkmeister being easy to tune by ear - and hated it.

I used to use an "18th Century Meantone" on a square piano and never dared put UT onto a "Modern" piano.

It was not until I heard Rose Cholmondley playing the second sonata of Chopin that I realised that Chopin was using unusual and deliberately unusual keys, the only explanation for which was that he was expecting the keys to add character to the music.

The effects that my recordings have demonstrated are on account of the tuning, not my (beloved) Bechstein: here they are on a modern Yamaha:
http://www.youtube.com/watch?v=8in_RJYbjGM

For other examples on that piano, please follow the video response links.

So how do I know Chopin was writing for UT? Well, when one has heard it, the music says so - and having become attuned to the UT interpretation, ET performances are bland, grey and without such dimension of emotion.

I'm not the only person to be saying this - there is an indepedant research, on the net, by Dr Miller, from memory and it's well worth a read and certainly I'm not the only person to have felt that the UT performance in http://www.youtube.com/watch?v=hgA1-I5MfNY was more emotional than the ET - certainly upon hearing all four movements together.

Which temperament? I don't know and don't pretend to and I don't say the one that I'm using is right. But from 6 or 7 years of concerts at Hammerwood, a year of concerts at Emerson College and now another concert instrument in Forest Row, we have the feeling that it gives good results even on modern repertoire:
http://www.youtube.com/watch?v=O7v5jYkw13w (Paart)

It's a version of Werkmeister but really there are a number of temperaments which are well behaved and I deliberately attempt to try out others when I have the opportunity:
http://www.youtube.com/watch?v=UwoglLif3ps

Well behaved - purity in home keys, stress in remote keys - nice progression from added accidental to added accidental. The difference is how pure in the home keys, the acelleration into stress with the increased accidentals and whether peaking on B, C sharp or A flat. There's room for experiment here.

A friend of mine was a tuner for a major opera house for decades and a staunch proponent of ET on Steinways . . . Having heard my results he's been so intrigued that he's started tuning his S&S to the temperament and reports that the result is creamy. The concert instrument he tuned the other night, noone noticed, so although it's strong enough for us to hear, the temperament leaves its effects to the realms of subliminity and perhaps in that is the magic. From memory some thirds are over 20-21 cents sharp, so we are not looking at the mildness of most modern schemes.

What is interesting is that an audience, not having noticed this UT in concert, would have not objected to it having been called an Equal Temperament, allowing playing in all keys. It's in this way that I think that considerable confusion has arisen - that there was a contrast between Meantone with wolves and the Good Temperaments of which equal in which some keys are more equal than others is one . . .

No doubt I've left out some points but hope this clarifies some areas.

Best wishes

David P
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/28/11 08:58 PM

David,

I almost included one of your arguments--that by listening to Chopin played in a well temperament, one can hear how the music suddenly opens up and contains new dimensions. And I feel this to be true.

But Bernhard is of course asking for concrete proof, and I must admit that while, to me, it is almost certain that Chopin was not composing in ET, given the extensive ongoing discussion of other temperaments, his love of Bach, etc, there is a possibility that he was using something closer to ET. Do you know Bernhard Stopper's work? I'll be the first to admit that he is far more knowledgeable about temperaments and tuning, and he may well know of written sources that I've missed.

By the way, do you know if Ms. Fliter has recorded anything using an older temperament? I've done the basic searches, but all of the recordings I've found seem to be in ET. She came up in an era in which an interest in older temperaments was growing, so I half expected to find what I couldn't find.
Posted by: Chris Leslie

Re: HISTORICAL ET AND MODERN ETs - 03/29/11 12:56 AM

Code:
Poster: Jake Jackson
Subject: Re: HISTORICAL ET AND MODERN ETs

Maybe it's the uncertainty that fuels so much speculation and so many arguments. If only we could know... 

By the way, did you like that Ingrid Fliter video of the nocturne? I do wish there was a way to hear
 her play in a well temperament. Too bad about those pesky kidnapping laws.


Yes I like her interpretation very much. She has an excellent control of dynamics in bringing out the melodic shape, the ebb and flow of the phrasing and the overall balance. Not overly dreamy. I have no desire to hear her on a well tempered piano, but rather just a more appropriate piano. That one sounds too shrill in the treble for me. Would Chopin have approved of this interpretation? I think yes. smile
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 03/29/11 07:13 AM

Dear Chris and Jake

I'm listening to the Ingrid Fliter Nocturne at the moment - very beautiful - and the other pianist to watch out for is Valentina Igoshina who played for Tony Palmer's film about Chopin.

However, whilst this performance is very beautiful I know from experience that in certain modulations the piano . . . the temperament tells the piano to say to the composer "surprise me". This is a tradition going back far and exploited by Couperin whose Masses often swing from pure love to angst - and this is after all a characteristic of romantic music too. Not only Beethoven, already discussed in this thread, but Schubert too, loses so much in the greyness of Equal Temperament. http://www.youtube.com/watch?v=uTGka9jFUCU is an example where the temperament adds a subliminal depth which makes this performance (sorry - not cd sound - camera microphone with automatic volume control so please make allowance for this) more emotional.

Temperament is an area which cannot be discussed meaningfully in the abstract - it's something that has to be experienced. Music is about perception and emotion. These cannot be appreciated in dry theory of abstraction. We have to say therefore "we know they exist - do they work - how do they work" and if we have the hunch that a composer was relying on key colour through temperament we simply have to run the music through the temperament and see what we hear . . .

It has to be an experimental science rather than merely a theoretical one . . .

Certainly Jorgensen in his book "Tuning the Historic Temperaments by ear" is absolute in his assertion that unequal temperaments were in use specifically up to the death of Chopin.

http://www.millersrus.com/dissertation/

What do the musicians say? Knowledge of the repertoire gained from intimate 8 hours per day practice perfecting the corners of performance and expression gives possibly the most reliable understanding of the mind of the composer into which the performer is having to enter in order to perform. http://www.youtube.com/watch?v=41xRupc3Hz8
http://www.youtube.com/watch?v=ZH2IXOfnBqw

http://www.youtube.com/watch?v=YXzSXWaQGmA

Best wishes

David P
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 03/29/11 09:57 AM

Hi!

I have been reading
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

A very impressive piece of analysis and utterly superb. Makes perfect sense and it is bound to bring out the most resonance of which a piano is capable . . .

For musicians who have never heard the effects of a Good Temperament, your CHaS tuning must be the bees' knees.

Best wishes

David P
Posted by: Phil D

Re: HISTORICAL ET AND MODERN ETs - 03/29/11 12:14 PM

It's good to see somebody from a UT background taking an interest in the CHAS theory, and recognising the brilliance of the analysis. I believe this to be a very precise description of the best possible ET tunable on any piano, and the recordings certainly support how good ET sounds when tuned this way. It is incredibly difficult to tune aurally though, as it calls for progressive beat speeds in all the intervals, something which is very difficult to achieve!

I'd like to see a similar effort put into an ETD program to tune CHAS, so more people could give tuning it a go. It would be very interesting to see how this tuning differs from the 'best' ET a particular EDT can produce in partnership with a highly skilled tuner.
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 03/29/11 02:34 PM

Dear Phil

Just because I recognise the excellence of the analytical approach does not mean that I'm in love with Equal Temperament in any shape or form - for the reason that although it may make the piano sound more harmonious: for what purpose?

It does nothing for the music.

When you have been watching colour television, one finds having to watch in black and white a retrograde step, however brilliant the definition. It's well known that artists congregated on the Cote d'Azur for the light, causing brilliance of colours, against which the light in the UK is always grey.

Music is made of basic dimensions:
Rhythm and timing
Pitch - melody, harmony and timbre
Dynamics
but composers from Couperin to Beethoven, with certainty, and I'm not unique in extending this to Chopin, Schubert, Mozkowski and possibly Mendlessohn, Liszt and Brahms had the dimension of key.

Pitch, being relative and not absolute - varying from A392 to A460 and higher (even 490), is not the key to key.

If intervals are always the same size, then key cannot be distinguished.

Only by using a Good Temperament can key be distinguished, setting up chords of tension which can resolve into another relaxed.

The CHaS temperament is supreme in so far as it puts harmonic accordance at the centre of the concept, but for the reason above, any attempt at _equal_ temperament cannot be the last word in research of a temperament suitable for performance of historic repertoire and actually to enable performers to convey the music in the mind of the composers to their audience.

I wonder if the search for equal temperament has merely been an obssessive challenge to follow just because it's so difficult to achieve and therefore academic fun, rather than actually relevant to the music that was and is intended to result?

I wonder if there has been academic kudos ascribed to whoever can do it, for the sake of doing it, without regard for the effect on the music in the removal of a dimension.

Were we to be limited to the three dimensions of space, we would be pretty bored, and meaningless. Only when one inserts the dimension of time does meaning take off . . . So it is with key in the dimensions provided by temperament. Similarly were no variations in the density of matter distribution to be allowed, we would only be part of an amorphous gas throughout space. It's only in the dimensions permissable by varying matter density that we exist. So it is as music within the dimensions permissable in the relationships of the 12 notes of the keyboard.

Temperament is not to be argued about - it's simply about trying it, experimenting and comparing.

In the promotion of purely Equal Temperament, musicians and audiences are being robbed of the dimensions that many composers expected to be heard to give interest to their music.

It's not surprising that a generation or two have lost interest in classical music - in so far as equal temperament has made it sound the same, and boring, I have sympathy with them. It's in the cause of bringing music back to life, not merely refining white sugar further, that I have been trying to encourage all associated with pianos to give us back our metaphorical brown sugar, molasses and honey.

Best wishes

David P
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/30/11 08:52 AM

Hello.

Thank you, Phil, for your words, you've been very kind. It means a lot to me knowing that this discovery is being shared.

Thank you, David, for your contribute. I'm still after your second last post...many things to elaborate on.

I understand that you say: let's leave some differences, otherwise we loose the character of each single key, which is what music is about. In all this discussion I doubt we can decide what music is about for each one of us. I'd say that music is continuously evolving, thanks to singular, individual interpretations. In fact, Chas "s" variable stands also for that.

So, while respecting your position, I think there is only one ground where we can proceed together, and that's logics. As for the rest, I'm happy to talk about our approach and preferences if not based on clichés.

You write:

..."I started from the premise that as a child I was told that there were differences between keys."...

Yes, there were differences between keys. If temperaments have developed is because we needed to manage those differences in the best possible way. Perhaps that premise was, for you, a kind of crucial information. In my case, I was addressed towards correct (in tune) playing and singing. That kind of practice with chords, major and minor scales and arpeggios. There I needed to be in tune. No fuss, no mess allowed.

For what I know, people started the war against ET, complaining about loss of character, color and emotion long before a perfect ET model could be tuned. Which color has gone lost? How much color could go lost in 1850 due to a perfect ET tuning? In my opinion, the first ET model, beside being impossible to tune, received back some (justifiable) criticism from theorists that got scared for nothing. Nobody could ever tune 12th root of two ET. In that sense, we would never miss "character".

..."It was not until I heard Rose Cholmondley playing the second sonata of Chopin that I realised that Chopin was using unusual and deliberately unusual keys, the only explanation for which was that he was expecting the keys to add character to the music."...

In my opinion, your explanation might be influenced by your own theses about having to add character to the music. Amongst other (unprovable) explanations, mine could be that Chopin wanted to hear those pitches, being closer to his voice and/or inner singing. But, perhaps that tonality, there and then, was the least out of tune on his piano? Or perhaps Chopin had got tired of more usual keys? Or he wanted to exploit a precise fingering? Or he wanted to impress through the use of an original/unusual key? I do not know. Due to the vast number of possible UT/WT (and tuners), a composer would have had to play and check the piano first, to understand what the last tuner intended for character and then re-adjust his/her emotional sphere. How strong? And let's see where, here or there?

If you read back in this thread, you'll also find ED's remarkable posts about UT/WT, character and emotions. What I understand is that you prefer to hear a precise effect, call it sweet'n sour, grace'n pain or what ever, you want to hear keys that have their own "character", not all of them equally euphonious as they can be (today). Also you like the idea of home-key, neighbor-keys and remote-keys.

You may think in terms of key (12 keys?), perhaps I think more in terms of intervals and pitch. For me, excluding 12ths and 15ths, every single interval, from the minor second up, has its own character expressed by unique beat-rate/tensions. A "strong" or stressish interval would twist and ruin the whole key. For example, I would not like thirds beating more like sevenths, nor 12ths beating like thirds.

I like feeling absolutely at home in any key, then I feel like I can enter a sound-whole, a superior order, the Home for all possible feelings of mine, where pleasure and pain are not physical, earthly routines anymore, but pure inner emotions.

Regards, a.c.


Chas tuning mp3 - live recording on Fazioli
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Tuning mp3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Article by Prof. Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte

Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 03/30/11 03:22 PM

Dear Alfredo

Thanks for your post and your benign reaction! I was worried that the sentiments I expressed were strong but I have a great respect for what you have done.

My personal opinion is that the way in which Couperin revelled in smooth pure chords to progress deliberately to those expressing angst and then to find the relief of relaxing the tension demonstrates exactly how composers were expecting to manipulate the keys in the pre ET context. Unarguably Chopin grew up in the context of use of UT/WT and therefore all concepts associated with that tradition. This is not a matter of mere taste but of fact - ET was simply not much to the fore in the 1820s and 30s. How far we progress applying WT/UT beyond Chopin is a valid matter of debate.

Whilst others have discussed WT/UT, there are not many people such as I who have tuned a concert instrument to an _audible_ WT and built up such a corpus of concert experiences and recordings of the repertoire viewed through the lens of a Good Temperament.

In the absense of documentation, we have to look at the music as its own documentation and therefore we have to listen to it through the ears not of a theoretician but a musician. We have to examine whether what we experience correlates with what the music is trying to convey. One effect is that a chord which might be painful might be played more lightly, and whether the resulting accents or deemphasis of notes changes or accords with the interpretation of dynamics in a meaningful way.

Whilst a gramophone fitted with a 78rpm needle might play a Stereo vinyl LP, the large needle will smooth out the detail you'll hear if you fit the right needle. So it is with ET which smooths out the detail of differences that a Well Temperament shows up. It's like the difference between an electron and optical microscope.

One day I sat in on Adolfo Barabino's tutorial for Miena Senada on the Chopin 4th Ballade. Suddenly it became apparent that the shifting of the shapes of the chords on http://www.youtube.com/watch?v=fJT5Q6HooyA at 10:07 brings them into a new prominance indicating to the performer to treat them with special care. In equal temperament this can be overlooked. It may be that the temperament, if on the verge of audience audibility, is merely a signal to the performer. But that signal is as important to the performer as is an altimeter to a pilot.

The bottom line is that there is no one right answer for everyone and that performers can proceed in their playing without altimeters if they like . . . but that they should be given a choice, an informed choice and not one based on the near universal prejudice in favour of equal temperament. . .

So very much music having been examined only through the ears of equal temperament for so very long, it's time for a reassessment of that position.

What is very interesting in your work is that you have correctly analysed and identified ways in which the instrument can achieve maximum harmony in equal temperament.

My thesis is that in Well Temperaments, one has rooted and unrooted chords - ones where the notes relate to a harmonic root and "lock" together meaningfully, and ones in which the notes are squeezed away from any harmonic series and become meaningless or uncertain or disconcerting. (This is exemplified with the Funeral March). I have had difficulty in tuning bass notes with inharmonicity and have been experimenting in using the harmonics to tie in either with thirds in the home keys or fifths where the fifths are pure, creating a more distinct change of character of the whole resonating instrument between keys.

Di Veroli has published recently demonstrating that the Werkmeister family of temperaments are a valid platform for performance and indeed, it is one of those which I use.

In view of our common aim to achieve maximum harmonic accordance within the instrument, it would be very interesting if you might turn your mathematics to the problem of analysing the Werkmeister family of temperaments, including the modern variations, to see if any achieve maximum harmonic relationships within the piano as an inharmonic instrument, particularly in the home keys of F C G and D. Possibly B flat but as traditionally A flat appears to have been on the danger list for UT performance - indeed Jorgansen identifies G# A flat as the final note of the scale to be derived and used, four flats is likely to have been more divergent from pure than four sharps.

So I hope that I might have inspired a second chapter to your work?

Best wishes

David P
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/30/11 06:26 PM

Originally Posted By: Unequally tempered


...and the other pianist to watch out for is Valentina Igoshina who played for Tony Palmer's film about Chopin.

David P


I love her playing, but was a little put-off by the costuming in some video's I'd seen, until you wrote that she was in the film. These must have recorded using the same set and costumes:

http://www.youtube.com/watch?v=gRCzEQTP_Ks

Off topic, perhaps, but I love the sound of the piano, here, too. I suppose it's in ET, but it's good.

Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 03/30/11 08:01 PM

Originally Posted By: Jake Jackson
Originally Posted By: Unequally tempered
...and the other pianist to watch out for is Valentina Igoshina who played for Tony Palmer's film about Chopin.


I love her playing, but was a little put-off by the costuming in some video's I'd seen, until you wrote that she was in the film. These must have recorded using the same set and costumes:
http://www.youtube.com/watch?v=gRCzEQTP_Ks
Off topic, perhaps, but I love the sound of the piano, here, too. I suppose it's in ET, but it's good.


Hi!

Yes - that's a scene from the film
http://www.google.co.uk/search?q=the+strange+case+of+delfina+potocka
and anyone interested in Chopin will find the film very well worth watching, accompanied all through by this amazing pianist who I hope might perform at Hammerwood one day. And one might well ask who needs WT when one has Valentina playing . . . :-) !!!

Best wishes

David P
Posted by: Elene

Re: HISTORICAL ET AND MODERN ETs - 03/30/11 08:29 PM

PLEASE realize that the Palmer movie about Chopin and Mme Potocka is based on letters that were intentionally faked. There is some mystery about their relationship, but the movie is way off base and doesn't deserve to be taken seriously. Igoshina is beautiful both to hear and to watch, but it's too bad she had to be associated with such a misguided production.

It took me a moment, when I saw the subject of this thread, not to think "extraterrestrial".... Just want to thank you all for your good work in keeping us all playing and helping us to understand how these wonderful, complex instruments really work.

Elene
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 03/30/11 08:30 PM

I hope that we can look forward to hearing more of Miena Senad playing this Hammerwood piano.

One thing I find so lovely about Valentina Igoshina's performance of the funeral march movement is how she gives it room to build, starting off softly, letting it grow louder, backing off and again letting it grow louder, and then again backing off and moving it to a climax. I've heard too many pianists start loudly and then play much of the piece with only little concern for dynamics other than broad strokes between soft and loud.

But I do hope to hear her play in a well temperament.


Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 03/31/11 03:04 PM

Dear Alfredo

A while back I did a YouTube video on piano resonance causing the piano to add different amounts in different keys which I think you'll find interesting.

http://www.youtube.com/watch?v=Pz0B0SwKpww

I'm sure that a video of harmonics in your ET system would demonstrate it interestingly compared with ordinary ET and that your mathematics would be usefully and interestingly applied to Good Temperaments to see which of the Werkmeister family temperaments give the most home key resonance to the instrument.

Best wishes

David P
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/22/11 12:48 PM

Hello,

some colleagues may find of interest this article where "An unequal temperament is described in which the fifths and fourths of the tuning chain have the same beat rate."

http://gfax.ch/literature/Equal_Beating_Chromatic_Scale--Silver.pdf

Also I thank you, David, for your elaborations and thank you, Elene, for your chiming in...btw, nice website, you too are involved in good energy!

To All, Happy Easter.

a.c.

Chas Tuning mp3 - 2011 - Live recording on Fazioli 278
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Tuning mp3 - 2009 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 04/22/11 01:01 PM

Thanks for posting this article, Alfredo. Do you know of any recordings of a piano tuned to this EBS temperament?
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/22/11 01:36 PM

Hello Jake,

Nop, unfortunatelly I've never heard this EBS on a piano. In any case, the author fixes pure octaves, still in the age-old/wrong idea that the octave is the module. Also, it is interesting (and somehow suite) how he is concerned about the "color" issue and ordinary difficulties in tuning our first ET. Just a coincidence?

Regards, a.c.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 04/22/11 07:41 PM

Alfredo,

Silver does at least see that there is room for exploration with octaves, although he doesn't take the idea very far. From page 478:

"The octave is commonly regarded as sacred and it is
given its just value in both ET and the EBS, but the
fact that "stretching" takes place during the tuning of
pianos, proves that some latitude is tolerated. The
possibilities opened up by a calculated tempering of the
octave are interesting and the chromatic stroboscope
may further research in this direction by overcoming
tuning difficulties."

Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/23/11 10:07 AM


Yes Jake, you are right. And Silver makes a difference between "small variations which creep in..." when attempting 12th root of two ET and the possibility "to reproduce inaccuracies with some regularity".

From page 479:

"The edge was taken off this criticism by the fact that ET is exceedingly difficult to tune accurately by ordinary methods and the small variations which creep in tend to produce a sensation of key color. There can be, of course, no standard colors under these circumstances for results may vary from tuner to tuner. Nevertheless it became fashionable, and still is, to demand certain tuners on account of the pleasant effects they obtained and this suggests that with practice it is possible to reproduce inaccuracies with some regularity."

Perhaps Silver was the pioneer in Equal Beating approach, I do not really know, perhaps Bill and other colleagues can add on. In any case I like his honesty and I think his efforts were well directed, towards pleasent, confortable and somehow regular tunings.

Regards, a.c.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 04/23/11 12:15 PM

Hmmm...Google brings up other Silver publications. These links just give the names or starts of the works, not the actual text, although the last two can be reached through JSTOR:

http://openlibrary.org/books/OL20237831M/Notes_on_the_duodecimal_division_of_the_octave.

http://www.jstor.org/pss/3614300

http://www.jstor.org/pss/2316896

Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/23/11 02:52 PM


"An unequal temperament is described in which the fifths and fourths of the tuning chain have the same beat rate."

http://gfax.ch/literature/Equal_Beating_Chromatic_Scale--Silver.pdf

Jake, I do not have access to the links you posted. Me too, I've looked for other material without success. And only recently I got to know about A. L. Leigh Silver's work. Where is he from?

a.c.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 04/23/11 04:32 PM

England. He was a physician and the son of an organist, one note says. See the editor's note at the bottom of http://www.jstor.org/pss/2316896 .

How did you run across his work?

I want to find a copy of his "Notes on the Duodecimal Division of the Octave." I can access the other two articles on JSTOR, as can anyone affiliated with a university with a library that subscribes. I can't post the articles, however, or links to them. And right now, it's the end of the academic term, here, so I'm stretched a bit too thin to even look them up.

(Highly recommended--as you probably know, in the past few years, most of the major journals have scanned their old editions and put them online. JSTOR is a set of servers that collects them all and makes them available so that each journal\university department doesn't have to have its own server. The J. of the American Acoustical Society, the Proceedings of the Royal Society, and many other journals are available, and can be accessed from home.)
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 04/24/11 12:55 AM

(But Alfredo, I must say that my impression is that your tunings, from what I've been able to learn from your posts, seem to be partly derived from your sense of chromatics and from the Italian tradition of tuning for singers. I love the sound of CHase, and partly understand the theory behind it, but I would like to learn more about the tradition of the tuners you studied with.)
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/24/11 02:43 PM


Hi Jake,

I'm going to PM you and, for what I can, tell you about the tuners I've met and studied with.

Don't you think it would be nice to compare Silver's EBS with other equal beating UTs? One is Bill's, do you know about others?

http://gfax.ch/literature/Equal_Beating_Chromatic_Scale--Silver.pdf

Regards, a.c.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 06/09/11 12:34 PM


Hello.

Three days ago I found a video I made last September with my pocket camera.

I hope you too will like it:

http://www.youtube.com/watch?v=IPfq0CJ1gOg

Regards to All, a.c.
Posted by: Inlanding

Re: HISTORICAL ET AND MODERN ETs - 06/09/11 02:20 PM

Very nice sound, Alfredo. Thanks for sharing the video.

Glen
Posted by: Jake Johnson

Re: HISTORICAL ET AND MODERN ETs - 06/09/11 05:33 PM


I hope you'll find the time to do more videos, Alfredo. Those that David did for his well temperament are wonderful. It would be nice to have a similar collection of performances, filmed close-up and collected over time. Do you ever go to England...?

Good to see you back on the forum. I'm looking forward to hearing more examples of the CHas when you get the time to record them.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 06/11/11 11:00 AM

Hello to All.

Thank you, Glen, and Jake for the input you gave me. Could you link David's well temperament for me?

I've found a professional video, one hour of very nice music. The piano is an F308, the artist is Mariangela Vacatello. The event is part of a festival that takes place every year in Milano and Torino.

Chas Tuning at MITO - September 2010 - F308:
http://www.mitosettembremusica.it/multimedia/video/2010-09-09-milano-9608.html

Your comments are welcome.

Regards, a.c.

Chas Tuning - 2010 - "Rina Sala Gallo" International Piano Competition
http://www.youtube.com/watch?v=IPfq0CJ1gOg

Chas Tuning mp3 - 2011 - Live recording on Fazioli 278):
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

Chas Tuning mp3 - 2009 - Amateur recording - Steinway S (5' 1" - 155 cm):
http://www.box.net/shared/od0d7506cv
Posted by: Jake Johnson

Re: HISTORICAL ET AND MODERN ETs - 06/11/11 04:10 PM

I’ll have to listen to your new recording later. Running around a bit today. For the moment, here’s one video using David’s temperament:

http://www.youtube.com/watch?v=9zxNrQuxfNY&feature=related

There are 508 of his videos here, most of them of pianos tuned to his well temperament:

http://www.youtube.com/user/latribe#p/u

And here’s the thread in which this variation of a well temperament was or is being discussed here on the forum:

http://www.pianoworld.com/forum/ubbthreads.php/topics/1590814/Some%20sweet%20video's:%20an%20older%20p.html#Post1590814
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 06/12/11 01:36 AM

Originally Posted By: alfredo capurso

Sounds like a very nice equal temperament tuning. How does it differ from a nice equal temperament tuning that is not "Chas"?

Kees
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 06/12/11 05:36 PM

Thank you, Kees, for your feedback. I'm glad you can now address to Chas.

You write:

"Sounds like a very nice equal temperament tuning. How does it differ from a nice equal temperament tuning that is not "Chas"?"

If I can ask, which equal temperament are you referring to? If you asked someone for the current definition of equal temperament, the answer may be that it is "a variant of 12th root of two". Notice, a "variant" that is based - logically speaking - on a lame model and an approximate iH calculation.

Today we can see that a "variant" of that kind stays to Chas model's geometry like a roundish figure stays to a circle.

In these terms, your comment and relative question would be:

"Looks like a very nice roundish figure. How does it differ from a nice roundish figure that is not a circle?"

Jake, thanks for those links.

Regards, a.c.

Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/31/11 06:25 PM

Thank you, Bill, for representing your 12ths/15ths equal beating tuning in explicit form.

Thread: Anybody Deliberately Tune Pure Twelfths?
Bill Bremmer RPT - July 31, 2011 04:29 PM

"I don't tune perfectly pure 12ths, I make them equal beating with double octaves. They sound very nearly pure but technically, they are not. However, when tuning the high treble from F6 to the top, I often tune pure double octave-fifths."...

Yes. In fact, how you tune F6 (as a double octave-fifths) is the direct consequence of how you have tempered F3, A#3 and the other notes in your temperament section. And more, the whole tuning will depend on how you have tempered the first 25 notes, i.e the number of notes you need for balancing 12ths and 15ths. You now understand why your 12ths and 15ths may invert.

You wrote: ..."The equal beating double octave and octave-fifths (the PTG Journal's preferred nomenclature) provide for excellent "beat masking" (as Bernhard Stopper calls it). I also think of beat masking as beat cancellation or beat suppression. When that exact compromise is achieved, (take the example of the F3-F5 double octave), playing F3-A#3-F4 and F5 at the same time will yield an uncanny stillness even though none of the intervals are actually beatless."...

I'm glad, you sound ready for sharing and (perhaps) supporting new conjectures and modern ET models. Thanks for specifing also:

..."This is true for ET, Quasi ET and any mild Well Temperament or mild Meantone or mild Modified Meantone. It makes the whole Midrange and well into the Bass and Treble sound very clean and in tune with itself, regardless of temperament."...

Indeed, equal beating double octave and octave-fifths may work also as a tool; to a certain extent it can "adjust" or "make up for" some inconsintences in the temperament...if you use it as a tool. If/When you gain that as THE scale ratio, namely as the natural and coherent* outcome of your settled tuning (in my experience), you get the top, you get right to the Reason.

..."I have done this for at least 25 years."...

Well done.

*: in terms of EB constants and intervals beat-curves

Best regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 08/19/11 06:47 AM


Hello.

Sometime ago I received some unexpected words from Professor Ernest G. McClain. He is an elderly researcher who has deepened on historical and religious issues concerning music and numbers...you too may find of some interest reading about his very relevant works:

http://www.ernestmcclain.net/

Yesterday I realized that Professor McClain had published our mailing, so I can share his comments on Chas model with you:

http://groups.yahoo.com/group/bibal/message/23949


In these days I'm working on a conference, within a symposium on "Dreams", trying to emphasize the relationship between geometry and our universal "harmonic" affinities. And, of course, trying to explain with graphs and numbers that today - in music - we can depart from the theoretical and practical "compromise" and consciously share and enjoy an Optimum. I will appreciate your thoughts and comments.

Regards, a.c.

CHAS Tuning mp3 - 2011 - Live recording on Fazioli 278
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Temperament - 2010 - "Rina Sala Gallo" Piano International Competiton
http://www.youtube.com/watch?v=IPfq0CJ1gOg

CHAS THEORY - Research report by G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Presentation on PW and discussion (May 07, 2009):
http://www.pianoworld.com/forum/ubbthrea...%20-%20CHA.html

Chas Preparatory Tuning (December 15, 2009):
http://www.pianoworld.com/forum/ubbthreads.php/topics/1383831/1.html


Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 08/19/11 07:17 AM

Originally Posted By: alfredo capurso

.....

I will appreciate your thoughts and comments.

.....


There are many roads to En-dor.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 08/21/11 07:52 PM


From: #1737002 - August 20, 2011 10:01 AM Re: ET vs 2 different well temperaments video [Re: Steve W]

Hi TunerFish, in turn...welcome on board!

Do you tune aurally?

When you say "Standard Equal Temperament", I do not know what you mean.

Please tell me/us: how do you tune "ET" 4ths, 5ths, octaves, 12ths and 15ths?

And, how do you expand your X favorite tuning outside the temperament area?

When you state: "...interpretation of the music must by necessity change when played on different tunings. Pianists will instinctively alter their interpretation based on what they are hearing. I do an entire lecture/recital on this very subject. For each tuning a pianist will quite subconsciously change tempo, phrasing and pedaling. If you don't, the music won't sound musical and it won't make sense. If, for example, you were to play something that is in a very lush key in a Well Temperament, you would be likely to play it more slowly so that you can enjoy the subtle nuances of the tuning. However, because there is no key coloration in ET and all these nuances are lost, if you played it that slowly in ET it would be deathly boring. So, the tendency is to play faster and look for other ways to make the music make musical sense. This, IMHO, is why most concert pianists for the last several decades tend to play everything too fast."...

I really think (with all due respect) you must have taken a tangent. And I'm not discussing your musical sense, what is lush and what is morbid, how long you like suffering on a wolfish interval, nor how long you like "staying" on a chord that pleases you. And I'm not discussing your "color" soil nor your struggle with boredom.

I'm just saying that, within your own sad and anachronistic war against ET, you ought to show respect for the many pianists that have mastered timing and philological interpretation for years and years.

You may also be able to realize how long a perfect tuning "form" (read ET geometry) may last on a piano (before it turns into a sort of WT), like on any tense/deformable structure which is exposed to external forces; more or less, it will last as long as these rings:

http://www.zoomin.tv/site/video.cfm/lang...i-fumo-perfetti

So, all in all, I'd say: are you happy with your WT tunings? Good for you, in a way you are lucky.

Do you want to speculate on ET tuning? Then, you could do your home work and learn more about modern ET's geometry.

BTW, what is your name?

Regards, a.c.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 10/19/11 11:27 AM

Hi.

From the thread: EBVT: key color vs bad tuning technique [Re: Steve W]
#1770312 - October 14, 2011 10:58 AM

Ed Foote RPT wrote:..."Bach's writings, if considered teaching aids, certainly could be showing how to effectively use the harmonic resources found in the normal tunings of his day, (and I don't think ET was one of them). The WTC pieces do this,(compare the treatment of the third in, say, the preludes of C and C#). When we consider Chopin's music, we can see how he often is using melodic fifths over a highly tempered background harmony. This is where the textural effect of WT's can be heard clearly, and interestingly enough, pianists playing Chopin on a temperament with 18 cent thirds seem to find it clearer. I think removing the haze of tempering that hangs over the equal temperament allows the true harmonic colors to be displayed.
I equate ET with the pollution that covered the Sistene Chapel ceiling. The true colors of the artist were greatly reduced by its effect, but people had become so used to it that when the first panels were cleaned, there were many that argued we should keep it all covered up, like it had been all their lives! I submit that the brash colors Michaelangelo used are far more beautiful than the soot-covered, dim, outlines of his work that time had left us with. I think the same thing about Beethoven's use of key color, and from my own experience, the piano world is gradually loosening its grip on the security of the familiar in favor of the challenge and beauty of the original."

- . - . - .-

Ed, you are certainly allowed to your own opinions (that I respect) but for me it is a shame when, moving from questionable premises, you get to more questionable conclusions. And it seems (to me) that you have not been able to acknowledge a couple of things about tunings.

You mention "harmonic resources". What is there behind these nice-sounding words, what do you mean? I can enjoy both Bach's preludes in C and C#, but both keys have to sound "in tune". And you should know that, in Bach's days - before any "color" claim could arise - theorists, composers and tuners had just one problem, a centuries-old problem. That problem was related to primes 2, 3 and 5, the numbers that within a 12-semitones span will define our octave, fifths and thirds. In those days "color" wasn't a problem at all. Actually, from your point of view, they had so much…color, many unequal temperaments that could not solve THE problem: How to make all keys and all intervals sound in tune?

You say that ET tuning, in Bach's days, was not "normal". Please, would you be able to tell what is today's "normal" ET tuning? When 12 root of two was introduced, the approach to the scale went different: from a 12-semitones span, where you would temper intervals by fixing single intervals ratios, they developed the idea of a geometric set, a set of N notes that could be ordered in a geometric progression and that could lead to a sound-whole.

Today, it is not by copying 12 or 16 notes from the temperament section that a tuner can achieve the ET geometry. And if you realize that we were left with the "pure-octaves" axiom, if you think about the tuning of fourths, fifths, octaves, 12ths, 15ths, if you acknowledge how these intervals are coped with, somehow artistically and/or mysteriously managed, how can you think in terms of "normal" ET tuning. Is it modern ETD's "variants" you are referring to?

You wrote: …"When we consider Chopin's music, we can see how he often is using melodic fifths over a highly tempered background harmony. This is where the textural effect of WT's can be heard clearly, and interestingly enough, pianists playing Chopin on a temperament with 18 cent thirds seem to find it clearer."…

How about 20 cent thirds? Wouldn't pianists find "textural effect" even clearer?

…"I think removing the haze of tempering that hangs over the equal temperament allows the true harmonic colors to be displayed."…

Here we are again onto the "color" conjecture, plus "harmonic", plus "true". I know that you refer "color" to your "pain and pleasure" experience, and how some keys should sound better than others. But doesn't "harmonic" (from harmonia, “joint, union, agreement, concord of sounds”) recall the USA motto "E pluribus unum", "Out of many, one"? And if "harmonic" refers to "one", if it refers to a "whole", which UT or WT, out of dozens, displays "true harmonic alternation of pain and pleasure"?

…"I equate ET with the pollution that covered the Sistene Chapel ceiling. The true colors of the artist..."…

About ET, I understand your frustration. To me, it seems that you haven't grasped the theoretical goal, and most probably you have not been able to experience ET's effects in practice. How do you tune fourths, fifths, octaves, 12ths and 15ths? How do you switch the acrobatic expansion of 12 semitones to the tuning of a sound whole?

..."...the piano world is gradually loosening its grip on the security of the familiar in favor of the challenge and beauty of the original."

What you describe might happen, the "familiar" being what we witness every day, UTs and WTs whether we like it or not. But this does not mean that we should give up; in my experience, we can achieve a coherent sound whole and restore Aristoxene's idea, let me say THE original idea of a perfect, harmonious temperament.

Your thoughts are welcome.

Regards, a.c.

CHAS Tuning mp3 - 2011 - Live recording on Fazioli 278
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Temperament - 2010 - "Rina Sala Gallo" Piano International Competiton
http://www.youtube.com/watch?v=IPfq0CJ1gOg

CHAS THEORY - Research report by G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Presentation on PW and discussion (May 07, 2009):
http://www.pianoworld.com/forum/ubbthrea...%20-%20CHA.html

Chas Preparatory Tuning (December 15, 2009):
http://www.pianoworld.com/forum/ubbthreads.php/topics/1383831/1.html
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 10/19/11 11:40 AM

Alfredo:

If you want to respond to a post it should be done in the Topic that the post was made in.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 10/20/11 06:58 AM


Hi Jeff,

I was able to read Steve's original post and thought that my reply to Ed (above) would have been off Topic.

.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 10/20/11 07:04 AM

Alfredo:

Hmmm, the problem is Ed (or anyone else) might not look for a reply to what he said in one Topic in another Topic. It might be best to make a short post in the first Topic saying that you have something to say in response in a second Topic. smile
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 10/22/11 12:11 AM

Greetings,
Alfredo writes,(in response to my posting);

>>Ed, you are certainly allowed to your own opinions (that I respect) but for me it is a shame when, moving from questionable premises, you get to more questionable conclusions. And it seems (to me) that you have not been able to acknowledge a couple of things about tunings.
You mention "harmonic resources". What is there behind these nice-sounding words, what do you mean?<<

What I mean about harmonic resources is the variety of tempering in the thirds, (and of course, the m3 and 6ths). In a well temperament, you have a variety of levels of stimulation, due to the variety of beat rate speed( or dissonance, if you prefer). These are the resources. A pure third causes one type of emotional reaction from listeners. A heavily tempered third causes something entirely different. A passage in a sonata that is meant to heighten the musical tension is almost always using a more highly tempered key. A passage designed to calm things down does not move into a more tempered key, it moves or is found in the keys with less tempering. This is so basic, I wonder why I am even asked about it.

>>I can enjoy both Bach's preludes in C and C#, but both keys have to sound "in tune". <<

And you are trying to say that a third that is 13.7 cents away from pure sounds "in tune" to you?? What the heck does a pure third sound like???

>>And you should know that, in Bach's days - before any "color" claim could arise - theorists, composers and tuners had just one problem, a centuries-old problem. That problem was related to primes 2, 3 and 5, the numbers that within a 12-semitones span will define our octave, fifths and thirds. In those days "color" wasn't a problem at all. Actually, from your point of view, they had so much…color, many unequal temperaments that could not solve THE problem: How to make all keys and all intervals sound in tune? <<

There is no way to make all the keys sound alike, unless you detune all the thirds and fifths. So there is a conundrum for you. In order to make all of them sound "in tune", you must somehow come to accept a 13.7 cent third as "in tune". I no longer hear it that way.

>>You say that ET tuning, in Bach's days, was not "normal". Please, would you be able to tell what is today's "normal" ET tuning? When 12 root of two was introduced, the approach to the scale went different: from a 12-semitones span, where you would temper intervals by fixing single intervals ratios, they developed the idea of a geometric set, a set of N notes that could be ordered in a geometric progression and that could lead to a sound-whole.<<

That sounds like gobbly-gook to me. Exactly what is a "sound-whole"? I have never heard anyone use the term before.

>>Today, it is not by copying 12 or 16 notes from the temperament section that a tuner can achieve the ET geometry. And if you realize that we were left with the "pure-octaves" axiom, if you think about the tuning of fourths, fifths, octaves, 12ths, 15ths, if you acknowledge how these intervals are coped with, somehow artistically and/or mysteriously managed, how can you think in terms of "normal" ET tuning. Is it modern ETD's "variants" you are referring to? <<

No, I am referring to the equality. If all your like intervals are not tuned exactly alike, it is not an equal temperament. If they are all tempered alike, there is no difference in the sound of like thirds, (unless you believe there is some magic that causes different keys to have different emotional qualities.

You wrote: …"When we consider Chopin's music, we can see how he often is using melodic fifths over a highly tempered background harmony. This is where the textural effect of WT's can be heard clearly, and interestingly enough, pianists playing Chopin on a temperament with 18 cent thirds seem to find it clearer."…

>>How about 20 cent thirds? Wouldn't pianists find "textural effect" even clearer?<<

Yes, I have heard that said about Chopin's music when played on a Young temperament, which has a 21 cent third in it. The clarity arises from the contrast of the pure fifths against a tempered background.

…"I think removing the haze of tempering that hangs over the equal temperament allows the true harmonic colors to be displayed."…

>>Here we are again onto the "color" conjecture, plus "harmonic", plus "true". I know that you refer "color" to your "pain and pleasure" experience, and how some keys should sound better than others.<<

Pardon me, but I haven't used the word "better", which is your subjective value judgement. Color is the same as tempering, and what you are calling pain and pleasure is a variety of stimulation. Trying to say that some keys sound better than others is naive. Beethoven's "Pathetique" sounds awful to some people when played in ET, or if it is transposed in a WT to an unoriginal key like C. It sounds deader than a doornail and boring as heck.

>> But doesn't "harmonic" (from harmonia, “joint, union, agreement, concord of sounds”) recall the USA motto "E pluribus unum", "Out of many, one"? And if "harmonic" refers to "one", if it refers to a "whole", which UT or WT, out of dozens, displays "true harmonic alternation of pain and pleasure"? <<

You are trying to use a very narrow definition to obviate a much larger concept. In ET, there is no agreement, since none of the partials of the thirds is in concord with one another. So, by your strict definition, there can be no harmony in ET.
As far as which WT's go, they all share the same form, simply changing the amount of contrast. There is far less difference between them than there is between ET and any of them.

…"I equate ET with the pollution that covered the Sistene Chapel ceiling. The true colors of the artist..."…

>>About ET, I understand your frustration. To me, it seems that you haven't grasped the theoretical goal, and most probably you have not been able to experience ET's effects in practice.<<

I am not frustrated by ET, I am repulsed by ET when used for music that was composed to take advantage of the resources I have already mentioned. And if you believe that I, after three decades of selling ET's to professional musicians, haven't "experienced ET's effects in practice", then I submit that you are delusional. My tuning of ET has passed the standards set by Bill Garlick, the PTG, and countless international artists, so I submit that I am as experienced with the concept as anyone.

>> How do you tune fourths, fifths, octaves, 12ths and 15ths? How do you switch the acrobatic expansion of 12 semitones to the tuning of a sound whole?<<

Once again, you are using a term you have not defined. expansion of the 12 semitones is stretching, which has nothing to do with equality.

..."...the piano world is gradually loosening its grip on the security of the familiar in favor of the challenge and beauty of the original."

>>What you describe might happen, the "familiar" being what we witness every day, UTs and WTs whether we like it or not. But this does not mean that we should give up; in my experience, we can achieve a coherent sound whole and restore Aristoxene's idea, let me say THE original idea of a perfect, harmonious temperament.<<

What is perfect about out of tune thirds? Unless you consider "in tune" to be what you are accustomed to? What I am describing is what I am observing in my practice. More and more pianists are becoming aware of how much more complex a WT is than and ET, and how boring ET in comparison.
Alfredo, are you a tuner? By that I mean, are you supporting yourself by tuning pianos, or are you debating this subject on the strength of theory? I am selling very expensive tunings to very discriminating professionals, and drawing my conclusions from their responses. I have yet to have an audience that favors ET when placed side by side with a WT, or even a mild Victorian style of UT. This includes classical, jazz, and pop musicians. I don't consider these to be "questionable" conclusions, but rather, conclusions that are supported by practice and money.
Regards,
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 10/22/11 12:31 AM

Originally Posted By: alfredo capurso
And you should know that, in Bach's days - before any "color" claim could arise

Of course, especially before and up to "Bach's days", the color phenomena of UT was well known, and extensively written about. Please educate yourself before spouting (provable) nonsense.

Kees
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 10/23/11 07:29 PM

Hello.

Kees, I think you can do better than that.

Thank you, Ed, for your detailed reply.

I must say that I've received no answer about what is "normal" ET tuning. Nor you have answered about how you tune ET fourths, fifths, octaves, 12ths and 15ths. Perhaps that would prove that "normal" ET tuning does not exist (yet).

If "normal" ET tuning does not exist, I do not know against what you and others are fighting. Wouldn't it be nice if your war could come to an end?

You wrote:..."What I mean about harmonic resources is the variety of tempering in the thirds, (and of course, the m3 and 6ths). In a well temperament, you have a variety of levels of stimulation, due to the variety of beat rate speed( or dissonance, if you prefer). These are the resources."...

In my experience all temperaments do preserve "harmonic resources", if that means "variety of levels of stimulation" and "variety of beat rate speed". The difference might be "where" we want variety to take place. The more you differentiate single keys, as you say by tuning thirds with different degrees of consonance, the more you mess up the meaning that chords may convey, being part of a structure. No matter which key, we can have control over the total number of chords and their "tension", and make sure that each chord is going to manifest its proper character. Within any key, both simple and complex chords will display their "expected tensions" in full respect of semantic hierarchies.

I like "variety of beat rate speed" too, I like when beats are justified by one proportional ratio and when "variety" is ordered in a logical, intelligible way. Whether the first ET model succeeded in helping harmonization I can not say, and why tuners could not put 12 root of two in practice is another story. In any case, giving credit to what you say, in Bach's days they had "color" in force of the WTs you mention. What were they looking for then, other than that? Why would anybody have moved away from that idyllic scenery?

..."A pure third causes one type of emotional reaction from listeners. A heavily tempered third causes something entirely different."...

No doubt about that, that "reaction" to a wolfish interval was exactly THE problem, perhaps that is why temperaments other than "meantone" were developed (?).

..."A passage in a sonata that is meant to heighten the musical tension is almost always using a more highly tempered key. A passage designed to calm things down does not move into a more tempered key, it moves or is found in the keys with less tempering. This is so basic, I wonder why I am even asked about it."...

You were not asked about that. You say..."almost always"...Please, can you propose steady concepts?

Me: I can enjoy both Bach's preludes in C and C#, but both keys have to sound "in tune". <<

You:..."And you are trying to say that a third that is 13.7 cents away from pure sounds "in tune" to you?? What the heck does a pure third sound like???"...

What does a pure third sound like, when we get to complex chords? And weren't you supporting "variety of beat rate speed"? Well, in my experience every third can beat proportionally and in a unique way, depending on its fundamental note. Thus, if we go for color, every pure third may represent a lost opportunity. BTW, there is one "idea" that is passed off as correct, but actually it is banally wrong: that ET thirds are all the same.

Me: >>And you should know that, in Bach's days - before any "color" claim could arise - theorists, composers and tuners had just one problem, a centuries-old problem. That problem was related to primes 2, 3 and 5, the numbers that within a 12-semitones span will define our octave, fifths and thirds. In those days "color" wasn't a problem at all. Actually, from your point of view, they had so much…color, many unequal temperaments that could not solve THE problem: How to make all keys and all intervals sound in tune? <<

You:..."There is no way to make all the keys sound alike, unless you detune all the thirds and fifths. So there is a conundrum for you. In order to make all of them sound "in tune", you must somehow come to accept a 13.7 cent third as "in tune". I no longer hear it that way."...

All the keys sound alike? Nop, I do not mean that. I mean euphonious, like when you play and you are not disturbed by an unexpected scream. It seems to me that you consider thirds on their own, being concerned about their cent value. I could not care less about cents and wanted to spread beating thirds proportionally and coherently, all along the keyboard.

Me: >>You say that ET tuning, in Bach's days, was not "normal". Please, would you be able to tell what is today's "normal" ET tuning? When 12 root of two was introduced, the approach to the scale went different: from a 12-semitones span, where you would temper intervals by fixing single intervals ratios, they developed the idea of a geometric set, a set of N notes that could be ordered in a geometric progression and that could lead to a sound-whole.<<

You:..."That sounds like gobbly-gook to me. Exactly what is a "sound-whole"? I have never heard anyone use the term before."...

Sorry, I did not find a translation for "gobbly-gook". Can you help me? Tomorrow I hope to be able to complete my reply.

Regards, a.c.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 10/25/11 03:36 PM


Hi Ed,

This is where we were:

Me: >>You say that ET tuning, in Bach's days, was not "normal". Please, would you be able to tell what is today's "normal" ET tuning? When 12 root of two was introduced, the approach to the scale went different: from a 12-semitones span, where you would temper intervals by fixing single intervals ratios, they developed the idea of a geometric set, a set of N notes that could be ordered in a geometric progression and that could lead to a sound-whole.<<

You:..."That sounds like gobbly-gook to me. Exactly what is a "sound-whole"? I have never heard anyone use the term before."...

You are right. Briefly, I give fundamental relevance to the entire amount of notes, of intervals and chords ready to be arranged (in our case) on the keyboard. All intervals, inside and outside the temperament octave, can draw precise beat curves; we can weave all beat curves into a unique form, namely a sound whole.

In this view, the usual temperament octave (or section) is extended to 88 notes; intervals and beats altogether give rise to a sound structure that can be described as a unity. A better word would be gestalt, in that it conveys also the idea of synergy. I consider beats as the source of energy, if beat curves are ordered coherently. And for this to occur, all intervals (octaves included) must share one beat-ratio, the scale "difference" ratio of which you can read in Chas research report. "Beating whole" is synonymous.

Me: >>Today, it is not by copying 12 or 16 notes from the temperament section that a tuner can achieve the ET geometry. And if you realize that we were left with the "pure-octaves" axiom, if you think about the tuning of fourths, fifths, octaves, 12ths, 15ths, if you acknowledge how these intervals are coped with, somehow artistically and/or mysteriously managed, how can you think in terms of "normal" ET tuning. Is it modern ETD's "variants" you are referring to? <<

You:..."No, I am referring to the equality. If all your like intervals are not tuned exactly alike, it is not an equal temperament. If they are all tempered alike, there is no difference in the sound of like thirds, (unless you believe there is some magic that causes different keys to have different emotional qualities."...

No, no magic but sensitivity. I do not think we need to theorize heavily tempered intervals anymore for the sake of contrast. Different keys do keep their different qualities on the basis of different levels of tension, established time after time by the fundamental tone and resonating within the entire sounding body. I admit, the word "equal" can be ambiguous. Perhaps we would not even mention the word equal, if only they had called the first ET model "progressive temperament", since it is a geometric progression. Or "common temperament", since each frequency value is found by multiplying the previous one by a fixed number called common ratio.

In 12 root of two ET, in order to find something "equal" we have to translate the scale values in cents, but does that mean that "like intervals are tuned exactly alike"? Is that how you understand ET? For me, that is not even simplistic but a distorted representation, since we (you included?) temper ET thirds (and not only thirds) so that their beat rate speed can be progressive. What is "alike" then, in your view?

You wrote: ..."When we consider Chopin's music, we can see how he often is using melodic fifths over a highly tempered background harmony. This is where the textural effect of WT's can be heard clearly, and interestingly enough, pianists playing Chopin on a temperament with 18 cent thirds seem to find it clearer."...

Me: >>How about 20 cent thirds? Wouldn't pianists find "textural effect" even clearer?<<

You:..."Yes, I have heard that said about Chopin's music when played on a Young temperament, which has a 21 cent third in it. The clarity arises from the contrast of the pure fifths against a tempered background."...

Perhaps you call "clarity" what I would call cacophony. At the end, you like pure thirds, you can explain 21 cent thirds, but you hate ET 13. something thirds because they sound alike. Mhhhh..?

You:..."I think removing the haze of tempering that hangs over the equal temperament allows the true harmonic colors to be displayed."...

Me: >>Here we are again onto the "color" conjecture, plus "harmonic", plus "true". I know that you refer "color" to your "pain and pleasure" experience, and how some keys should sound better than others.<<

..."Pardon me, but I haven't used the word "better", which is your subjective value judgement. Color is the same as tempering, and what you are calling pain and pleasure is a variety of stimulation. Trying to say that some keys sound better than others is naive. Beethoven's "Pathetique" sounds awful to some people when played in ET, or if it is transposed in a WT to an unoriginal key like C. It sounds deader than a doornail and boring as heck."...

See what you are saying, I'm sure you would be able to detect a transposition even in the very mildest WT, as I've explained above. Also in my opinion color (meaning outcome of overtones) is obtained with tempering, but once you get to complex chords and harmonization you realize how dramatically everything changes, and how it is naive (using your expression) moving the heaviest tempered intervals in remote keys.

Me: >> But doesn't "harmonic" (from harmonia, “joint, union, agreement, concord of sounds”) recall the USA motto "E pluribus unum", "Out of many, one"? And if "harmonic" refers to "one", if it refers to a "whole", which UT or WT, out of dozens, displays "true harmonic alternation of pain and pleasure"? <<

..."You are trying to use a very narrow definition to obviate a much larger concept. In ET, there is no agreement, since none of the partials of the thirds is in concord with one another. So, by your strict definition, there can be no harmony in ET. As far as which WT's go, they all share the same form, simply changing the amount of contrast. There is far less difference between them than there is between ET and any of them."...

I see, ET thirds are not in concord with one another, while WT's have variable amount of contrast. Perhaps you'll be able to deepen on this and on a larger "harmonic" concept.

You: ..."I equate ET with the pollution that covered the Sistene Chapel ceiling. The true colors of the artist..."...

Me: >>About ET, I understand your frustration. To me, it seems that you haven't grasped the theoretical goal, and most probably you have not been able to experience ET's effects in practice.<<

..."I am not frustrated by ET, I am repulsed by ET when used for music that was composed to take advantage of the resources I have already mentioned."...

Leave my own opinion aside, I can not understand your repulsion. You are talking about a very extreme feeling but…we hear what pianos sound like, when we are asked to tune them. And here in PW (but not only) we have seen how difficult it is to distinguish a WT from, say, a "variant of ET". You talk about "music that was composed to take advantage of the resources…", I would not be so sure. Some artists may be inspired by what is there, others are able to project entirely new dimensions and take mankind elsewhere.

..."And if you believe that I, after three decades of selling ET's to professional musicians, haven't "experienced ET's effects in practice", then I submit that you are delusional. My tuning of ET has passed the standards set by Bill Garlick, the PTG, and countless international artists, so I submit that I am as experienced with the concept as anyone."...

I apologize, I meant modern ET's.

Me: >> How do you tune fourths, fifths, octaves, 12ths and 15ths? How do you switch the acrobatic expansion of 12 semitones to the tuning of a sound whole?<<

You: ..."Once again, you are using a term you have not defined. expansion of the 12 semitones is stretching, which has nothing to do with equality."...

Now "sound whole" is defined (above). Expansion, in my ET tuning, is tempering. Perhaps now you can answer my question.

You: ...the piano world is gradually loosening its grip on the security of the familiar in favor of the challenge and beauty of the original."...

Me: >>What you describe might happen, the "familiar" being what we witness every day, UTs and WTs whether we like it or not. But this does not mean that we should give up; in my experience, we can achieve a coherent sound whole and restore Aristoxene's idea, let me say THE original idea of a perfect, harmonious temperament.<<

You:..."What is perfect about out of tune thirds? Unless you consider "in tune" to be what you are accustomed to? What I am describing is what I am observing in my practice. More and more pianists are becoming aware of how much more complex a WT is than and ET, and how boring ET in comparison.
Alfredo, are you a tuner? By that I mean, are you supporting yourself by tuning pianos, or are you debating this subject on the strength of theory? I am selling very expensive tunings to very discriminating professionals, and drawing my conclusions from their responses. I have yet to have an audience that favors ET when placed side by side with a WT, or even a mild Victorian style of UT. This includes classical, jazz, and pop musicians. I don't consider these to be "questionable" conclusions, but rather, conclusions that are supported by practice and money."

I would never question your success nor your commitment. Yes, I'm a piano tuner.

Regards, a.c.
.
Posted by: Jake Jackson

Re: HISTORICAL ET AND MODERN ETs - 10/28/11 10:21 PM

Alfredo,

Wading in where I shouldn't, I must say that I still think that you and Ed just have different but equally valid goals. You want a new and better ET while Ed likes both the nearer consonance of the popular keys and the larger range of variation that comes from a WT. A WT may also be closer to what the composer heard and intended from the late 17th century to the early 20th century, although we can't, of course, always be sure what temperament Chopin, for one, heard while writing.

Can't we just say that a UT and Chas, and more conventional variations of ET, are valid and have their beauties?Speaking for myself, I hear Chas as wonderful, but I also love the sound of David P's well temperament and the Bremmer EBVT. We are not in a beauty contest in which there can be only winner.
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 10/29/11 03:51 AM

Greetings,
Am out of town on a honeymoon but will return next week. First thing that will have to be done is definition of terms, since my definition of "equal" does not include a temperament in which like intervals are intentionally tuned to different sizes!
Regards,
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 10/30/11 02:27 PM


Hi,

Very nice posts, thank you.

Jake, I appreciate your intentions. You are right, this is not a beauty contest, though beauty (read harmoniousness, in objective terms) is very relevant in tuning, and so are tuning history and present sceneries. Ed and I are exchanging our views and checking each other's contents and means. Your comments, Jake, are always welcome.

Ed, I wish you a great time. I look forward to knowing your thoughts at your convenience.

To All, have a nice Halloween!

Regards, a.c.
.
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 10/31/11 11:24 PM

Hi!

Please excuse me for the meat of this post should be in another topic kindly started by Jake . . . but the latest recordings at Hammerwood Park by Kazimierz Morski support clearly Ed Foote over Alfredo in this topic:

Rachmaninoff:
http://www.youtube.com/watch?v=ajMy45C4HeY
Chopin:
http://www.youtube.com/watch?v=zNFRTrO8XA4
Mozart
http://www.youtube.com/watch?v=bdnlQnzPx8U

For completeness perhaps these links should be duplicated on that thread. . .

(I had terrible problems tuning for this recital. Flies multiplied in their 10000 at the windows during the day providing a constant effective tinnitus both to the ears and to the computer running TuneLab97. I then battled between TuneLab with an inharmonicity curve applied and my ears particularly in the Tenor C octave and half the octave below, possibly on account of the IH curve wanting to rely on equal temperament. So in that region I tuned octaves by ear and then followed through other harmonics as appropriate to the note in the temperament. In the treble, however, I followed the TuneLab IH curve entirely.)

I have deliberately kept the Chopin recordings in one as the jump between keys in pieces contrasts mood well. The effect on the audience was extraordinary: the UT moved the audience much much more than any ET can - http://www.youtube.com/watch?v=hgA1-I5MfNY is the demonstration of this. As just two movements it might sound merely academic but when the temperament provides a soundscape for a whole sonata rather than merely part, the effect is quite profound. The UT version in concert brought tears to my eyes whilst the ET performance left me cold in comparison - it was just another performance despite the excellence of the pianist.

In the latest recordings I'm aligning much more with Alfredo's ideas of harmonic accordance but applying it to the unequal temperament and I think the latest Morski recordings have that advantage over the Barabino and Miena Senada recordings for which I tuned in the past.

Incidentally, the temperament that I'm using is not my own but I'm not letting on what it is at this stage because Adolfo Barabino deserves first bite of the commercial recording cherry . . . It's a temperament on the Vallotti Kirnberger spectrum with a lot of perfect fifths and that's all I'm willing to disclose. If anyone hits on what it is I would ask them not to publish what it might be, please.)

I have been looking at the relation between temperament and harmonic accordances for a long time - readers here may or may not be familiar with my YouTube video on this - http://www.youtube.com/watch?v=Pz0B0SwKpww which I hope may be useful in this discussion.

Best wishes

David P
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 11/01/11 12:05 AM

Originally Posted By: Unequally tempered

I have deliberately kept the Chopin recordings in one as the jump between keys in pieces contrasts mood well. The effect on the audience was extraordinary: the UT moved the audience much much more than any ET can - http://www.youtube.com/watch?v=hgA1-I5MfNY is the demonstration of this. As just two movements it might sound merely academic but when the temperament provides a soundscape for a whole sonata rather than merely part, the effect is quite profound. The UT version in concert brought tears to my eyes whilst the ET performance left me cold in comparison - it was just another performance despite the excellence of the pianist.


The UT sounds much warmer and evocative I agree. However I can't put the idea out of my head that he unconsciously played much more dead and mechanical in the ET tuning. His phrasing and dynamics seem to want to show ET is inferior.

As far as keeping your UT secret; just about any possible UT has been tried and passionately defended for many centuries, I can not believe you have found some magic bullet.

That being said I agree UT can make a big positive difference, but I think it is a refinement that should be tuned (pun intended) for the music at hand. For almost all 17th century music 1/4' meantone, for early 18th century music adapted meantone or strong UT's (1/4'), for Bach it's unclear as his music sounds great even on a neglected barroom piano, but the 1/6' schemes make a lot of sense.

Later on the 1/6' schemes avoiding Pythagorean thirds remain a viable option, but so does ET with the pianoforte replacing the harpsichord. The bad M3's are much less painful on the piano than on the harpsichord, as plucking excites the offending beating harmonics much stronger than striking with a hammer.

Kees
Posted by: Jake Johnson

Re: HISTORICAL ET AND MODERN ETs - 11/01/11 03:08 AM

David,

More recordings from the Hammerwood Park piano in your temperament? Thank you so much. I just listened to the Chopin. Lovely.

(But if there must be an argument over which temperament should win the pageant, I must note that we have no recordings of this same pianist playing these pieces on this piano tuned to Alfredo's CHas ET, however. To attempt a serious comparison, wouldn't Alfredo have to set your piano to CHas and ask Mr. Morski to play the same pieces? Yes, I want you to bring Alfredo to Hammerwood and record the results.)
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 11/01/11 06:51 AM

Doel: your assertion that Adolfo Barabino was wanting to demonstrate that ET was inferior simply proves the point that it is, for there was no such conscious intention at all. The fact that it may have an unconscious effect is another matter - the temperament moves the sensitive pianist . . . so if there is any difference between the quality of performance, it's the temperament giving the effect, not the pianist - let alone the assertion that he thought about it. The ET concert was in a particularly prestigious venue at a castle in the middle of a lake and there was not a shimmering of the conscious intention you ascribe to his performance.

Jake - I'm with Ed Foote on this. The point is that ET of any sort whatever cannot give the effects that we hear in these performances of cycling through keys and then finding the lock to which the one marked "home" fits . . .

In this concept, ET is akin to a torture of perpetual sex without finding orgasm. Romantic music cannot cope with that. ET literally makes it impotent.

There is another simile which I believe to be valid relating to the mathematics of music and in particular Entropy*. Much of music has within it contrasts of order vs disorder and God is to be found within "Order" (Pythagorean Music of the Spheres) equating with "God". This was particularly part of the consciousness of composers who were Freemasons. (I realise that I'm leaning towards the link about Ernest McClain and apologise as I have not read this thread in detail so apologise for any duplication of ideas which might have sprung to life before). The effect of this, however, is that the music cycles through periods of turmoil seeking ways of resolution and the finding of order. With ET, the sound is always disordered and order cannot be found.

It's for this reason that UT enured into 19th century romanticism and composers who were conscious of what they were doing would find chords, even in disordered keys, that locked into order. This is found in Morski's performance http://www.youtube.com/watch?v=zNFRTrO8XA4 and is apparent in Miena Senada's playing of the 4th Ballade under the direction of Adolfo Barabino where the temperament pointed to the finding of order amidst the turmoil on the 4th Ballade http://www.youtube.com/watch?v=fJT5Q6HooyA at 10:09 - and the visitor comment to that video is interesting. However, that tuning was before I had started looking at the TuneLab IH facility to assist the harmonic locking process.

(The Chopin 2nd sonata 3rd movement is such a piece where the first chord locks whilst the second is disordered.)

Apologies for the failed upload of the Mozart - it should now be on http://www.youtube.com/watch?v=0qRuPwQ7314

I will finish today preparing the videos of Kazimierz Morski playing Bach and Schumann and if these might be useful will post the URLs here.

Best wishes

David P

* (see note in italics on
http://www.organmatters.com/index.php/topic,1038.msg4632.html#msg4632 )
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 11/01/11 02:15 PM

Hi!

Further videos now on -
Bach
http://www.youtube.com/watch?v=0kLuwsz1VYk
Schumann Schubert
http://www.youtube.com/watch?v=C7R684k9A3g
Chopin Fantasie Impromptu
http://www.youtube.com/watch?v=RFyLkgYGBpw
Something interesting which may be removed
http://www.youtube.com/watch?v=5ztXIk0HWio

On the theme of keys and finding the one that fits the lock to home, one can perceive the music as travelling on a succession of journies, and the contrast between travelling and being still. Even more, finding "Home".

Many of the current world seek how to be still but cannot escape from always being moving. In ET one cannot find that stillness.

I hope that these recordings and these ideas reached independently of Ed Foote but clearly in parallel perhaps bring his concepts to life and understanding perhaps from an easier to understand perspective and backed up with a solid aural demonstration.

Aldfredo - I am with you on your efforts to bring harmonic accordance to the instrument to make the sound sound as one rather than a collection of notes - as it is exactly that that I have been trying to achieve using the locking together of the Unequal Temperament to lock together the natural intervals of the harmonics as far as might be achievable and as distorted by the inharmonicity inherent of piano strings.

My intervention in this thread is hopefully to demonstrate to you the use of your techniques in tuning unequal temperaments in the same way. Whilst it is a start, piano tuning is not as simple as getting out the Korg instrument tuner and tuning to the needle, as the piano does not behave like that - and that's the interest we find in these discussions . . .

Best wishes

David P
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 11/02/11 08:38 AM


Hi.

ED wrote:…"expansion of the 12 semitones is stretching, which has nothing to do with equality."…

Perhaps it hasn't been acknowledged that 12 root of two ET is a geometric progression, it is the first attempt at gaining a "tuning form" that should be extended beyond the temperament octave, a precise geometry that should include the entire range of notes. In fact, every semitone is strung together by the scale incremental ratio.

As a consequence it should be evident that, in order to talk about ET theory and normal tuning, the expansion of the 12 semitones is fundamental. Understanding how deeply "expansion" had to do with our historical ET and has to do with any "equal" form is first step. "Expansion" may explain why tuners could never put 12 root of two into practice. And eventually it will explain why ET needed to string together also our octaves, that is what Chas ET has accomplished.

So David, for the time being let's leave orgasms aside and let me ask you too the same basic question: How do you tune ET thirds, fourths, fifths, octaves, 12ths and 15ths? How do you manage the expansion of 12 semitones and the tuning of 88 notes into that notorious, precise, geometric form? What are the rules of your normal ET tuning?

Regards, a.c.
.
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 11/02/11 02:15 PM

Originally Posted By: alfredo capurso
So David, for the time being let's leave orgasms aside and let me ask you too the same basic question: How do you tune ET thirds, fourths, fifths, octaves, 12ths and 15ths? How do you manage the expansion of 12 semitones and the tuning of 88 notes into that notorious, precise, geometric form? What are the rules of your normal ET tuning?


Dear Alfredo

I entered this thread not to upset you but simply because my work and results support what I saw Ed Foote saying on this thread and are therefore relevant, and add further in the directions he has indicated.

How do I tune ET thirds?

I don't.

I don't tune ET.

How do I tune ET fifths and 12ths?

I don't: I don't tune ET.

This afternoon I was working with Kazimierz Morski on a recording and he was playing Mussorgsky and Ravel without at all needing the services of ET. ET is an outmoded 20th century encumbrance which has dulled the senses.

In the days when a 55 comma scale was used and semitones were recognised as major and minor semitones http://www.hoboy.net/Hoboy/BeyondTemperament.html
"Good musicians know how to use the different effects of the intervals, and prove their value by the expres­sion and variety they are able to draw from them."

Equal temperament is a system of blunting the differences between keys, robbing them of their eccentricities and colours, for people drilled mechanically into shape as machines in corporations . . . . to behave like robots. And leading ultimately to "music" constructed in boys bedrooms on computers to be played by machine at nightclubs engendering jumping together as machines and subsequent behaviour as robots.

smile Of course the above opinion is extreme, and I don't believe it . . . entirely . . . but put it in such terms merely to make the point.

I tune many fifths pure, many twelths pure - and with string inharmonicity leading to sharp harmonics, the bass notes go a bit flatter. Where the 17th accords with the intervals more pure than ET in the UT temperament, often I strike a balance between the 12th and the 17th, often with the 15th being spot on . . . and in this way, the temperament enables the tuning to hold together as a resonant whole. Sometimes I even listen to the 7th harmonic, the flat 21st, and make sure that it's not screaming against something. Music with thirds comes out sweet in keys that it's meant to, and shimmer where it's meant to, and music with 5ths comes out solid - an effect which Chopin exploited with 5ths in one hand and shimmering confusion in the other . . .

Morski comes to the piano as a conductor to an orchestra, and this too is Barabino's approach. The number of classical symphonies which feature ending on a chord with a prominent major third is significant. Standard ET on the piano ruins them.

Were you to apply your mathematical approach of achieving better harmonic structure as you have with ET but to the UT temperaments you would do the musical world a considerable service.

Best wishes,

David P

Posted by: Chris Leslie

Re: HISTORICAL ET AND MODERN ETs - 11/02/11 08:51 PM

I think that, tuning-wise, the closer to ET a modern piano is (i.e. the best compromise between progressive 5th and M3rds) then the better it sounds for any period of music.
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 11/03/11 08:31 AM

Originally Posted By: Chris Leslie
I think that, tuning-wise, the closer to ET a modern piano is (i.e. the best compromise between progressive 5th and M3rds) then the better it sounds for any period of music.


Chris - have you been following my YouTube recordings? ET leads to a reliable and constant shimmering in all keys. Is that what "real" music is about? Would you rather live in a temporary inflatable house with wobbling walls and floor or prefer one with at least a solid floor for your feet to be on the ground?

:-)

Best wishes

David P
Posted by: Jake Johnson

Re: HISTORICAL ET AND MODERN ETs - 11/03/11 10:27 AM

Originally Posted By: Unequally tempered


Dear Alfredo...

Were you to apply your mathematical approach of achieving better harmonic structure as you have with ET but to the UT temperaments you would do the musical world a considerable service.

Best wishes,

David P



This is a lovely idea--if Alfredo were to, as an experiment, build a UT.

By the way, David, do you know when Adolfo Barabino plans to release his album in the UT that you are using?

(I must say that I hope the sound is similar to that on the videos. I actually prefer it to the sound of the albums, or at least to the sound of the albums as they are reproduced on his site--the sound on the cd's seems to have more compression applied than I like, while the sound on your videos, while not perfect, is more natural and intimate--the sound of a piano when we are sitting near the piano. Is he recording it at Hammerwood, using your pianos there, by any chance?)
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 11/03/11 11:47 AM


..."ET leads to a reliable and constant shimmering in all keys."...

Well, David, that's something!

..."Is that what "real" music is about?"...

I would be pleased to know: what is "real" music about?

..."Would you rather live in a temporary inflatable house with wobbling walls and floor or prefer one with at least a solid floor for your feet to be on the ground?"...

That would depend on what comes along with your idea of "solid floor". You don't seem to be talking about one reliable architecture nor a smooth geometry. Have you checked the laying of your (floor) tiles? Then, why "temporary"? Why "inflatable"? Why "wobbling" as the only possible alternative? And why "a...house" to live in, instead of THE house to live over?

Regards, a.c.
.
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 11/03/11 04:37 PM

Dear Jake

The old CDs were done by a professional company before I met him and before he discovered the Hammerwood UT Bechstein . . .

Finding a recording company that is interested is proving to be a bit of a challenge but we are working on it.

The videos' sound are done with a H2 Zoom recorder about a meter away from the instrument
_______
| ___)
|_/ *

and aren't processed in any way - so they are as natural as can be . . .

However, after 27 years of concerts the hammers are worn and need refelting so are about to go away to Abel. Today I was working with Kazimierz Morski who wanted to record the instrument and, whether or not it is recent concerts (not Adolfo's special touch) that have been the straw to break the camel's back, but under the microscope of the microphone played through the detail of Lowther speakers, unevenness of the hammers began to show up and was actually quite annoying. So a good recording of the instrument will have to be on hold.

Alfredo - I was trying to get across in my description of ET the situation where everything is moving. Without purity anywhere other than octaves, and with IH octaves aren't "pure" either, nothing is still, nothing is focussed. In contrast in UT, keys cause music to shift and then be still, and also to "lock".

Kazimierz Morski's partner is a Professor of Aesthetics and Philosophy in Music in Italy and has written on the subject "What is Music?" so it's no coincidence that Kazimierz wanted to play and to record the instrument at Hammerwood in UT . . .

I'm not writing wanting to annoy you but simply to encourage your mathematics to UTs as well as ET.

Best wishes

David P
Posted by: Chris Leslie

Re: HISTORICAL ET AND MODERN ETs - 11/03/11 05:09 PM

Quote:
Chris - have you been following my YouTube recordings? ET leads to a reliable and constant shimmering in all keys. Is that what "real" music is about? Would you rather live in a temporary inflatable house with wobbling walls and floor or prefer one with at least a solid floor for your feet to be on the ground?

Yes, David, I have seen your videos and followed this argument for some time now in this forum so I don't want to flame another war. You create a false impression that key colour is a universal concept in musical appreciation throughout musical history, and throughout musical forms, rather than an artefact of keyboard design. For example, no vocal or chamber group would ever have any desire to deliberately produce a temperament-derived key colouration. However, they would be influenced if a keyboard is part of the group.

On the other hand, and grant it, the vibrato produced by harpsichords with their upper harmonics under ET is a bit sour, so there is a natural reason to temper the tuning and then be restricted to certain optimal keys. Then there was the concept of relaxation and tension derived from contrasting chord purity.

Modern pianos are a different beast and temperament-derived vibrato sounds much more acceptable. The development of modern pianos therefore fostered and permitted the development of harmonic and tonal complexity not possible during earlier times . Key colour became less important than the developing richness of the harmonic language. ET was a natural requirement of this harmonic complexity.

For your analogy, I would rather have a house that wobbles consistently all over than a house that is half steady but where you liable to fall through unforeseen rotten floor sections.
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 11/03/11 10:53 PM

Dear Chris

Thanks for your reply - and I agree with your argument that there are inconsistencies but . . .

I'm tuning modern Steinways as well as older instruments and on one the owner's mother comments (dispassionately and as a lay listener familiar with the instrument's standard sound) that she's never heard it so "in tune". The tweaking of temperament in the remote keys is not actually a great deal away from ET but the result is most wonderful purity elsewhere. When harmonic accordance is achieved, to which Alfredo is striving, then the sound in the badly tuned keys becomes more pure but is musically interesting.

Furthermore, now with considerable experience of the repertoire and its relationship with UT, there are many composers of the 19th century who drove phrasing and musical construction through passages of turmoil in order to resolve them by way of stillness and purity. The chords chosen, even in poorly tuned UT keys chosen for "special effect" avoided notes of poor intonation. We have noted passages where Liszt quite litterally wanted to achieve the effect of skating lightly as if upon glass or ice, particularly to find solid land on the other side of the phrase or passage. Ubiquitous ET has blinded us to these effects.

It may well be that the _beauty_ achieved by UT recordings does not come through in recording and standard electronic reproduction, particularly through the poor medium of computer compressed audio. But in real life, in the room, the effect can be particularly moving and, close to the piano, where effects are heard which cannot be recorded http://www.youtube.com/watch?v=0JpSH4YTypE

So in real life, rather than the mere abstraction of recorded sound particularly as by YouTube http://www.youtube.com/watch?v=nPvHq8HvTKg the performer is particularly aware, and possibly even more so than the audience, of the particular effects and this influences phrasing and accentuation.

Ed Foote has noted these phenonomae independently and I have entered this thread only because what I have been doing corroborates all that he has been saying.

I encourage you simply to try tuning a piano in a good temperament (UT) and to experience the effects, or tune one for a musicologist to note its interaction with repertoire. If UT tunings can have the benefit of Alfredo's mathematical analysis of concepts of harmonic accordance beyond my empirical practice, that has to vary between piano and piano, all the better . . .

In practice the central octave must be pure temperament, the treble octave above similarly certainly up to G5 and ideally most of the tenor octave, the octave below the middle certainly down to G3 or F3 or lower. I find that inharmonicity below G3 down to below the break on many pianos can start to vary wildly and find this really confusing in creating a reliably predictable result. From memory, I think that I referred to this on my last post in Jake's thread about my videos and discussion about how one copes with these caprices of the strings and weaves them into a rational scheme would be worthy of discussion and helpfully so. I gave inharmonicity figures for a clutch of instruments that I have worked on recently.

Best wishes

David P

Postscript:


I suspect that the piano tuner of my childhood talked of making some keys better than others and certainly my music teacher talked of keys having different characters. I thought I was a bad musician because I could not hear them . . . until I tuned UT . . . I suspect that achieving purely mechanical equality of differences between notes has really only come in with Communism and took hold in homes beyond the ivory towers of concert halls during the period of the Cold War. But with the fall of the iron curtain, looking beyond the confines of communism between the keys is a little overdue.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 11/05/11 10:56 AM


I was expecting some simple answers, but I can only read words to which no meaning can be assigned.

..."I'm tuning modern Steinways as well as older instruments and on one the owner's mother comments (dispassionately and as a lay listener familiar with the instrument's standard sound) that she's never heard it so "in tune"."...

With all respect, I don't know what to do with that feedback.

..."The tweaking of temperament in the remote keys is not actually a great deal away from ET but the result is most wonderful purity elsewhere."...

Purity elsewhere? Where? In complex chords?

..."When harmonic accordance is achieved, to which Alfredo is striving, then the sound in the badly tuned keys becomes more pure but is musically interesting."...

I can not follow you: When is "harmonic accordance" achieved? "...badly tuned...pure...musically interesting"? Honestly, these words puzzle me. I'm still waiting for Ed Foote to deepen on his "harmonic" concept and his own ET tuning, and for you to explain what "real" music is about. Do think in terms of "accordance", and you may want to grasp what has recently been achieved. At some stage, you'll see that intervals and beats have all been harmonized; you will understand that intervals wider than an octave have found their "beat" rule, that all intervals have their assigned tensions, and the decanted color palette is wider than ever, if referred to intervals beat speed variety and combinations.

..."Furthermore, now with considerable experience of the repertoire and its relationship with UT, there are many composers of the 19th century who drove phrasing and musical construction through passages of turmoil in order to resolve them by way of stillness and purity. The chords chosen, even in poorly tuned UT keys chosen for "special effect" avoided notes of poor intonation. We have noted passages where Liszt quite litterally wanted to achieve the effect of skating lightly as if upon glass or ice, particularly to find solid land on the other side of the phrase or passage. Ubiquitous ET has blinded us to these effects."...

I've tried, but it seems impossible (for me) to understand how you can talk about "ubiquitous ET". Which ET have you experienced? Which ET could you tune? Was it the tuning of the temperament octave?

..."It may well be that the _beauty_ achieved by UT recordings does not come through in recording and standard electronic reproduction, particularly through the poor medium of computer compressed audio. But in real life, in the room, the effect can be particularly moving and, close to the piano, where effects are heard which cannot be recorded"...

It may well be that temperamental theory evolved because of those "special effects", that many musicians, close to the piano, could hear. I did ask why temperaments evolved, but you don't seem to be interested in history and evolution.

..."So in real life, rather than the mere abstraction of recorded sound particularly as by YouTube http://www.youtube.com/watch?v=nPvHq8HvTKg the performer is particularly aware, and possibly even more so than the audience, of the particular effects and this influences phrasing and accentuation."...

Let me say, in real life each piano and every tuner's tuning will produce different effects; it is the mere comparing of theoretical tunings that opens to mere abstraction. If you refer to real life you could have no problem: nobody could ever put our first ET into practice. If this is true, your abstractions have become an obsession.

..."I encourage you simply to try tuning a piano in a good temperament (UT) and to experience the effects, or tune one for a musicologist to note its interaction with repertoire. If UT tunings can have the benefit of Alfredo's mathematical analysis of concepts of harmonic accordance beyond my empirical practice, that has to vary between piano and piano, all the better . . .

David, as a matter of fact for centuries temperamental models have "sliced" frequency values, elaborating only a "foreground". Even 12 root of two ET did so, and payed dearly for some erroneous axioms. I departed wrong axioms and worked on "differences", that I see as the "background", in the idea that a perfect sound whole could be experienced in real life and represented numerically. Today, what theories of the past had not accomplished has been achieved. Now I can only suggest tuning practice and attentive work on the expansion of the temperament octave, this is how I shape my tuning into Chas form.

Pardon me if I leave out your postscript.

Regards, a.c.

CHAS Tuning mp3 - 2011 - Live recording on Fazioli 278
http://myfreefilehosting.com/f/07c3ca3905_6.32MB

CHAS Temperament - 2010 - "Rina Sala Gallo" Piano International Competiton
http://www.youtube.com/watch?v=IPfq0CJ1gOg

CHAS THEORY - Research report by G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Presentation on PW and discussion (May 07, 2009):
http://www.pianoworld.com/forum/ubbthrea...%20-%20CHA.html

Chas Preparatory Tuning (December 15, 2009):
http://www.pianoworld.com/forum/ubbthreads.php/topics/1383831/1.html
Posted by: Unequally tempered

Re: HISTORICAL ET AND MODERN ETs - 11/07/11 10:55 AM

Hi!

The start of unravelling what I'm saying perhaps is to identify to which "ET" I am referring - the answer to that is any tuning whereby the proportional relationship of the middle note to the ones at the sides of one triad is the same as the triad of the semitone up, the two triads having the same aural shape and effect.

Whatever ET has been used, it's been ubiquitous for the past century.

"Purity elsewhere? Where? In complex chords?"

In a sensible UT, purity robbed from the remote keys is given to the home keys with few sharps and flats.

Ed Foote will understand what I have been writing about.

Best wishes

David P

Postscript
Some more definitions:

"Rooted" and "unrooted" chords
Rooted chords are those where the beat frequencies between two notes equate exactly or nearly exactly with a fundamental note of which the two notes sounding are on a harmonic series. If loud enough, the beat frequency is audible as a note - violinists know them as Tartini notes, I believe, and the effect is used on Acoustic Bass 32 organ stops.

Unrooted chords are those where beat frequencies of notes have no musical relation to either note, and are ignored.

Rooted chords, if the fundamental note is played or other notes also on the harmonic series "lock" together and are solid.

Unrooted chords have "no meaning" and are disconcerting.

Equal temperament is unpleasant as the beat note of a major third is 1/4 tone sharp.

"Harmonic accordance" When I refer to a piano in harmonic accordance I'm referring to notes falling near exactly upon the harmonic series of bass notes. In the Unequal temperament I use this occurs mainly in keys B flat, F, C and G with chords involving thirds and in a number of the remote keys with fifths. This gives a different effect to the keys making the home keys resonate warmly and the remote keys resonate stridently - but most of them resonate. The instrument "locks" together in different ways depending upon what key is employed.

http://www.youtube.com/watch?v=g6QT3e-Mqh0 demonstrates B major as a key where Liszt is causing the sound to skate as on ice. http://www.youtube.com/watch?v=Pz0B0SwKpww demonstrates harmonic series resonances. The way music moves through these resonances is another dimension of the contrast between moving and still http://www.organmatters.com/index.php/topic,1060.msg4681.html#msg4681 .
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 11/08/11 08:13 AM


Hi.

David wrote:..."...to which "ET" I am referring - the answer to that is any tuning whereby the proportional relationship of the middle note to the ones at the sides of one triad is the same as the triad of the semitone up, the two triads having the same aural shape and effect."...

Perhaps I understand what you do not like: when the shape and effect of two chromatic triads don't sound different enough for you to hear a difference.

It is evident that you are referring to the ET tuning of the temperament octave only. In fact, we all know that the "expansion" of the temperament octave has never been strictly ruled. In other words, the expansion of the temperament octave is normally left to the tuner's own personal discretion.

So, what you, Bill, Ed are really referring to it is the tuning of 12 notes, i.e. when 12 notes are tuned to a perfect ET. And you argue that the perfect ET tuning of 12 notes is responsible for the loss of key character. You would say that, also listening to the entire piano, you do not get the chords hierarchy nor the emotions and atmospheres that you, me, us, all tuners, musicians and audiences should and could experience, were the temperament octave tuned to a WT. And that the ET tuning of 12 notes would betray and misinterpret the composer's intensions. Last, you say that ET, no matter how the individual tuner expands the temperament octave, is ubiquitous.

Is all this correct? Please, can you check?

Regards, a.c.
.
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 11/08/11 09:19 AM

Greetings,
As this thread unravels into fractal opinions, it may be of some utility to step back and get a global view of what we are talking about before we split nits and scrutinize esoteric, arcane, opinions.
As I understand it, Alfredo holds the point that all 88 notes on a piano should be united in one whole, mathematically symmetrical unit. With this approach, there is no difference in the amount of tempering of the intervals. Bill Garlick basically taught us that proper tuning was an 88 note temperament, though you cannot hear thirds as anything but dissonant below F2,(critical band becomes inclusive). The original width of the temperament octave was thus in control of the stretch throughout, the clarity of the octaves, the purity of the fifths, and the overall level of stimulation that the tuning can cause.
My point is that there is a physiological effect that humans exhibit when exposed to different levels of dissonance, and that this differentiation has musical value when a composer aligns his composition to take advantage of the effects of consonance and dissonance. These are the "harmonic resources" I spoke of , and I don't know of a clearer way to explain them than to say that the resources are differing levels of stimulation caused by differing levels of dissonance. It is scientifically proven we involuntarily respond to higher levels of dissonance with higher levels of attention, as measured by heartrate, blood pressure, galvanic skin response, pupil dilation and several other markers I can't recall. That composers would use strident keys for expressive-stimulative purposes and calm consonant keys for expressive-sedating reasons seems to me to be so logical that I haven't yet heard a more plausible reason for the key choices that were made between 1700 and 1900.

AC writes:
>You say that ET tuning, in Bach's days, was not "normal". Please, would you be able to tell what is today's "normal" ET tuning? .<<

Today's "normal" ET is a tuning that evenly divides the comma between all 12 notes. Why are we even discussing what ET is? No particular approach changes the fact that every third is equally dissonant, thereby obviating any variety of physiological effect.

AC: I give fundamental relevance to the entire amount of notes, of intervals and chords ready to be arranged (in our case) on the keyboard. All intervals, inside and outside the temperament octave, can draw precise beat curves; we can weave all beat curves into a unique form, namely a sound whole.<<

Ok, that means that any difference between keys is no more than a difference in pitch. One who doesn't recognize pitchs as identities,("perfect pitch", which I do not have), will hear all keys as having the same level of stimulation.

I wrote>.. I am referring to the equality. If all your like intervals are not tuned exactly alike, it is not an equal temperament. If they are all tempered alike, there is no difference in the sound of like thirds, (unless you believe there is some magic that causes different keys to have different emotional qualities."<<

AC >, no magic but sensitivity. I do not think we need to theorize heavily tempered intervals anymore for the sake of contrast. Different keys do keep their different qualities on the basis of different levels of tension, established time after time by the fundamental tone and resonating within the entire sounding body.

Sensitivity to what? What are the "different levels of tension" that arise from the "fundamental tone". If you tune a piano in Chas tuning, but do it 100 cents flat from A-440, will the key of C maintain its level of tension, even though you are playing it a 1/2 up on the keyboard? I think not.


AC: In 12 root of two ET, in order to find something "equal" we have to translate the scale values in cents, but does that mean that "like intervals are tuned exactly alike"? Is that how you understand ET? For me, that is not even simplistic but a distorted representation, since we (you included?) temper ET thirds (and not only thirds) so that their beat rate speed can be progressive. What is "alike" then, in your view? <<

What is "alike" is the physiological effect. We hear logrhythmically, so the the level of stimulation is the same, regardless of the octave it is found in.

AC: Perhaps you call "clarity" what I would call cacophony. At the end, you like pure thirds, you can explain 21 cent thirds, but you hate ET 13. something thirds because they sound alike. Mhhhh..?

The 13 cent third is an important size, it equates to the tempering in the key of A and Eb in most WT's. I don't hate any size thirds. I am simply disgusted by the loss of resolutions that having everything the same produces. I hate hearing music stripped of important effects for the convenience of tuning.

When I wrote;.."I think removing the haze of tempering that hangs over the equal temperament allows the true harmonic colors to be displayed."...

AC writes>Here we are again onto the "color" conjecture, plus "harmonic", plus "true". I know that you refer "color" to your "pain and pleasure" experience, and how some keys should sound better than others.<<

You have misunderstood. I haven't said any key sounds better or worse. I have said that keys should have different characters, since they are used for different purposes in classical composition. The only pain I experience is that of sheer boredom listening to music modulate into more of the same. Color is a metaphor, "true harmonic colors" refers to the distinct sounds produced by intervals of different sizes.
In an ET, of any persuasion you care to create, there is not physical difference between the keys, and we are left to sense the effects of modulation from an intellectual perspective, only. In a WT, that same modulation carries more information, and much of that information is sensual, not intellectual. The sensual difference is where the WT has the advantage, and for me, the enjoyment of music is the sensual experience. When I am listening, I am not trying to think, I am trying to feel.

AC> > But doesn't "harmonic" (from harmonia, “joint, union, agreement, concord of sounds”) recall the USA motto "E pluribus unum", "Out of many, one"? And if "harmonic" refers to "one", if it refers to a "whole", which UT or WT, out of dozens, displays "true harmonic alternation of pain and pleasure"? <<

In the search for universal truth, we are always tempted to simplify. In music, harmony is not referring to "one", but rather, to the result of blending dissimilar pitches. Tempering creates a vibrato. Would it be boring is a singer was always using the same speed of vibrato? I think so. A skillfull vocalist will match differing levels of vibrato to the intent of the music. Horn players use various pitches for the same note, depending on the score. I submit composers used various keys for various intentions. Reducing the keys to the same tempering robs the music of effect. But not for all listeners, just the ones that have awakened to the additional complexity and richness that the WT palette offers.
I am not tuning WTs because I like them, I am tuning them because paying customers love them. I also tune ET for the same reason. I submit there are two kinds of tuners, those that tune multiple temperaments and those that tune only one. Or, to phrase it another way, there are tuners that believe all temperaments have value, depending on venue, and there are tuners that believe they have found the one temperament that is superior for all music and all others are inferior. I suggest that the latter is the more limited expertise.
Regards,
They that have ears, let them hear....
Regards,
It would be quite boring to always hear pure intervals, or always hearing 13.7 cent intervals, or always hearing 40 cent intervals. There are many WT's, but they all share the same organization; more accidentals in the key, more tempering in the tonic thirds. It is a simple palette, and a very logical one that composers of the era could work with.
Posted by: Withindale

Re: HISTORICAL ET AND MODERN ETs - 11/08/11 10:52 AM

Ed

The link in your signature should be:
http://www.piano-tuners.org/edfoote/
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 11/08/11 01:22 PM

hmm, Ok, I think I changed it.
Thanks,
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 11/08/11 04:23 PM

Greetings,
I wrote, (poorly), "We hear logrhythmically, so the the level of stimulation is the same, regardless of the octave it is found in."

"Logarithmically" was the word, by which I mean that the phase difference we are calling beats, color, character, etc., is sensed not on a linear scale, but an exponential one. The 13 cents in the F3-A3 3rd is not sensed as any more or less stimulative than 13 cents in the A3-C#4.

Thirds control the harmonic color of the triad. There, I said it, so, if we need to debate that, please, somebody, anybody, call up another thread name!

The raising of pitch is often associated with increasing tension, and in ET, a move upwards is likely to have that effect. If, however, you are playing the F3 triad with a 8 cent third and modulate to an A triad with a 15 cent third, you are going to react involuntarily with a slightly higher degree of anticipation, (as in,"Where the heck is that Bb I am needing to hear!!?).
regards,
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 11/09/11 02:36 PM

Hi.

..."As I understand it, Alfredo holds the point that all 88 notes on a piano should be united in one whole, mathematically symmetrical unit. With this approach, there is no difference in the amount of tempering of the intervals."...

ED, it seems to early to talk about Chas ET, maths and beat symmetries, let's talk about ET in general. I needed to understand how you interpret ET (in general), and for this reason I wrote: In 12 root of two ET, in order to find something "equal" we have to translate the scale values in cents, but does that mean that "like intervals are tuned exactly alike"? Is that how you understand ET? For me, that is not even simplistic but a distorted representation, since we (you included?) temper ET thirds (and not only thirds) so that their beat rate speed can be progressive. What is "alike" then, in your view?

Today you reply:..."What is "alike" is the physiological effect. We hear logarithmically, so the the level of stimulation is the same, regardless of the octave it is found in."...

So you too say that ET thirds beat rate speed is progressive, but (you say) "…We hear logarithmically, so the level of stimulation is the same".

I now understand that you talk about "stimulations" and dissonances that go beyond the idea of "proportion". We do hear logarithmically, perhaps we are able to aurally detect a sense of proportion and this, in my view, is how we can tell whether instruments and singers are "in tune" or not. Now I understand that your argument it is not really "variety in beat rate speed", but dissonances that in WTs mess up that sense of proportion. You aim at consonant and over-dissonant intervals, so that we can get in and out that sense of proportion, so our emotions can flow. My emotions don't flow in the same way as yours and, in my opinion, once we get out of proportions, there is very little left that we can share.

..."Bill Garlick basically taught us that proper tuning was an 88 note temperament, though you cannot hear thirds as anything but dissonant below F2,(critical band becomes inclusive). The original width of the temperament octave was thus in control of the stretch throughout, the clarity of the octaves, the purity of the fifths, and the overall level of stimulation that the tuning can cause."...

How do you tune ET 4ths and 5ths, octaves, 12ths and 15ths? How do you expand your ET temperament octave? Did Bill Garlick tell you what the rules (outside the temperament octave) were, in order to achieve a "normal" 88-notes ET form? Did he tell you that we needed strict rules for the whole piano?

..."My point is that there is a physiological effect that humans exhibit when exposed to different levels of dissonance, and that this differentiation has musical value when a composer aligns his composition to take advantage of the effects of consonance and dissonance. These are the "harmonic resources" I spoke of , and I don't know of a clearer way to explain them than to say that the resources are differing levels of stimulation caused by differing levels of dissonance. It is scientifically proven we involuntarily respond to higher levels of dissonance with higher levels of attention, as measured by heartrate, blood pressure, galvanic skin response, pupil dilation and several other markers I can't recall. That composers would use strident keys for expressive-stimulative purposes and calm consonant keys for expressive-sedating reasons seems to me to be so logical that I haven't yet heard a more plausible reason for the key choices that were made between 1700 and 1900."...

You say "...logical" and "plausible reasons..."; I remember offering other plausible reasons but, in any case, "That composers would use strident keys for expressive-stimulative purposes and calm consonant keys for expressive-sedating reasons..." needs to be proved. You say: they had WT's; WT's had different key characters; thus composers exploited WT's for stimulative/sedating reasons. It becomes a problem when, against evolution and musical analysis, we need to prove the validity and the exclusivity of your sequenced points.

AC writes:
>You say that ET tuning, in Bach's days, was not "normal". Please, would you be able to tell what is today's "normal" ET tuning? .<<

..."Today's "normal" ET is a tuning that evenly divides the comma between all 12 notes. Why are we even discussing what ET is? No particular approach changes the fact that every third is equally dissonant, thereby obviating any variety of physiological effect."...

Lucky we can discuss what ET is. I was not asking about theory but tuning practice. As I have mentioned, ET is not the tempering of 12 notes only, but a precise geometry that must be extended to the whole keyboard; in order to expand the ET temperament octave, what you call stretching, tuners do not follow precise rules; consequently, each individual tuner (or ETD) tunes a variant of 12 root of two; sum up these elements and be sure that "normal ET" (the normal ET you would not discuss) does not exist.

AC: I give fundamental relevance to the entire amount of notes, of intervals and chords ready to be arranged (in our case) on the keyboard. All intervals, inside and outside the temperament octave, can draw precise beat curves; we can weave all beat curves into a unique form, namely a sound whole.<<

..."Ok, that means that any difference between keys is no more than a difference in pitch. One who doesn't recognize pitchs as identities, ("perfect pitch", which I do not have), will hear all keys as having the same level of stimulation."...

I'm afraid we are going in circles. That means that all intervals, also those wider than the octave, have their precise proportional tensions. This, if anything, is how we achieve variety of stimulations. And I'm sure, if you were to be "stimulated" you would like to think that all tensions, all dissonances are under control. Once again, for this to occur you need to rule the expansion of your temperament octave.

ED wrote>.. I am referring to the equality. If all your like intervals are not tuned exactly alike, it is not an equal temperament. If they are all tempered alike, there is no difference in the sound of like thirds, (unless you believe there is some magic that causes different keys to have different emotional qualities."<<

AC >, no magic but sensitivity. I do not think we need to theorize heavily tempered intervals anymore for the sake of contrast. Different keys do keep their different qualities on the basis of different levels of tension, established time after time by the fundamental tone and resonating within the entire sounding body.

..."Sensitivity to what? What are the "different levels of tension" that arise from the "fundamental tone". If you tune a piano in Chas tuning, but do it 100 cents flat from A-440, will the key of C maintain its level of tension, even though you are playing it a 1/2 up on the keyboard? I think not."...

I'm not sure I understand your question, in any case you can check (*): tune your version of ET, play Bb2 together with Bb4-D5-F5, and transpose all the equivalent to F2 and E3, perhaps you too will hear different levels of tensions.

AC: In 12 root of two ET, in order to find something "equal" we have to translate the scale values in cents, but does that mean that "like intervals are tuned exactly alike"? Is that how you understand ET? For me, that is not even simplistic but a distorted representation, since we (you included?) temper ET thirds (and not only thirds) so that their beat rate speed can be progressive. What is "alike" then, in your view? <<

..."What is "alike" is the physiological effect. We hear logarithmically, so the the level of stimulation is the same, regardless of the octave it is found in."...

You have related "levels of stimulation" to dissonances and beats variety. Now I know you'd like over-dissonances, yet I would never say that ET thirds sound alike.

AC: Perhaps you call "clarity" what I would call cacophony. At the end, you like pure thirds, you can explain 21 cent thirds, but you hate ET 13. something thirds because they sound alike. Mhhhh..?

..."The 13 cent third is an important size, it equates to the tempering in the key of A and Eb in most WT's. I don't hate any size thirds. I am simply disgusted by the loss of resolutions that having everything the same produces. I hate hearing music stripped of important effects for the convenience of tuning."...

Convenience of tuning? We are not discussing that, but tuning models and practice through history and at present times.

Ed:..."I think removing the haze of tempering that hangs over the equal temperament allows the true harmonic colors to be displayed."...

AC writes>Here we are again onto the "color" conjecture, plus "harmonic", plus "true". I know that you refer "color" to your "pain and pleasure" experience, and how some keys should sound better than others.<<

Ed..."You have misunderstood. I haven't said any key sounds better or worse. I have said that keys should have different characters, since they are used for different purposes in classical composition."...

It sounds like you are turning your conjecture into an axiom. This kind of "expansion" is a problem.

..."The only pain I experience is that of sheer boredom listening to music modulate into more of the same."...

Yes, I understand your pain. It happens to me too, when out of tune intervals modulates into more of the same.

..."Color is a metaphor, "true harmonic colors" refers to the distinct sounds produced by intervals of different sizes. In an ET, of any persuasion you care to create, there is not physical difference between the keys, and we are left to sense the effects of modulation from an intellectual perspective, only."...

What is more intellectual than the abstract representation of an ET model that nobody could put into practice. I think you are not considering the gap between the first ET and our tuning practice, then you may suffer from the effects of your own perspective.

..."In a WT, that same modulation carries more information, and much of that information is sensual, not intellectual. The sensual difference is where the WT has the advantage, and for me, the enjoyment of music is the sensual experience. When I am listening, I am not trying to think, I am trying to feel."...

For me that information might not be sensual at all. You translate WT informations and your sensual experience into WT vs ET differences, this is intellectual. In regard to music, I'm sure everybody would go for feelings.

AC> > But doesn't "harmonic" (from harmonia, “joint, union, agreement, concord of sounds”) recall the USA motto "E pluribus unum", "Out of many, one"? And if "harmonic" refers to "one", if it refers to a "whole", which UT or WT, out of dozens, displays "true harmonic alternation of pain and pleasure"? <<

..."In the search for universal truth, we are always tempted to simplify. In music, harmony is not referring to "one", but rather, to the result of blending dissimilar pitches."...

We agree then, "the result of blending..." as one.

..."Tempering creates a vibrato. Would it be boring is a singer was always using the same speed of vibrato? I think so. A skillfull vocalist will match differing levels of vibrato to the intent of the music."...

Again, we agree!

..."Horn players use various pitches for the same note, depending on the score. I submit composers used various keys for various intentions. Reducing the keys to the same tempering robs the music of effect. But not for all listeners, just the ones that have awakened to the additional complexity and richness that the WT palette offers."...

Try the experiment above (*), then tell me whether the vibratos are the same or what.

..."I am not tuning WTs because I like them, I am tuning them because paying customers love them. I also tune ET for the same reason."...

Really? Well, that is not my case. Leave my customers aside, I love Chas and the preparatory tuning.

..."I submit there are two kinds of tuners, those that tune multiple temperaments and those that tune only one. Or, to phrase it another way, there are tuners that believe all temperaments have value, depending on venue, and there are tuners that believe they have found the one temperament that is superior for all music and all others are inferior. I suggest that the latter is the more limited expertise."...

Two kinds only?

Regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/02/12 04:44 PM


Hi,

I'm glad to be able to share the recording linked below: W.A. Mozart - Sonata in Do maggiore KV309

http://www.mediafire.com/?lbryz9ale6aha2n

Here I would like to thank the artist, Federico Colli, and his father, both people of rare sensitivity.

Regards, a.c.
.
Posted by: Grandpianoman

Re: HISTORICAL ET AND MODERN ETs - 02/02/12 09:30 PM

Very enjoyable Alfredo. Is this Chas?

I guess it's my 'expert' tuning ear that I have acquired since learning how to tune....lol....there are a few treble unisons out...its a bit disconcerting every time they are struck...never the less, the piece is very pleasant to listen to...and I enjoyed their interpretation.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/03/12 05:14 PM


Hi Grandpianoman,

You are welcome. Thank you for your comment, I too find that recording very enjoyable, that's one of the reasons why I decided to share it despite some tuning and voicing imperfections. One month later this young pianist, Federico Colli, won the 1st prize at the 2011 Mozart International Piano Competition, in Salzburg.

Another reason is that it is not so frequent to be able to release a recording in this way, and I think it is very generous on Federico Colli's part getting involved in the divulgation of Chas ET.

A third (major) reason is this sonata's tonality - C major - which historically is thought as the "home" key (!), together with the interpretation's speed which I find a little bit slower than usual, so making our possibly severe "listening" easier. Perhaps this sonata too can offer one more chance to deepen on some recurrent tuning issues, like cadenza, or on consonant and dissonant chords, home-key locking, on stimulations, emotions, in tune, sound whole, on true or perfect ET, and on some other arguments and clichés that we are discussing in this thread. I look forward to knowing your thoughts.

Chas ET recordings of Chopin, Schumann and Stravinsky are available on Chas website, what would you start with?

Regards, a.c.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/22/12 07:13 PM


Hi All,

From another thread:

#1848259 - February 20, 2012 05:43 AM
Re: Better unison makes louder?

[Re: Weiyan] rxd: ..."Our wide M3rds, for example, are regarded as a problem inherent to in equal temperament. It is anamolous that players of melodic instruments and singers hear them even wider. Its inversion, the minor 6th they want to play or sing very wide (melodically) and is more of a 'problem' with ET. This is where unequal temperaments really gain favour with singers."...

Hi rXd,

May I ask you to expand on the above statements? Ordered one by one:

1 - Our wide M3rds, for example, are regarded as a problem inherent to in equal temperament.
2 - It is anamolous that players of melodic instruments and singers hear them even wider.
3 - Its inversion, the minor 6th they want to play or sing very wide (melodically)...
4 - ...and is more of a 'problem' with ET.
5 - This is where unequal temperaments really gain favour with singers.

Regards, a.c.
.
Posted by: rxd

Re: HISTORICAL ET AND MODERN ETs - 02/25/12 06:29 PM

Sorry. I don't normally follow temperament threads and I was only just told this was here. The intervals of vertically structured temperaments and the melodic intervals as perceived and performed by say, gypsy violinists and opera singers simply cannot be reconciled.

Shifting pitch bases is the answer to this quandary. I am currently researching the BBC archives for a recording that exemplifies this extremely well.

I remember being called in to a piano trio recording where the musicians could not understand why the 'cellist had a few measures solo and his final note did not match the piano entry. His intonation in the solo was exemplary string players intonation. So much so that he gained pitch in the few measures that he played alone. I advised him not to play a minor 6th not quite so wide and a he finished in tune with the piano. It took a great deal of concentration on the 'cellists part but he was not "wrong". The result is out there on a commercial recording somewhere. I didn't think enough of it to remember the label never thinkng that this information might one day become useful.

A little thought would make it evident that, even if I had re-tuned an unequal temperament on the piano, this problem would still exist, perhaps in a more exagerated form.

This has little to do with the title of this thread but I am willing to expand on this should anybody be interested.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/27/12 05:57 AM


Thank you, rXd, for your reply.

Yes, I'm interested in knowing your thoughts, hearing about your own tuning experience and analyzing some conclusions, and I hope some other colleagues too are willing to share their own experience and deepen on one crucial issue, namely "intonation".

You said: …"The intervals of vertically structured temperaments and the melodic intervals as perceived and performed by say, gypsy violinists and opera singers simply cannot be reconciled."…

That seems to recall two kinds of "intonation", one for vertical chords structures and a second one for horizontal melodies, based on how intervals are perceived. Is that what you are referring to?

You kindly reported one case and said: …"His intonation in the solo was exemplary string players intonation."…

Do you have other cases? What would you say is "string players intonation" like?

And, if you would like, we could cover some other questions from your other post (above), at your convenience:

Who does regard our wide M3rds as a problem? Do you?
Would you yourself hear ET wide M3rds even wider?
How wide would players of melodic instruments and singers hear minor 6ths?
How do you expand your equal tempered octave?
Where do unequal temperaments gain favour with singers? Do you refer that to UT 6th? To one precise key?

Regards, a.c.
.
Posted by: Coolkid70

Re: HISTORICAL ET AND MODERN ETs - 02/28/12 02:00 PM

Originally Posted By: alfredo capurso

In all this sharing, I would like to make one point and three questions.

In my opinion, 12th root of two ET may well be considered a Historical Temperament too, since it pays for the "pure octaves" ancient dogma, and today it could well be referred to as the first algebraic/geometrical model, just by acknowledging other new ET models.

Why do I get the impression that Time stopped with 12th root of two ET?

People featuring non-equal temperaments or UTs say that they have more "colour", that "tempering" from just results in (in meaning) tone's colour. This may be fair enough. Personally, I'm in favour of beats and you may well know why.

What I do not understand is: what is difficult about acknowledging modern ETs, i.e. new algebraic geometrical models, new degrees of harmoniousness, new tonal effects, new spectral fusions, and accepting that also 12th root of two ET could evolve, actually it has evolved.

What is then "true" ET?
Does (in your opinion) modernity make people giddy?

a.c.

.


I know that this thread was started a few years ago, but I see that it is still active. I'm not a piano technician or tuner, but I am a graduate student in mathematics who studies number theory and a bit of music theory. I saw a few posts talking about / questioning the validity or long-time-use of the 12-TET tuning system. If you anybody is willing to deal with some basic high school mathematics and is interested in the subject, I can try to illuminate the construction of 12-TET to show where it comes from and at the same time explain its strengths and weaknesses.

Just let me know!
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/28/12 06:55 PM


Hi Coolkid70,

It is very kind of you offering your knowledge and mathematical tools in order to expand on our (can I say?) historical ET and, as you say, on "the construction of 12-TET". I'm sure that like myself, many tuners and musicians will appreciate that, if not all.

You also mention "...where it comes from...", "...its strengths and weaknesses.", I look forward to reading about that too.

Thank you, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/20/12 07:33 AM


Hi All. I would be happy to be able to deepen on an issue that was recently being discussed in Jeff's thread:

#1863436 - 03/16/12 11:35 PM Re: "I've made up my mind about Bach's WTC and ET"

Originally Posted By: Alfredo
I'd rather talk about the "lack introduced by" having to manage the wolf, both in theory and practice. And whether you sing in a choir or play in an orchestra, or brass or wind band... you'd still have to manage complex chords, correct?

Tunewerk wrote: ..."Actually, you just rephrased exactly what I said. The wolf results from the keyboard compromise.

In a choir, you do not have to manage this. This is a critically important technicality.

Voices auto-adjust to find pure intervals or complex chords adjusted within themselves for optimum consonance. It is the fixed scale that forces the wolf compromise.

A choir is the same thing as an auto-adjusting keyboard would be: each string moving slightly to accommodate the new chord for the desired effect or consonance."...

- . - . - . -

I apologize, I realize that I was jumping from one issue to another one, so perhaps I should first re-state my point: There is no way we can sing three (or more) notes simultaneously, and obtain pure (perfectly consonant) intervals only. In other words, when more than two notes are played simultaneously, we end up having to face the same (fixed scale) problem: how do we (referring to any ensemble) make complex chords sound "in tune"?

Originally Posted By: Alfredo
What about violin players or singers, when they practice... do they (think about the 9 commas between whole tones)?

Tunewerk wrote: ..."Yes, they do. But they do not typically know it. The advanced players do know this and understand. They auto-adjust to 9 commas or more to get correct intonation on specific intervals and scales. This is what makes a great violinist."...

Well, I have a different opinion, perhaps based on my personal observation and experience: singers and all bows, actually all ear equipped musicians, practice in order to get correct intonation not on specific intervals, as if they were to prefer pure intervals, they practice intonation and scales within the whole tonal complexity. But I agree, they do not typically need to know, and yes, great musicians are capable of "bending" notes consciously (on lyrical (slow) passages only), depending on the desired effect or perhaps in the effort to improve the ensemble overall intonation. Is this what you mean, that fixed tone instruments cannot improve the overall intonation in real time? I would agree.

But in general, in my view, when going for "correct" intonation, we do not refer to pure consonance anymore (as that is simply not possible, unless we are willing to crash other intervals), but to the best distribution (allocation?) of all commas, that is also what we (would) do on fixed tones instruments.

I know I'm going against a well established idea, that non-fixed tone instruments can "adjust" or as you say "auto-adjust", and so achieve better/correct intonation in absolute terms but, if this is what you think, I ask: isn't all this related to the questionable idea that intervals, at least some intervals, in order to sound "in tune" should be pure? Isn't it true that pure consonant intervals would cause other intervals be less consonant? In case more than two notes are played simultaneously, what would they try to adjust on?

Regards, a.c.
Posted by: Tunewerk

Re: HISTORICAL ET AND MODERN ETs - 03/20/12 10:22 PM

Hey Alfredo,

I just stumbled upon this. I'm honored that you would consider reposting my information, and of course you are welcome to.

I am posting here because I want to clarify and not be misunderstood. It's difficult to talk about abstract concepts on this message board where one cannot interject to clarify..

Originally Posted By: Alfredo
There is no way we can sing three (or more) notes simultaneously, and obtain pure (perfectly consonant) intervals only. In other words, when more than two notes are played simultaneously, we end up having to face the same (fixed scale) problem: how do we (referring to any ensemble) make complex chords sound "in tune"?


This is possible. It just requires movable, unequal divisions in-between. Let's run a little mathematical proof:

Let's say we have a choir at our disposal and order a perfect open fifth to be sung:

Tonic Voice = 1
Harmony #1 = 3/2

Here we have two notes and one interval interaction [2,1].

Now, we add a third:

Tonic Voice = 1
Harmony #1 = 3/2
Harmony #2 = 5/4

Now we have three notes and three interval interactions [3,3].

Let's look at it. We have the tonic note, at 1, the perfect M3rd at F1*[5/4] and the perfect 5th at F1*[3/2]. That's two relationships, so what about the third? This interval is described by [3/2]*[4/5], which equals exactly [6/5], the perfect m3rd.

The reverse justification, which might be easier to think about is [5/4]*[6/5] = [3/2].

Extending outward for all chordal combinations, this runs a geometric progression of [(n^2-n)/2]:

[1,0]
[2,1]
[3,3]
[4,6]
[5,10]
etc..

So, let's look at another chord, this time with 4 notes:

Tonic Voice = 1
Harmony #1 = 3/2
Harmony #2 = 5/4
Harmony #3 = 9/5

This is more interesting, adding on the most common pure ratio approximation for the just dominant 7th. Point 4 from our series yields 6 interactions, so we should list them out:

F1*[3/2] = perfect 5th
F1*[5/4] = perfect M3rd
F1*[9/5] = perfect d7th
[3/2]*[4/5] = [6/5] perfect m3rd
[9/5]*[2/3] = [6/5] perfect m3rd
[9/5]*[4/5] = [36/25] = [6/5]^2 two perfect m3rds

To get deeper into other chordal combinations yields the same result: non-irrational pure interval consonances. I have not completed a mathematical proof out to infinity, but these relationships are well known in analytic number theory.

Any combination of rational consonant values, will have rational consonance in-between. The consonance may be thin, but it will be a traceable pure rational interval.

Another way to think about it is: Each time a vocal chord is formed, a new geometric shape is being formed mathematically. The consonance ratios build the sound outwards into a distinct shape that by law of its rational parts, has complete consonance through and within.

This is not to say there wouldn't be any beats.. depending upon the harmonics generated by the voices. Any closely coinciding partials will generate beats and one would have to calculate the intensity, bandwidth and location of all generated partials within relative proximity to see if a few intersected close enough to cause beat effects.

Standard equal temperament aligns all notes by the equal logarithmic division of the 2^x curve. This produces irrational frequency values (numbers not generated by an integer ratio), constrained to the 2^x curve. Combining these fixed tones in chord structures introduces beats into any chord, except for octave derivatives, because none of the other ratios align to the 2^x curve (only 2/1). Further misalignment is found as partial value is increased.

If the resolution of the 12-TET scale were increased, this would help the problem, the best solution being 53-TET under the 60-tone division threshold. However, finer division will never purely solve the problem, it will only introduce finer levels of hysteresis around the 2^x curve. I posted earlier about this. Here's an image of what's going on in standard cents:



If a flexible string instrument were used, the geometries could change for each harmonic and melodic alignment to provide perfect consonance continuously with new geometries internally aligned, not preformed to the 2^x curve. Each time the chords changed, the frequency values would shift.

I suppose this takes off directly into derivation of the 12-tone scale and its mathematical basis. Here's an illustration I previously posted as well, showing total deviation in relative cents (1/100 of the native semitone) for all ET octave division schemes up to 120-TET.



It's clear, from the deviations shown, for all note division schemes under 18, 12-TET is the best solution. I wonder how this was first found empirically?

These are all the inclusive major deviations for ET schemes up to 1000-TET. The lower the dot appears, the purer the yield that scale division provides. Good scales could be thought of as those that yield lower than 40 relative cents cumulative deviation for the 4 major intervals.

Posted by: Coolkid70

Re: HISTORICAL ET AND MODERN ETs - 03/21/12 02:58 AM

Thanks for some of the empirical results, Tunewerk. I've been meaning to get around to posting some material myself, but I've been very busy with my own work.

There are a few things that I'd like to comment on that are a little bit strange, from the professional mathematics perspective.

Quote:

Extending outward for all chordal combinations, this runs a geometric progression of [(n^2-n)/2]:

[1,0]
[2,1]
[3,3]
[4,6]
[5,10]
etc..

So, let's look at another chord, this time with 4 notes:

Tonic Voice = 1
Harmony #1 = 3/2
Harmony #2 = 5/4
Harmony #3 = 9/5

This is more interesting, adding on the most common pure ratio approximation for the just dominant 7th. Point 4 from our series yields 6 interactions, so we should list them out:

F1*[3/2] = perfect 5th
F1*[5/4] = perfect M3rd
F1*[9/5] = perfect d7th
[3/2]*[4/5] = [6/5] perfect m3rd
[9/5]*[2/3] = [6/5] perfect m3rd
[9/5]*[4/5] = [36/25] = [6/5]^2 two perfect m3rds

To get deeper into other chordal combinations yields the same result: non-irrational pure interval consonances. I have not completed a mathematical proof out to infinity, but these relationships are well known in analytic number theory.


You use terms here like "geometric progression" and "analytic number theory", but I'm pretty sure that isn't what you mean - neither of those terms apply here. But in any case, in the first part of this quote, it seems to me that you are trying to count the number of pairs of tones (i.e. dyads) you can make if you have N tones to work with. If this is the case, there is a result from combinatorics / graph theory called the Handshake Lemma which gives you the correct formula. The Handshake Lemma says that if there are N people who want to shake hands with one another, there will be a total of N(N-1)/2 (or equivalently, (N^2-N)/2) handshakes. This is exactly the formula that you were trying to justify (thinking of a dyad combination as a handshake).

In the second part of the quote, you say that multiplying combinations of rational numbers will be "non-irrational". Actually, this is true almost by definition of rational numbers and their arithmetic. To prove this, take two fractions a/b and c/d. Then, (a/b)*(c/d) = (ac)/(bd), which is rational. That this is true for any (finite) number of multiplications should be clear.

Quote:
I suppose this takes off directly into derivation of the 12-tone scale and its mathematical basis. Here's an illustration I previously posted as well, showing total deviation in relative cents (1/100 of the native semitone) for all ET octave division schemes up to 120-TET.

[A chart was shown here]

It's clear, from the deviations shown, for all note division schemes under 18, 12-TET is the best solution. I wonder how this was first found empirically?


There is actually a way to analytically obtain the result that 12-TET is the one of the best rational approximations for the exponential function that you referred to a few times. (You can do better if you are willing to accept more tones.) I hope to be able to say more about it when I get the time. The solution uses some basic arithmetic and logarithms, so I hope that it will be accessible.

Thanks again for the neat charts and information!
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 03/21/12 03:08 AM

Originally Posted By: Tunewerk
non-irrational pure interval consonances. I have not completed a mathematical proof out to infinity, but these relationships are well known in analytic number theory.

This reminds me somehow a DVD I have of a show on the Riemann hypothesis which was called "music of the primes" I think.

Looking forward to what you and Alfredo come up with next in this thread.

Kees
Posted by: Tunewerk

Re: HISTORICAL ET AND MODERN ETs - 03/21/12 03:55 AM

Thanks for telling me what I was trying to do, Coolkid. wink

I look forward to hearing your insights.

Yes, Kees, definitely. I hope to hear some of your thoughts also.
Posted by: UnrightTooner

Re: HISTORICAL ET AND MODERN ETs - 03/21/12 08:55 AM

I am enjoying this discussion, too. Just remember that when inharmonicity is a factor, things change.
Posted by: Coolkid70

Re: HISTORICAL ET AND MODERN ETs - 03/21/12 10:35 AM

Originally Posted By: DoelKees
Originally Posted By: Tunewerk
non-irrational pure interval consonances. I have not completed a mathematical proof out to infinity, but these relationships are well known in analytic number theory.

This reminds me somehow a DVD I have of a show on the Riemann hypothesis which was called "music of the primes" I think.

Looking forward to what you and Alfredo come up with next in this thread.

Kees



I've heard Terrance Tao (a Field's medalist) describe the distribution of primes in this manner, in reference to the complex-analytic proof of the prime number theorem. (It states that the number of primes less than or equal to x is roughly x / log x.) The idea is to define a function that is "noisy" on prime numbers only, that is, it spikes up when it touches a prime (or prime power) and is zero otherwise. Then, you smooth it out with a signal transform (akin to things like Fourier transform in signal processing), and then you can apply tools from analysis to determine its behaviour, which eventually leads to the x / log x estimate.

Originally Posted By: UnrightTooner
I am enjoying this discussion, too. Just remember that when inharmonicity is a factor, things change.


Definitely. I think that the program is really to explain where the theory of ET comes from, so that we have some justification for why some version of it is sought after in practise. (Unfortunately, what we want in theory isn't always what we get in real life!)
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/21/12 05:42 PM


Thank you All.

Tunewerk wrote:…"It's difficult to talk about abstract concepts on this message board where one cannot interject to clarify.."…

You are right, and it is very kind of you making an effort.

Originally Posted By: Alfredo
There is no way we can sing three (or more) notes simultaneously, and obtain pure (perfectly consonant) intervals only. In other words, when more than two notes are played simultaneously, we end up having to face the same (fixed scale) problem: how do we (referring to any ensemble) make complex chords sound "in tune"?

…"This is possible. It just requires movable, unequal divisions in-between."…

I'll use your way, Tunewerk, and give a basic example in order to explain briefly what I was referring to:

Tonic voice, at 1;

I'm asked to sing the P5th, at F1*(3/2);

You are asked to sing a M3rd two octaves above the tonic, that is a M17th.

Using pure (consonance(?)) ratios, you can calculate different values for your M17th, for example:

F1*((3/2)^2)*((4/3)^2)*(5/4) = 5
or
F1*(3/2)^4 = 5.0625
or
F1*(5/4)^7 = 4.7684…
or
F1*(3/2)*(4/3)*(5/4)^4 = 4.8828…

If you calculated the P5th backwards, from your M17th = 5 you would not get 3/2. How would you move unequal division in-between? Which is the consonant M17th?

..."...the program is really to explain where the theory of ET comes from, so that we have some justification for why some version of it is sought after in practise."...

Good thing, thank you Coolkid70.

Regards, a.c.

P.S.: For those who are familiar: "THE RULE BEHIND THE OCCURRENCE OF PRIME NUMBERS"
Matteo Arpe - Claudia La Chioma

pdf available in the web.
Posted by: Tunewerk

Re: HISTORICAL ET AND MODERN ETs - 03/22/12 02:36 PM

Well, it's true, in these cases you sacrifice one major harmony for another. In the examples you gave, using harmonies built on 5, 4, 7 and 6 voices respectively, the last 3 differ from the first, in that you use sections of a curve instead of the ratios as points, with complementary parts* (which usually occur in natural chords).

If a choir did sing these strings of 5ths 4ths or 3rds, they'd have to temper their intervals to achieve a 5/1. However, the difference between that and the piano, is all harmonies would be built on rational interference between waves.. meaning at least one wave pair in ratio, from each dyad, would constructively interfere.

You may have [3/2]^4 = [81/16], but this is still a consonance, just a thinner one. At some point the ear decides the constructive alignment is too thin and it becomes a dissonance.

Without being confined to the irrational frequencies of the 12-tone [2/1] curve, there are no fixed compromises based on one curve, and every frequency can adjust and build to a new chord based on the best possible divisions. This is what I meant by movable and unequal.

That is not to say there would not be compromised choices, but all curves would be available to micro adjust by, and all compromises would result in some kind of rational interference, which by definition is always consonant.

PS - Alfredo, thank you for the primes paper. I'm going to take a look. I wasn't aware that the distribution pattern for the primes had been solved.

* Complementary intervals, as I call them, are a really interesting concept. Many intervals we have come to regard in music arose from subdividing larger intervals. For example, the m3rd [6/5] is the source of the M6th [5/3], from the point division of the octave [2/1]. This is literally the source of that interval. This brings to mind that any integer ratio [n/n] is consonant. The question is only the degree, which regards psychoacoustics instead.

The ratio [n+1]/n is the smallest way to define consonant intervals, but it isn't the only source. As a result of interval splitting, most chord consonance was built around these structures. Perfect consonance could happen through this. This is what I was alluding to through the concept of geometric structure. In most, if not all common chord combinations, compromises are unnecessary because of this unequal but symmetric division of tone.

I would argue that it was the mechanization of music on keyboard instruments that resulted thinking in terms of compromises bound to curves as opposed to naturally evolving and changing tone structures, consonant within themselves.
Posted by: Coolkid70

Re: HISTORICAL ET AND MODERN ETs - 03/22/12 06:44 PM

Originally Posted By: alfredo capurso

P.S.: For those who are familiar: "THE RULE BEHIND THE OCCURRENCE OF PRIME NUMBERS"
Matteo Arpe - Claudia La Chioma

pdf available in the web.


I skimmed through this paper, and I actually failed to see what the point was. It seems like the authors are just restating the Sieve of Eratosthenes using some modern notation. I didn't see anything obvious about the distribution of prime numbers. Could you maybe point out what I need to be looking for?
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/24/12 10:39 AM


Hi Coolkid70,

You'll be able to read about the authors point in section 1, page 2 and 3.

Hi Tunewerk,

Thanks for your attentive reply. On the first half:

..."Well, it's true, in these cases you sacrifice one major harmony for another. In the examples you gave, using harmonies built on 5, 4, 7 and 6 voices respectively, the last 3 differ from the first, in that you use sections of a curve instead of the ratios as points, with complementary parts* (which usually occur in natural chords).
If a choir did sing these strings of 5ths 4ths or 3rds, they'd have to temper their intervals to achieve a 5/1."...

Ok, that's the point I wanted to "fix": in general, any ensemble (choir included) in order to sound harmonious must temper their intervals. In other words, the necessity to temper intervals derives from having to combine prime-numbers ratios, 2/1, 3/2, 5/4, etc (that's the centuries-old problem). Now we may have to reason on how all intervals can (should) be tempered within a steady, coherent geometry.

..."However, the difference between that and the piano, is all harmonies would be built on rational interference between waves.. meaning at least one wave pair in ratio, from each dyad, would constructively interfere."...

Perhaps I do not understand: Would they choose to play "at least" one pure ratio? You say "one wave pair in ratio, from each dyad, would constructively interfere", meaning "interfere" what on?

..."Without being confined to the irrational frequencies of the 12-tone [2/1] curve, there are no fixed compromises based on one curve, and every frequency can adjust and build to a new chord based on the best possible divisions. This is what I meant by movable and unequal.
That is not to say there would not be compromised choices, but all curves would be available to micro adjust by,..."...

Indeed, what we understand from literature is that (1) non-fixed instruments have a higher degree of freedom in that they can always "adjust"; and we are told that, as a consequence, (2) non-fixed instruments can achieve a higher degree of consonance, and that (3) only fixed-tones instruments need to "compromise".

Point (1): Once we "fix" the reference, i.e. the "common" pitch (A4 or any other note), what would they "micro adjust" on? Would they favor one interval? Which one? Which "unequal" variant, amongst many, will represent THE "ad-just-ed" chord geometry?

Point (2): Do they sing/play along chord-by-new-chord consonance? Say yes, which is the "new chord" best possible division? (edit: would that be the next "new" compromise?)

Point (3): We have seen that also non-fixed ensemble need to compromise, we can see why. You say: ..."all compromises would result in some kind of rational interference, which by definition is always consonant."...

Please, could you give an example of one "kind of rational interference", so I'll be able to understand what you mean?

...* Complementary intervals, as I call them, are a really interesting concept."...

I agree, only I have to postpone my reply.

Regards, a.c.
Posted by: Tunewerk

Re: HISTORICAL ET AND MODERN ETs - 03/24/12 04:17 PM

Very glad to, Alfredo. I'm interested in thinking through these things.

Originally Posted By: Alfredo
Ok, that's the point I wanted to "fix": in general, any ensemble (choir included) in order to sound harmonious must temper their intervals. In other words, the necessity to temper intervals derives from having to combine prime-numbers ratios, 2/1, 3/2, 5/4, etc (that's the centuries-old problem).


Well, where this is true in a static example.. can you name one piece in choir music, where a choir sings stacked M3rds, 4ths or 5ths to that degree? Even if it is the case, then they do not also try to sing the octave or M17th.. they already have a rational harmony for that chord. They simply choose one rational harmony over another.

The prime number ratios only need to be tempered when treating them as curves and not scalars. If prime number ratios are combined with their complementary ratios, within other intervals, then tempering is unnecessary.

Tempering occurs when you define any scale by one prime number ratio (or a composite, but those are just composed of primes). If you do not define a scale, then you do not have temperament problems. The age old problem is true, but I think a little short sighted.

Euler once said, "Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate."

I think this is similarly the level of difficulty in visualizing and understanding the temperament problem.. why it hasn't been resolved for centuries. The underlying structure of temperaments are based on the primes and the composites that contain them. The very aligning of wave patterns works the same as the Sieve of Eratosthenes. Very similar problems, in the deep underlying structure.

I was looking into Harry Partch's work the other day and I was reminded of an important term he created, called 'limit' - or upper bound to the complexity of harmony. This term is extremely accurate and useful because it's been applied through the ages but only recently was the concept realized.

Limit is essentially the same concept as in the Sieve of Eratosthenes, when to find all the factors of a term, you only have to define all the primes up to the square root of that number. The largest prime in this case, would be the limit.

The largest prime in the denominator of the harmony ratio roughly defines the resolution of the scale necessary to contain the limit.. or the structure of the unequal temperament necessary. In our music, with 12-TET, we are generally 5-limit. The 3rds contain the prime 5 in their harmony as well as their complementary 6ths. I wouldn't go so far to say that our scale is 7-limit because the tritone is more a figment of the scale which was chosen for its alignment to the 4th and 5th.. not for the ratios 7/5 or 10/7 (lesser and greater septimal tritone).

Harry Partch composed mostly off the 43-tone scale in 11-limit harmony. If you look at the above illustrations I posted, you can see the 43-tone scale.. however, I was only analyzing to 5-limit.

1) There is no single adjusted chord geometry. Or a single fixed pitch. One starts on pitch, but may not end on the same pitch. The natural form of music (before unnatural fixed scales) was a flexing, moving geometry through time. Chords grew out of one another, perhaps never repeating exact note twice. When the concept of fixed notes did not exist, there was only ratio.

2) I'm not sure what you're saying here, but the chord geometries simply adjust to the new desired position to get the effect wanted. Since all harmonies would be rational, it is only a matter of which rational harmony to choose from. Tempering is not necessary.

3) No. Non-fixed ensemble does not necessarily need to compromise. They only need to choose. Since all harmony can be rational, they only make musical choices, which then alter the note frequencies slightly.

An example of rational interference is any whole number ratio of base frequencies that produces an interval: 2/1, 3/2, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8, 10/9, 11/10 - or - 3/1, 5/3, 7/5, 9/7, 11/9 - or - 4/1, 5/2, 7/4, 8/5, 10/7, 11/8 - or - 5/1, 7/3, 9/5, 11/7, etc..
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/25/12 09:32 AM


Hi Tunewerk,

I too am enjoying your posts.

Originally Posted By: Alfredo
Ok, that's the point I wanted to "fix": in general, any ensemble (choir included) in order to sound harmonious must temper their intervals. In other words, the necessity to temper intervals derives from having to combine prime-numbers ratios, 2/1, 3/2, 5/4, etc (that's the centuries-old problem).

..."Well, where this is true in a static example.. can you name one piece in choir music, where a choir sings stacked M3rds, 4ths or 5ths to that degree?"...

You are right, perhaps it was a "static" example, but in order to make my point I intended to use simple numbers; I'd appreciate if you could show me which "unequal" variant, amongst many, would represent THE "ad-just-ed" chord geometry. As for singer examples, I'd try not to mix theory with general practice, because then it may really get subjective, depending on individual skills. Nevertheless, you (All) may judge and decide the degree to which an ensemble "stacks" intervals, we are all allowed to our own opinion.

‪I'm sure you'll enjoy Monteverdi's - "Si dolce è'l tormento"‬:
http://www.youtube.com/watch?v=g6e43zjwGr8

..."Even if it is the case, then they do not also try to sing the octave or M17th.."...

Well, in my view either it is the case - so ensemble too need to temper and compromise - or it is not. On top of that, I do not understand that line.

..."...they already have a rational harmony for that chord."...

Take my example above, please would you put "rational harmony" and new chord "best possible division" in simple numbers?

..."They simply choose one rational harmony over another."...

Do you refer to some "rational harmony" which they would have agreed on? Hmmm...

..."The prime number ratios only need to be tempered when treating them as curves and not scalars. If prime number ratios are combined with their complementary ratios, within other intervals, then tempering is unnecessary."...

I'm a bit confused, are you thinking in terms of intervals "within other intervals"?

..."Tempering occurs when you define any scale by one prime number ratio (or a composite, but those are just composed of primes). If you do not define a scale, then you do not have temperament problems. The age old problem is true, but I think a little short sighted."...

I see. In my view, even before the definition of a scale, the problem originates from multiple intervals combinations; as I could show in my other post, tempering becomes an evident issue every time you play more than two notes simultaneously. And yes, the problem was short sighted, due to the age-old equality "pure ratio = consonance = in tune", plus the unexpanded 2:1 octave module and the odd aversion for irrational numbers.

..."Euler once said, "Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate."...

BTW, have you had a look at that paper?

..."I think this is similarly the level of difficulty in visualizing and understanding the temperament problem.. why it hasn't been resolved for centuries. The underlying structure of temperaments are based on the primes and the composites that contain them. The very aligning of wave patterns works the same as the Sieve of Eratosthenes. Very similar problems, in the deep underlying structure."...

Well, I do not think that understanding the temperament problem is that difficult, nor mysterious. In Chas paper (section 1.2) it required a few lines only.

..."...Harry Partch's work..."...

Yes, interesting work although related again to pure ratios. I preferred to go for interrelated beats, where pure ratios (1:1, 3:1, 4:1) can justify and comprehend proportional deviations.

..."1) There is no single adjusted chord geometry. Or a single fixed pitch. One starts on pitch, but may not end on the same pitch. The natural form of music (before unnatural fixed scales) was a flexing, moving geometry through time. Chords grew out of one another, perhaps never repeating exact note twice. When the concept of fixed notes did not exist, there was only ratio."...

Even if that was the case, they still needed to combine intervals, in theory and in practice.

..."2) I'm not sure what you're saying here, but the chord geometries simply adjust to the new desired position to get the effect wanted. Since all harmonies would be rational, it is only a matter of which rational harmony to choose from. Tempering is not necessary."...

Hmmm..., I was asking: which is the "new chord" best possible division?

..."3) No. Non-fixed ensemble does not necessarily need to compromise. They only need to choose. Since all harmony can be rational, they only make musical choices, which then alter the note frequencies slightly."...

To me, this might be a respectable idea of yours; admittedly I'm a bit confused about your outlook. Is "harmony = rational" your fundamental premise? What happens to the frequency when they slightly "alter" the note? Will that still represent a whole integer ratio?

..."An example of rational interference is any whole number ratio of base frequencies that produces an interval: 2/1, 3/2, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8, 10/9, 11/10 - or - 3/1, 5/3, 7/5, 9/7, 11/9 - or - 4/1, 5/2, 7/4, 8/5, 10/7, 11/8 - or - 5/1, 7/3, 9/5, 11/7, etc.."...

I see. So, they agree on a single whole number ratio and forget about all other intervals?

Regards, a.c.

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Article by Professor Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte

Chas Tuning samples:
http://www.chas.it/index.php?option=com_content&view=article&id=64&Itemid=44&lang=en
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/01/12 02:54 AM


Hi All,

Quite an interesting article I found by chance:

The Foundations of Scientific Musical Tuning, by Jonathan Tennenbaum.

http://www.schillerinstitute.org/fid_91-96/fid_911_jbt_tune.html

And perhaps we will be able to expand on what is arbitrary-assumption and more...

Have a nice Sunday,

a.c.
Posted by: Robert Scott

Re: HISTORICAL ET AND MODERN ETs - 04/01/12 07:14 AM

Originally Posted By: alfredo capurso

Hi All,

Quite an interesting article I found by chance:

The Foundations of Scientific Musical Tuning, by Jonathan Tennenbaum.

http://www.schillerinstitute.org/fid_91-96/fid_911_jbt_tune.html

And perhaps we will be able to expand on what is arbitrary-assumption and more...

Have a nice Sunday,

a.c.

It is funny that something with "scientific" in the title so thoroughly abuses the notion of science. But I get it. April 1st, right? They do that in Italy too?
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/01/12 12:28 PM


Hi Robert,

Yes, here too is April 1st... how funny! I was surprised too, not only for the title, also for what the author asserts. I could only skimm it but found strange how things are ...mixed in? And the author seems to be an advisor... and that institute seems to really exist. Hmmm...

Regards, a.c.
Posted by: Jake Johnson

Re: HISTORICAL ET AND MODERN ETs - 04/01/12 01:25 PM

I understand most of the sources--Pythagoras, the music of the spheres, etc, and the strange mistakes (thinking that Helmholtz believed in a perfect partial series, for one, and that he originated the idea).

And I'm glad to know that earth is a G.

But from whence comes the notion that "A sound wave, we know today, is an electromagnetic process involving the rapid assembly and disassembly of geometrical configurations of molecules. In modern physics, this kind of self-organizing process is known as a 'soliton'"?

At first I thought he was he talking about how the force bumps air molecules against each other, but I get lost in his mention of an "electromagnetic process."

Thanks for the smile, Alfredo.
Posted by: Chris Leslie

Re: HISTORICAL ET AND MODERN ETs - 04/01/12 06:18 PM

Alfredo, I think we would be wasting our time discussing the arbitrary assumption from this pseudo-science rubbish.
Posted by: Jake Johnson

Re: HISTORICAL ET AND MODERN ETs - 04/01/12 07:13 PM

Originally Posted By: Chris Leslie
Alfredo, I think we would be wasting our time discussing the arbitrary assumption from this pseudo-science rubbish.


(Did you see that it was an April Fools day joke?)
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/02/12 01:50 PM


Hi, nice reading you.

Well, really I could not refrain... "...A=440 is an insane tuning...", "...The equal-tempered system is only an approximation of a rigorous well-tempered system whose details have yet to be fully elaborated."..., "...Our solar system functions very well with its proper tuning, which is uniquely coherent with C=256. This, therefore, is the only scientific tuning."... I thought I should share that with my PW friends!

But wait: some cited concepts and geometries have sense (on their own), also in relation to what can be observed in nature; it is wanting to prove the original conjecture that messes everything up. In the end though, what counts for Mr. Tennenbaum should count also for us… so, let's double check each other.

I look forward to being able to expand on "in tune" singing, "stacked intervals" and "best possible divisions".

Any idea?

Regards, a.c.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/13/12 09:50 AM


#1875203 - 04/07/12 02:29 PM
Re: Measuring Inharmonicity [Re: johnlewisgrant]

johnlewisgrant:

"dialoguing with myself..... within a few cents accuracy probably wouldn't even be noticed by the general public (who will only notice whether the unisons sound "nice")! So the question is papably MOOT for MOST tuning situations.

But for concert pianists in performance--with good ears to boot--the question matters A LOT.

Also, for fanatics like me, who just can't STAND the piano sitting in my home being even slightly out of tune, and I don't just mean the unisons!, it's also a big deal.

That's why we fork out the big bucks (relatively speaking) for these tuning programs: they permit us to keep our babies sounding as good as they possibly can at ALL times!!!

hence my question about microphones!!"

- . - . - . -

I would like to thank you, JG, for that post of yours. When I read it I suddenly felt less lonely. Today, after much discussing in this Forum, I realize that many issues about tunings and "out of/in tune" are messed up by some "literature" that is based more on fashionable opinions than provable facts. And I realize that my own approach, like you suggest, may well be described as "fanatic".

Curiously enough, I have been able to share my "in tune" sense with all musicians I've met, but when it comes to theory, practice, ETD's, non-unified few-cent-science and colleagues... I understand that some colleagues are ready to swear they would sing "pure" 3rds, they do not need to temper; others would offer and argue different (pure?) intonations for choirs and bow instruments, though when they are asked to prove their arguments some of them prefer to, what's the word, vanish? Many others seem to prefer a "home key" to a "whole-home" tuning, and say that we all (ear equipped music lovers) are able to tell whether some notes Are or are Not in tune..."and I don't just mean the unisons!".

I too happen to dialog with myself..., I too think that's a big deal, in my opinion too your question matters a lot, I too would not stand a piano being slightly out of tune, actually not only a piano but a singer too, a violin too, a harp too... hence my questions...

And thanks for your thread, I'm getting to know more about ETD's approximations and the so called "true" ET tuning. I better understand why the fixed-intonation of a piano can turn into a nightmare.

To All,

Last night I melted on my armchair, listening to the Italian TV News... I woke up on Rachmaninoff's concert n. 2, really enjoyed it, hope You like it too:

http://www.rai.tv/dl/RaiTV/programmi/media/ContentItem-725046ba-3c94-437a-b33d-27a2ab01feaf.html

Hi Tunewerk,

Would you say that bows adjust their intonation all over, perhaps every now and then? I haven't told you, but I think they Do stack all intervals, possibly all "in tune" intervals they have been practicing for long long years.

Here is a list of statements of yours (from 03/20/12) that I found confusing:

- If a flexible string instrument were used, the geometries could change for each harmonic and melodic alignment to provide perfect consonance continuously with new geometries internally aligned, not preformed to the 2^x curve. Each time the chords changed, the frequency values would shift.

- If a choir did sing these strings of 5ths 4ths or 3rds, they'd have to temper their intervals to achieve a 5/1. However, the difference between that and the piano, is all harmonies would be built on rational interference between waves.. meaning at least one wave pair in ratio, from each dyad, would constructively interfere.

- Without being confined to the irrational frequencies of the 12-tone [2/1] curve, there are no fixed compromises based on one curve, and every frequency can adjust and build to a new chord based on the best possible divisions. This is what I meant by movable and unequal.

- Tempering occurs when you define any scale by one prime number ratio (or a composite, but those are just composed of primes). If you do not define a scale, then you do not have temperament problems.

- There is no single adjusted chord geometry. Or a single fixed pitch. One starts on pitch, but may not end on the same pitch. The natural form of music (before unnatural fixed scales) was a flexing, moving geometry through time. Chords grew out of one another, perhaps never repeating exact note twice. When the concept of fixed notes did not exist, there was only ratio.

- the chord geometries simply adjust to the new desired position to get the effect wanted. Since all harmonies would be rational, it is only a matter of which rational harmony to choose from. Tempering is not necessary.

- Non-fixed ensemble does not necessarily need to compromise. They only need to choose. Since all harmony can be rational, they only make musical choices, which then alter the note frequencies slightly.

I look forward to knowing your (and all colleagues) thoughts and comments.

Regards, a.c.
.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 04/13/12 11:00 AM

Hi ALfredo,


I hope you are doing well, I am pleased to see you writing on that forum smile

as you are may be aware, I am deeply using your tuning approach and , lets say philosophy, since we meet a few sciecles ago.

Something I noticed about justness, if that what seem to add to the justness sensation, or impression, is the level at which the piano sound in phase with itself (and its environment).

Then, all depends of the instrument when we put it in front of an ET intention :

Some instruments will nicely use the space left by the iH and the deviations from straight "rule" to gently install themself in a self resonating system (as you state at 1/3 1/4 level equilibrium. Others, (very few in my experience) I've find, find that when the 12/15 equilibrium is attained, the octave begin to sound a little instable, less calm than with the plain 2:1 type of Japanese tuning for instance (which sound dull to my ears generally , so to say) . It may have to do with the level of iH and the voicing, but also for sure with the kind of tone reinforcement that the instrument and the room are able to accept (and certainly the room acoustics).
Well I had comments from some pianists that the tuning was not possibly what they prefer for their instrument, so, as I like and the method and the result, I begin to use a little water in the vine, that mean, I keep the temperament method, but stick to a shorter octave for the end of the mediums (when going up) , then, I chase for the resonance in the beginning of the treble, and so I have yet a little of both worlds, less active fast intervals progression, but a "stretch" based on the acoustical answer coming from the lower note of the Chas ratio.

I believe I have get so much used to that state of resonance and equilibrium that I refine it when tuning the unisons, that mean,if I am not aware of the sympathetic resonance of the lower note 12-15 my unison is not good. (sometime I use the tonal pedal to help, but it works without it, and the tonal pedal tend to make the notes tuned a tad too high (for what reason ?)**

There is something that happens when the Chas tuning is installed, the resonance is globally way stronger in all regions of the instrument. It tend to lower the contrast between portions of scale, so making a hair of step under Chas in the mediums leaves that contrast more apparent , while keeping the singing and clear treble present (one of the most evident feature of Chas, melody is always audible) for instance when the musical phrase begin in the mediums then raise to the treble there is an added impression, which makes the musical phrase more lively, in my impression).

I have been using the "pre tensionning tuning" method since our meeting, and I wait to find something more lmogical or more efficient, I stated it lately, I could make huge PR in one pass because of the very good habit to feel how much the notes will lower during the tuning ; when used to anticipate a few cts lowering and being sure it have nothing to do with string rendering of tuning pin settling back, it gets easy to feel what happens in the instrument, acoustically speaking. It makes the tuner very confident (and the result appreciated !)

The "how far from Chas resonance am I" test (it is simply an energy test most probably) is invaluable for many situation as instantaneously know where a note is while tuning...
Then it is also less tiring to have some "listening distance" from the fast intervals, chasing only for their progressiveness ans only a little for their real speed, those pesky intervals are playing the game nice generally and they fall gently in place one following the other, without me doing much effort in the direction of their speed, simply aligning the energy...

I would add something to my comment above, I suppose that , if we play with the unison opening (regulating the attack stabilization delay and the phase difference between doublets of strings at different times) we can take an instrument that originally ask for a dark romantic tone and push it in the Chas envelope nicely, to me I have been doing that constantly just because I appreciate to get the maximum energy coming from the rest of the instrument when a note is played. Some pianists (2 , up to this day, one with a Yamaha U and the other with a BOsendorfer 2.20) told me that they appreciate the more lively behavior of the instrument and that they are aware of the justness impression, but simply they find that slightly limiting for some reason they could not explain me, I had to chase by myself (all others tend to post me little mails saying that they never heard their instrument sounding so nicely and that they where not even aware it could sing as much !!) .

SO I looked for some reason, and I find that low IH instruments in a little dull environment seem to need close harmony in the medium range (may be only one octave and a half as A3 E5, that is the kind of zone I stay attentive to 2:4 resonance in that case). Probably, mostly the slightly faster thirds where too much noticed...

I Wish you all the best, I hope we meet again.

Friendly wishes

Isaac


Posted by: Tunewerk

Re: HISTORICAL ET AND MODERN ETs - 04/14/12 02:26 AM

Hello Alfredo,

The only reason I didn't respond further, is I noticed you defending your CHAS idea in light of my comments. What I said is really not related to your CHAS concept and I don't intend to threaten your beliefs or understanding. If anything, I have come to believe we may view tuning similarly based on our independent experience.

I also don't believe I could say what I intended to say any clearer.

I essentially drew a difference between open ensemble and fixed string instruments. Temperament is a problem for fixed string instruments.

Chorus and non-fretted string ensembles can require musical situations that involve temperament, but that is by choice. Proving this is exhaustive. All rational frequency combinations result in some form of consonance. No matter what pattern, this is true. The degree of consonance is the only question.

Fixed-tone instruments introduce irrational (beating) relationships when attempting to equally space tones on a single prime curve. These irrational relationships require temperament to find a solution of best fit.

I had some energy this morning to add on these ideas for the public forum, and I remembered that what is essential to what I am saying is the concept of movable tones. Pure progressive chord structures require note frequencies that shift slightly to account for their different internal interconnected ratios, as well as the leading tones that connect them.

Melodic lines tend to go sharp or flat depending on their direction. Cellos and violins rise in their intonation when playing upwards along a melodic line. They fall in their intonation when descending.

Without the harmonic constraint of a fixed scale, melody tends to be greatly expanded and chords can occur in new locations, as dictated by the progression of the melodic line.

To analyze keyboard music on this system becomes problematic because many tones, the 2nd and tritone for example, are germane to the 12-TET scale. Music composed in a system of temperament is then dependent largely on that system.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/14/12 05:06 PM


Dear Isaac,

I'm glad you are again taking part to this Forum and contributing with your feedbacks. Good news from your customers... I really think your success has to do with your own constant commitment, your passion and sincere desire for improvements. For some reasons, I feel more comfortable to reply to you privately. Be sure, I too look forward to meeting you again.

Un caro saluto,

Alfredo

- . - . - . -

Hi Tunewerk,

..."The only reason I didn't respond further, is I noticed you defending your CHAS idea in light of my comments. I don't intend to threaten your beliefs or understanding. If anything, I have come to believe we may view tuning similarly based on our independent experience."...

Thank you for your reply. I was ready to post mine... now I'd better read your latest adding and see if my reasoning can still make sense. I need to precise that my comment was not addressed to you, so I apologize for having been ambiguous.

I also need to say that Chas is basically a temperament model and it is meant to describe a new approach to the ordering of a sound scale; Chas scale is modeled on pure ratios (1:1, 3:1 and 4:1) and enables the representation of an inter-modular ruled tone-geometry as one of infinite (s) solutions. I hope you understand that nothing there needs to be defended.

Hopefully I'll be able to post tomorrow.

Regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/15/12 09:18 AM


..."I have come to believe we may view tuning similarly based on our independent experience."...

Hi Tunewerk,

I would not be surprised if we were to view tuning similarly and I look forward to being able to expand on piano tuning, both in theory and practice. In fact, even now I would feel ready to ask you:

- Do you think we could succeed in sharing tunings 100%, with a theoretical model that could only rule 12 semitones?

- How do you tune chromatic 4ths, 5ths, octaves, 12ths and 15ths? Do you follow any rule?

The latest issue: "Tempering for chorus and non-fretted string ensembles". On the theoretical side, I would still like to understand, either through numbers or out of logics or common sense, which is the "best possible division" you mentioned, when considering complex chords.

I have read your adding. On that, I'll post separately.

You wrote: ..."Temperament is a problem for fixed string instruments. Chorus and non-fretted string ensembles can require musical situations that involve temperament, but that is by choice."…

Please, help me "translate". Perhaps you mean: There exist musical situations where chorus and non-fretted ensembles have to temper; the difference is that they can choose how to temper, depending on desired effects?

If that is correct, we would agree on one (simplified) point: There exist musical situations where chorus and non-fretted ensembles have to temper. And I'd rather consider "choice" and "desired effects" as two other different issues, in the "harmony - in tune" chapter.

..."Proving this is exhaustive. All rational frequency combinations result in some form of consonance. No matter what pattern, this is true. The degree of consonance is the only question."...

Ok, let's say that is true. Now let's consider the "degree of consonance". I get the impression that you move from these premises:

(1) consonance = rational. No problem, this is within tradition.

(2) harmony = rational. Problem. If that is true, then:

(3) consonance = harmony

We know that, in case of complex chords, favoring one single rational (pure) frequency combination would go to the detriment of all other combinations, precisely in those terms of consonance = harmony you refer to in your premise. As a consequence, consonance cannot equal harmony. This evidence takes me directly to the question: what drives chorus and ensembles towards the highest degree of harmony, as you say, towards the "best possible division"? Can it be one single "rational" combination? And can we talk about a "choice" or will it be more a "must"?

..."Fixed-tone instruments introduce irrational relationships when attempting to equally space tones on a prime curve. These irrational relationships require temperament to find a solution of best fit."

Indeed, it is that concept, perhaps how we order factors, that I'm trying to double check. Adopting your words, this is what I can say (after some numbers):

Prime curves require temperament when dealing with complex chords. These prime curves introduce irrational relationships when attempting to space proportional tones and find a solution of best fit.

One consequential question: Would you (All) say that "rational = consonance" equals "in tune"?

Regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/16/12 02:03 PM


Hi,

Thank you, Tunewerk, for adding.

..."...what is essential to what I am saying is the concept of movable tones. Pure progressive chord structures require note frequencies that shift slightly to account for their different internal interconnected ratios, as well as the leading tones that connect them."...

Please, help. I do not understand whether you refer "Pure" to the word "progressive" or to "chord structures". In case of complex chord structures, even if we are enabled to shift frequencies, there is no way to "interconnect internal ratios" and get them all "pure". This is to say that "Pure ...chord structures" would not make sense to me. As you wrote a few days ago,

..."If a choir did sing these strings of 5ths 4ths or 3rds, they'd have to temper their intervals to achieve a 5/1. However, the difference between that and the piano, is all harmonies would be built on rational interference between waves.. meaning at least one wave pair in ratio, from each dyad, would constructively interfere."...

And we would still need to prove that in order to build harmonies we need "rational interference".

Movable tones. Yes, singers, chorus and non-fretted tones are movable indeed but that, objectively, can only translate into movable temperament, and I doubt how convenient that can sound. I remember your reply to one of my points:

..."1) There is no single adjusted chord geometry. Or a single fixed pitch. One starts on pitch, but may not end on the same pitch. The natural form of music (before unnatural fixed scales) was a flexing, moving geometry through time. Chords grew out of one another, perhaps never repeating exact note twice. When the concept of fixed notes did not exist, there was only ratio."...

As you say, singers do not have a single fixed pitch, they might start on one pitch but may not end on the same pitch (it seems that the tendency is to go flat), but if that occurs it is considered a problem. Bows do have fixed pitch, 4 free strings at fixed pitch. That's why they would not go for movable temperaments.

..."Melodic lines tend to go sharp or flat depending on their direction. Cellos and violins rise in their intonation when playing upwards along a melodic line. They fall in their intonation when descending."...

I do not know if what you say is scientific, it is not what I hear. In any case that does not prove they are released from having to temper. Do you agree? In my view this last one is a different issue, namely "intonation".

..."Without the harmonic constraint of a fixed scale, melody tends to be greatly expanded and chords can occur in new locations, as dictated by the progression of the melodic line."...

Well, what I can say is that chorus, yes, if (for any reason) they were to change the original pitch, rising or falling, they would have to find new chord locations. But this is not to say "they do not need to temper". I hope you acknowledge that this is not a question of personal opinion nor believes, but numbers: non-fretted instruments have their fixed pitch too, that is what determines the constraints; assigning chords a "new location" would cause an obvious problem, in fact free strings would not sound in tune.

I hope we can share this (numerical and musical) notion: one single integer ratio, one single wave pair in ratio, although producing as you say "high density" consonance, cannot make for harmony. Before any fixed scale, "prime curves" deriving from one single fixed pitch are enough to determine melodies-within-harmony constraint, making temperament a must. Perhaps we should go to the source to find the first cause of constraint and the reason why temperament is required always, whether we sing or play; perhaps we would see that it is not "fixing" but "ordering" tone steps in a scale, two different issues. In fact fixing can simply be fixing, while ordering can result in a poor, out of tune tuning.

Last but not least, I do not see any reason why our musical ear should fear irrational relationships. Do you?

Regards, a.c.
.
Posted by: Tunewerk

Re: HISTORICAL ET AND MODERN ETs - 04/16/12 04:55 PM

Alfredo, I respectfully bow out of further discussion.. I just don't have time to give the proper attention to the litany of questions you have detailed, as well as the parsing of semantics.

I will perhaps write on this subject further in my online journal when I have the time. I have just pointed to some mathematical facts here.

If you prefer beating relationships and want to call that harmony, great, more power to you.

I look forward to other substantive additions on these topics.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/16/12 05:49 PM


Thank you, Tunewerk, for those mathematical facts you have been able to point out. Let me know where I can find a link to your online journal, there too I would surely appreciate your further elaborations.

Regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/20/12 02:36 PM


Hi,

One thought on what has recently been said about "intonation", "having to temper" and "movable tones".

We tuners happen to deal with pianos, what we call a fixed-tone instrument, and the majority of pianists are not enabled to improve their piano's intonation, in fact tones are "fixed" there where we leave them. Yet, when I tune pianos I've learned how important it is thinking in terms of "movable tones", perhaps I should say ever "adjusting tones", in that tones tend to adjust in time, tones "move" regularly even during our tuning, when we modify the strings tension and the load onto the entire structure.

On the other hand, singers and bows, although allowed to "movable tones", are always enabled to master their intonation and their tones, exactly where they hear them "in tune". One "alternative" picture might then be this:

Pianos are fixed tone instruments, we have to deal with their "movable" tones.

Singers and non-fretted instrument musicians are allowed to master their intonation and enabled to play in tune... "fixed" tones.

The video linked below reminded me of when I studied violin, when I was practicing intonation, looking for the "best possible division", wanting to hear my scales "in tune" always. One day I opened the case and my small chinese toy raised… the finger board had come unstuck…

http://www.youtube.com/watch?v=KmhDgpnnIZU&feature=related

Perhaps you want to share your thoughts.

Regards, a.c.

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. - Department of Mathematics, University of Palermo - 2009, Italy:
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Article by Professor Nicola Chiriano - published by P.RI.ST.EM (Progetto Ricerche Storiche E Metodologiche) - University "Bocconi" - Milano, 2010 - (Italian):
http://matematica.unibocconi.it/articoli/relazioni-armoniche-un-pianoforte

Chas Tunings:
http://www.chas.it/index.php?option=com_content&view=article&id=64&Itemid=44&lang=en
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 05/18/12 06:26 AM


Hi,

There is one cliché that may cause one more point of confusion; this, in my view, unfortunately allows for mystification and it may open to ignorance as a consequence. Briefly, the cliché I'm talking about was again reported last year by an Interlocutor of mine:

Int.: ..."Also, not all instruments regard Equal Temperament as their standard, so any intended improvement on Equal will be mostly irrelevant to players of those other instruments, and a good portion of the rest aren't even aware that there is anything to improve on."...

Me: Which other instrument are you referring to? In my view, all instrument players might be happy to adopt the most correct reference and the most performing ET frequency scale.

Int.: "What I am referring to is that the players of instruments such as brass and woodwinds automatically adjust their playing with the intention of achieving beat-free intervals against other players,...//.snip.//... Since "in tune" ideally means beat-free intervals, then calling beating intervals (albeit with a different compromise of beats and key color than 12th root of two ET) "in tune" or not will always be subjective.//.snip.//... Free intonating instruments (horns, reeds, strings) do not need to use an equal temperament and will always gravitate to Just Intonation or "Natural" tuning as the more consonant sound; to them the piano is an out of tune instrument to be tolerated rather than imitated."...

- . - . - . -

Focusing on "in tune" and "Beat-free intervals"... had I thought that a piano "is an out of tune instrument to be tolerated...", 30 years ago I'd have gone for gardening.

I'm sure All of you understand that, once more, I'm addressing to temperament and intonation, a simple word that has a precise meaning and yet it seems to be loosing sense day after day, also amongst... Piano Tuners!!

Now, those simple numbers I recently showed can well prove that chords "must" be tempered, thus including chorus and non-fretted instruments.

Today I'm pleased to be able to share a recording of Chas tuning with an orchestra. Two more concerts had just been played on that piano and I did not correct anything, as that was a competition and this final was performed all in one go. I'm offering the last fourth of the whole recording not casually, but hoping we can discuss more about whole fusion, stability, sound coherence, singing tones and above all...intonation.

Sergej Rachmaninov, hope you enjoy:
http://www.youtube.com/watch?v=SQ9BYCbJOfs

Regards, a.c.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 05/18/12 12:09 PM

Thank you so much for the recording ALfredo.

That piano sound nicely in tune with itself, and the orchestra is like "in its bed" in the tuning.



Did you talk with the conductor about the orchestral justness ?

Nicely done ! congratulations !

I certainly wish to hear more of that...


I thought of writing that for free, but yes I will accept your check, Alfredo...



Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 05/18/12 03:44 PM


blush

You Editor! Come'n pass me your bank account... smokin
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 05/18/12 03:50 PM

I forget this was a public forum !

See Alfredo, when you stay aware, you can do a reasonably good job ! Do you have perfect pitch ?
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 05/18/12 03:55 PM


You mean pit-chas? 3hearts
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 05/18/12 04:15 PM

Originally Posted By: alfredo capurso

You mean pit-chas? 3hearts


You got me but no I am not Pitch - assed (nor pitch locked for what is worth)
I am a pitch chas floater , unique rare model smile
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 05/20/12 09:10 AM


Hi All,

A few days ago I posted again about an issue that I've always considered fundamental, namely "intonation". I'm wondering whether I've managed to explain how important it is for me the possibility to share the meaning of that word, how I consider good (if not perfect) intonation as being the foundation of all music, together with a sense of rhythm that we are able to share, in my view, to the same extent.

I'm realizing now that, perhaps, I may have made a (life-long) mistake in taking my own idea for granted and, perhaps, I should be better aware and learn that I'm simply wrong, that good intonation is not fundamental in music and that intonation is a notion that can be shared only partially.

It all started when I read in PW about the (apparently common) idea that whether one likes a tuning or not, it is a question of personal preference. Then I asked myself: how is it that ear equipped people can tell if one note sounds out of tune? How is it that a whole bunch of people might agree on saying that a note is simply out of tune?

On top of that I received a comment (below) that gave me a measure of how far I might be from the actual widespread outlook:

..."What I am referring to is that the players of instruments such as brass and woodwinds automatically adjust their playing with the intention of achieving beat-free intervals against other players,...//.snip.//... Since "in tune" ideally means beat-free intervals, then calling beating intervals (albeit with a different compromise of beats and key color than 12th root of two ET) "in tune" or not will always be subjective.//.snip.//... Free intonating instruments (horns, reeds, strings) do not need to use an equal temperament and will always gravitate to Just Intonation or "Natural" tuning as the more consonant sound; to them the piano is an out of tune instrument to be tolerated rather than imitated."...

On the one hand, I think I can hear which tuning free-intonating instruments gravitate to, how the polyphonic attraction can change, on the other hand I could never think that "...the piano is an out of tune instrument to be tolerated rather than imitated."...

I would be very grateful if you helped me "adjust" my believes, and that is why I linked a piano concert, so that you could know about my premises and help me correct my view.

Sergej Rachmaninov, hope you enjoy:
http://www.youtube.com/watch?v=SQ9BYCbJOfs

Have a nice Sunday,

Regards, a.c.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 05/20/12 10:57 AM

Hi dear ALfredo,

You are a little too obsessive about that, what I understand.

I would be temped to believe that the musician adjust his intonation depending of the place where he plays, and that his intention is primarily to "feel" that what he plays/sing sound "just" in the context he is using.

The piano is not much considered as an instrument which is "just" naturally, but it contains a certain dose of justness that can be used, as you do nicely with Chas. My brother's wife which is a harp player in a good orchestra, told me when she heard the Chas that it was "the first time she heard a piano sounding just"

I am trying to do some experiments and compare the tone of pianos in regard of the orchestra in different situations, with the kind of "fixed intonation" I have on my own piano.

Usually the Chas tuning make the melodic section very clear and it can be heard better in an ensemble or in a piece even with heavy harmony in the low mediums. The treble also sings nicely, as it can be heard in the Stravinsky piece you provided on Youtube, where the high treble does not ask for more raise in my opinion.

Then , the limit, to me is that with a strong harmony, things can be a tad static, as when we compare the broken octave to the octave played with the 2 notes at the same moment.

I feel that some motion in intonation can be used, probably more on the piano than on pure tones instruments . That is how I felt the tuning approach beforethen, compacting some regions so they add force to the zone one and 2 octaves above, enlarging some others so to have more crispness in arpegiated parts, ALl that supposedly while keeping progressive beating of the FBI, just changing the acceleration.

ALl that "acoustic treatment" could mostly be done with many intervals, but due to the attention the tuners usually have to octaves, it is done with octaves and doubles that are enlarged, highly enlarged, or tuned plain and even smaller than "pure" sometime.
In most concert tunings one can hear a pinch of Chas ratio, (often not enough to my desire) and other consonance nodes used while the FBI progress at different rates. compact = low level of consonance to me .

The standard concert tuning instructions some 20 years ago where to tune a nicely spanned octave with good 5th, 4ths, 3ds 6th and the like, then to stretch all following notes to the max so to adsorb the iH. Then depending of the largeness of the first octave the intonation can focus on a zone in the 5_6 octave then raise more and more just to add noise as are doing the duplex scales.
The larger the initial octave, the less contrasted the progression

The resonant nodes give the piano a particular timbral behavior.
I noticed yet that the larger the tuning is in the mediums, the straighter his progression, but at the same time it takes some distance from its own voice at the lowest level of harmony (3d and 5th) Your findings and model find an elegant solution to this, and at the same time allow to raise the consonance of the whole instrument, at the same time a certain coloration of the chords install itself.

I for one also like the piano while it is rubbing and harsh a little with itself , in some cases if the consonance is too fast it makes the tone very kind, chords are soon policed in the next consonance node available, so at the same time that perfection is admirable, and at the same time is it what other instruments are used to as an intonation ?
Are not the violinists playing sharper and sharper in the treble, do the singers have also a tendency to raise their high pitched notes in the idea they will be heard farther or stronger ?

I am probably not a good candidate for that analysis as I use purely my musical sense and my hearing to decide if an interval speed pleases me or not, in a given context .

I hope you will have other answers, may be mine is not what you where asking for

KInd regards

Isaac
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 05/20/12 01:42 PM


Thank you, Isaac.

Although my issue (above) is not referring to one precise tuning model nor to Pro technicalities, you have definitely given a pertinent answer: "...I use purely my musical sense and my hearing...".

- . - . - . -

Not focusing on one temperament, I'm offering one recording (above) so that we may have two options, the general/personal idea and one practical ground. I really hope others can tell what "intonation" means for them, to what extent we can expect to be able to share our musical sense, and-or simply tell if the idea that "the piano is an out of tune instrument to be tolerated rather than imitated" should be taken for granted.

Thank you in advance, a.c.

Edit: My last post was cut off, now it is complete. Sorry for that.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 05/21/12 02:30 PM

Weh ALfredo, the "CHAS" tuning is highly addictive !

I tested a software ETD , DIrk's tuner (who does a very good job, I tend to believe the tuning model is really well setup, better even that the basic model of Verituner or RCT if memory serves, the progression of all intervals is nicely set.

Well I did that tuning while at the same time use a standard temperament 4th 5th to get top FBI's so I only followed the proposed octave size (which is around 0,3 bps open on the temperament).

Finally I had a piano sounding very just, no problem there, with the treble sounding clear , octaves double triples are nice.
compact, when playing I am using the sustain pedal to add some resonance way more than with the CHAS form.

Indeed there is a consonance that is heard at the octave level, even the 12ths are correct, but no way to have that so fast reaction from the instrument at each note...

I wonder if it is not due mostly on the tuning not coming from above like with your method, it indeed deflates a bit when unisons where tuned ...
Well so to say, anyway, no strong impression of intonation ... in fact it is similar as the so many pianos tuned with much evolved compromising and no focus as obtained in pianos tuned by ear only.

Well I am addicted to the elegance of the CHAs ! (also it allows for a less fast speed raising of the 17th so the treble is quieter)

I am amazed that the difference is so large ! Ill try to record something but this is not a very good piano..

Best regards
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 05/21/12 07:27 PM


Hi Isaac, thank you for your feedback. I shall reply in the Pre-Tuning thread.

Oh, hope you don't get too... expensive? wink

A443, Aussy, BDB, Bill, Bob, Bojan, Chris, Dan, Daryl, Dave, David, Del, Diane, Ed, Emmery, Erich, Gene, GranpM, Ian, Jake, Jeff, Jerry, Jim, John, Jurgen, Kees, Keith, Kent, Loren, Mark, Phil, Rafael, Robert, Ron, Roy, Scott, Tunewerk, and All... yesterday I found this:

pdf. : Sundberg, J. - "In tune or not? A study of fundamental frequency in music practise"

Of course... it's all relative. I'll appreciate your comments.

Does "intonation" make sense?

Regards, a.c.
Posted by: Phil D

Re: HISTORICAL ET AND MODERN ETs - 05/21/12 08:57 PM

Got a link?
Posted by: Dave B

Re: HISTORICAL ET AND MODERN ETs - 05/22/12 12:14 AM

Ok , I'm coming into this thread late and can't figure out what a "CHAS" tuning is? And, How many different Historical Tunings are there?
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 05/22/12 02:34 AM


Hello !
here is a Chas tuning checked by the pianist :
https://docs.google.com/open?id=0B6GjQDkF_AMQS3c0T0VzaUszQUk

I talk under the control of my Master A.C. who developed and invented the C.H.A.S wink
I dont like those acronyms, I would prefer to say "harmonic temperament", but then, what is the definition of a temperament ? does it apply to CHAS, I guess yes as it is a method to define the intervals between the notes and chords , as the "COrdier tuning" relatively well known and used in France, ore the "STopper duodecime tuning" . All based on mathematical assertions that can be verified in the field, and modify the consonance of the partials within the instrument.
I guess this category of temperament could be names "even beating temp"

For the historical ones I guess you could report them to 3 classes, all dividing the octave with different generation models and methods.

The 4 th and 5th temperament can also be considered as a generation method, and the ladder of thirds too, but those 2 methods relate also to historical families (ladder of thirds could be related to meantone for instance)

Those days with all the alchemists of the HT, who are creating a new model every then, I believe that the real number of stated temperaments cannot be known, and in the end dont make an interesting importance in my opinion.

Some music have been clearly written at an era and place where a type of temperament was used, It is probably only for older family of classical music in occidental culture.
Then , as tuners use may differ from place to place, the different tuning schemes and the different forks certainly gives tunings where the Fast beating intervals where not as smooth and even than today , using that to pretend to a return to authenticity lay me relatively meditative, particularly when I hear the singing quality of the so tuned pianos, who is often a good level under what can be done.

So I tend to consider that as a way to hide substandard work in face of a non educated audience, or a desperate quest to some kind of harmony .
It is a little sad as there is certainly something that can be searched seriously that will lend to simple comprehension of what happened in those eras, assuming instruments with adequate tone are used.

The modern piano with its relatively pure sound is not the good candidate for those experimentations IMO.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 05/22/12 02:40 AM

Originally Posted By: Phil D
Got a link?


http://www.speech.kth.se/prod/publications/files/qpsr/1982/1982_23_1_049-078.pdf

Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 05/23/12 05:11 PM


Originally Posted By: Dave B
Ok , I'm coming into this thread late and can't figure out what a "CHAS" tuning is? And, How many different Historical Tunings are there?


Hi Dave, you mention a good point: what is Chas tuning?

I'll report a sort of definition made by an interlocutor of mine not long ago, perhaps you can tell me if you would like to know more:

..."...I am beginning to see where you are coming from. This is a model for saying what more advanced tuners do, and to maybe help many in the tuning community look at the piano scale frequencies and temperament in a new way? Many tuners view temperament in all manner of old ways, not the least of which is the antiquated, strict doubling of the octave."...

Let me ask you, Dave, are you concerned with intonation, either for yourself or your customers?

Hi All,

are you concerned with intonation, either for yourself or your customers?

Regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 05/24/12 12:45 PM


Hi,

Perhaps by investigating some issues related to temperaments we have finally got to the nerve centre of tuning, namely intonation.

I must acknowledge that it is not easy to talk about intonation... some of us are definitely able to say when something is out of tune (see Mark R. and many others) while some others may not. And I understand that many techs may have approached our job with different motivations, perhaps being more concerned about the market place, the environment or general mechanical factors and/or job specifics.

Intonation, tuning stability, timbre and touch/keyboard dynamics are all deeply related to the piano sound and the pianist' performance. I know that the idea of "clean unisons being all we need" achieves widespread success, personally I would only end that sentence saying "...all we need to start with". At least that is how I started, trying to get decent stability, good intonation and unisons out of old broken pianos stockpiled in a basement.

I find no better way to close this chapter with a nice video I found, while looking for barbershop singing. Unfortunately I do not understand a word of what they say, though I hope you like it. Thank you All for your contributions.

http://www.youtube.com/watch?v=QmDGntpZC3I

Regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 12/30/12 10:34 AM


Hello,

Two more interesting works, I hope you too find them interesting:

By Eitan Ornoy:

An empirical study of intonation in performances of J.S. Bach's ...
www.tau.ac.il/arts/music/hebrew/Publications/download/Ornoy.pdf

By J. Murray Barbour:

Tuning and Temperament - A Historical Survey (1951)
http://www.unz.org/Pub/BarbourJMurray-1951?View=ReadIt

To All,

20' Happy New Year '13

a.c.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 03/11/13 09:07 PM


Hi All,

Hello rxd, let me move your recent contribute in here:

Originally Posted By: rxd
Originally Posted By: Olek
...........


Those are sensitive subjects, when askingvwhat kind of tuning the colleagues realise it sound as obscene , as if I asked the colors of their underwear.

But I believe this come from the difficulty with analysis (envelope, power, projection. You can see the tuner in Pianomania, tweaking unisons and regulation to provide an adequate ambiance, (while it could suffice to propose different instruments, the budget is not the same)

Greetings



There is a reason for colleagues not speaking of tuning techniques, styles, etc.

Whenever anybody has mentioned anything remotely about tuning in this forum, take a close look at your reply.



Perhaps now you are ready to talk about tuning, following a post of mine, although some time has passed. I have been missing your reply:

Posted here, #1852385 - February 27, 2012 09:57 AM Re: HISTORICAL ET AND MODERN ETs [Re: alfredo capurso]


Originally Posted By: alfredo capurso

Thank you, rXd, for your reply.

Yes, I'm interested in knowing your thoughts, hearing about your own tuning experience and analyzing some conclusions, and I hope some other colleagues too are willing to share their own experience and deepen on one crucial issue, namely "intonation".

You said: …"The intervals of vertically structured temperaments and the melodic intervals as perceived and performed by say, gypsy violinists and opera singers simply cannot be reconciled."…

That seems to recall two kinds of "intonation", one for vertical chords structures and a second one for horizontal melodies, based on how intervals are perceived. Is that what you are referring to?

You kindly reported one case and said: …"His intonation in the solo was exemplary string players intonation."…

Do you have other cases? What would you say is "string players intonation" like?

And, if you would like, we could cover some other questions from your other post (above), at your convenience:

Who does regard our wide M3rds as a problem? Do you?
Would you yourself hear ET wide M3rds even wider?
How wide would players of melodic instruments and singers hear minor 6ths?
How do you expand your equal tempered octave?
Where do unequal temperaments gain favour with singers? Do you refer that to UT 6th? To one precise key?



Regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/11/13 02:46 PM


Hi rxd,

I have moved our replies from the "Best UT for Voice Teacher" thread in here for two reasons, because I do not like the idea of going off topic there, and because I like thinking that we (All) can share our pro experience, and perhaps help young colleagues with more indications.

Originally Posted By: rxd
I don't think we disagree on anything of any consequence.

Perhaps the ET that can be told is not the eternal ET to paraphrase Lau Tsu.

Philosophically, is the mathematical model still ET when transfered to any instrument? Who can possibly be that pedantic?

I was taught a two octave temperament. Over the years, the piano has become one huge extended temperament for me.
As part of a team of 5 that tunes all the major concert and studio pianos here, (yes, there is so much work, it takes 5 and sometimes more, plus a scheduling office of two people), we work interchangeably. There must be over 1000 salaried top flight musicians among our 5 major symphonies and smaller orchestras and theatres, plus as many or more freelance musicians with never a problem they welcome a stable and predictable reference point. If anybody wants anything different, we can accommodate them. Other than the occasional request for 442 which is usually covered by putting in another piano that is stable at that pitch, we are rarely asked for any other temperament. The last time was eight years ago for a new work that hasn't been performed here since.

We simply haven't time to get any weird ideas about tuning. We did have one who started to tune too sharp in the treble. He only had to do it for a day or two before his colleagues had to dissuade him, it created too much extra work and was noticed by our musicians immediately.


This was my reply:

..."I don't think we disagree on anything of any consequence."...

I am glad, rxd, all in all... good news.

..."Perhaps the ET that can be told is not the eternal ET to paraphrase Lau Tsu."...

Nice citation; on the other hand I hope one day you and I together will be able to address ET without having to say "Perhaps...".

..."Philosophically, is the mathematical model still ET when transfered to any instrument?"...

Your question doesn't sound philosophical to me, but kind of "technical", and I would say that there is going to be a substantial difference, depending on the model. Which ET "mathematical model" are you referring to in these days?

..."Who can possibly be that pedantic?"...

Well, in my own perspective things are a bit different: in my opinion, if a tuner were to refer to a wrong model and (say) expect to be able to transfer that (wrong) model on an instrument, the tuner in question would not be "pedantic" but simply wrong.

I think that, in general, mathematical models are taken in consideration only when they can be transferred in actual practice successfully, without even thinking about "pedantic", I would say beyond any possible attribute, here meaning either the model works or it does not.

..."I was taught a two octave temperament. Over the years, the piano has become one huge extended temperament for me."...

Good news, really. I too think that the usual (traditional and theoretical) concept of "temperament" is to be extended to the whole piano, that is what I do in practice and what I am sharing in Modern ET theory.

Today, every time I think of it, I find all that (teaching and) fighting around "12-tempered-semitones" so deceptive, as if 12 semitones could ever define or be representative of the whole tuning. I cannot really explain this illusory phenomenon either... they too are piano tuners, some of them even talk about "whole harmony", they might well understand (?).

Now I am very curious about the two octave temperament you were taught (I mean the sequence, including 4ths, 5ths and octaves) and look forward to knowing how you expand the first two octaves (reference points).

..."As part of a team of 5 that tunes all the major concert and studio pianos here, (yes, there is so much work, it takes 5 and sometimes more, plus a scheduling office of two people), we work interchangeably. There must be over 1000 salaried top flight musicians among our 5 major symphonies and smaller orchestras and theatres, plus as many or more freelance musicians with never a problem they welcome a stable and predictable reference point. If anybody wants anything different, we can accommodate them. Other than the occasional request for 442 which is usually covered by putting in another piano that is stable at that pitch, we are rarely asked for any other temperament. The last time was eight years ago for a new work that hasn't been performed here since."...

Thanks for letting me know about your team and your practice.

- . - . - . -

Regards, a.c.
.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 07/14/13 04:43 PM


Hi All,

I have had some very busy days but, once a week.. always at PW, reading what my friends/colleagues are willing to partecipate :-)

For the time being, I would like to trace Jim's post, and Ed's, Bill's and not least... Isaac's, my... favorite :-)

The original thread is "My Piano in the "Equal Temperament via Marpug" 'Quasi' ET", the post below from July 07, 2013 02:32 PM

To all, my regards, a.c.

Originally Posted By: jim ialeggio
Originally Posted By: Ed Foote
and the difference between it and one that has all fifths sharing the same DNA and the thirds ascending like a ladder will be lost on many of them.

Originally Posted By: Bill Bremmer RPT

There is no such thing as a perfect piano anywhere at any time. It is all a matter of degree and the best that can be accomplished under any given circumstances. The problem of both temperament and inharmonicity are ultimately irresolvable. One can only try to seek a better solution for each and to say that there is only one best solution under all circumstances leads not to the betterment of music from the piano but to mediocrity.

Originally Posted By: Olek
The fact that a very organic and direct contact between the body/ears of the tuner and the whole ensemble tuning pin/wire/soundboard, is necessary is something that some subtle pianists or musicians can understand better than tuners that rely on their "ears" and do not analyse the sensations the instrument is providing.


The last three posts in this thread, for me, all point in a similar direction...though, I understand that the above posters very well may not agree with my interpretation.

1-given the mathematically restrictive definition of ET, ET in the reality of an instrument as unruly as a piano, is largely a fiction. Or, if it is a reality it is an extremely fleeting one. Owing to the structural and material complexities involved, not to mention the complexity of the brains that perceive the instrument's sounds, ET in its strictest mathematical sense cannot actually exist for any length of time, if at all. So it boils down to "pretty darn close", or diverting from the mathematical values but below the level of perception. I would offer that the amount that the tuning can deviate from the mathematical, and still musically below the threshold of perception is larger than we might think. This says to me that functionally, the best ET is still kind'a "wet"...dirty.

2-if the above point is accepted, unisons by definition, that is, mathematically pure unisons, are as much a mathematical fiction as mathematically pure ET is. Clean crisp "pure" unisons are also somewhat "wet"...uhhh...dirty...(mathematically speaking)

Factoring out the poor communication...which is endemic, since this is all so hard to talk about...I see a "common denominator". The common denominator I see says, from a musical perspective, all these voices are telling a surprisingly similar story.

That's good news...at least in my view.

Jim Ialeggio

ps This thread has crystalized for me musically what I have been doing in all my tunings...though without knowing what I was doing. I do prefer ET's "even-ness" of "disciplined" 4ths and 5ths, but really as the 4ths and 5ths I enjoy are equal beating, it appears to me I like my ET a bit "wet". More important to me than the temperament,is the fact that those equal beating 4ths and fifths (equal beating being a relative term) are extremely important in constructing the octave stretches which I find so musiclaly critical in constructing a seven octave wide resonant stretch...a stretch which easily meets the "musicality perceptible" threshold.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 11/01/13 05:08 PM


Hi,

I need to trace ED's reply, I think it may explain some circumstances related to our practice. I will reply in turn.

To All, have a nice w.e., a.c.


#2173061 - October 28, 2013 11:30 AM Re: Who says an ETD isn't good enough? [Re: Ed Foote]

Originally Posted By: alfredo capurso
Originally Posted By: Ed Foote
Greetings,
By any measurement, ETD's do some things better than humans. My results come from what I think are the strong points of an ETD used to assist my own judgement.

The machine has us beat by a mile on consistency. There isn't a human alive that can maintain 1/2 cent consistency in the top octave from say, the first to the last of 10 tunings over four days. At its best, an ear/tuning fork standard will just barely reach the accuracy of the most basic devices. We change, the machines don't. How is this of value?

Once we have a tuning in place, recorded on an ETD for a given piano, we have a consistent template. This is valuable for a tuner, as it allows us a perspective on ourselves, i.e. "Gee, this didn't sound that sharp last week"... I guarantee that most of us will disagree with a recorded version of our own tuning, replicated from the machine on the same piano, the first time we hear it. We will find some things that can be improved on when we listen to that tuning, again. And if we alter the ETD's info to match what our ears tell us, the next time we use that template, we will change less, and the third or fourth time we repeat that "massaging" of our template, the changes will be so small that we realize we are the only ones that know there has been a change. It is at this level of resolution that differences between like pianos might be seen, but once again, I have never found it of any more than academic benefit to chase that small of a target.

This level of judgement is all good in a clinical world, but hard to apply to real time use, since fluctuations during a given tuning can have more effect on overall width of our triple octave than any variability of the machines'. This modeling of an ETD tuning over a broader sample can remove the variation caused by localized pitch changes we encounter in any one tuning. And after the template has been refined from numerous applications and modeling, I think it more truly reflects the ideal track through the 88 note scale. When I get a piano that is already at pitch, all across, these tunings can really express what I think a great sounding piano should be.

The modern ETD also allows a great control over stretch, giving us numbers to match what we hear. I can sell either tight or stretched bass tunings, depending on the requirements, with consistent ease, and if someone performing a concerto starts talking about "adding some sharpness for brilliance" I can deliver as much as they want, every time.

Some of the best ears on the planet have complimented, unprompted, tunings done with an ETD, using the straight, unmodified FAC numbers. Refining beyond that is something I have done for myself, but I am under no illusions, there are very, very few people that could tell the difference between my best aural, recorded and refined, and the machine's preset idea of how a concert grand should be tuned. I have tested this theory with some really critical ears,(who had money riding on the quality of the project), and the differences seem to be academic.


Hi Ed,

You wrote: ..."By any measurement, ETD's do some things better than humans."...

Well, perhaps a fair distinction amongst "humans" ought to be made :-) especially when (as many other say) there is room for some kind of artistry? But... please note that I comprehend the use of electronic equipment for any kind of reason, even when someone aims at a form of art.

..."The machine has us beat by a mile on consistency. There isn't a human alive that can maintain 1/2 cent consistency in the top octave from say, the first to the last of 10 tunings over four days. At its best, an ear/tuning fork standard will just barely reach the accuracy of the most basic devices. We change, the machines don't. How is this of value?"...

That is perhaps related to your own experience? And the problem might be that a basic device can only reproduce its standard, a "human" can change (as you say), our standard oscillates, and IMO we need to go through ups and downs, they help us speculate, learn more and improve.

..."Once we have a tuning in place, recorded on an ETD for a given piano, we have a consistent template. This is valuable for a tuner, as it allows us a perspective on ourselves, i.e. "Gee, this didn't sound that sharp last week"... I guarantee that most of us will disagree with a recorded version of our own tuning, replicated from the machine on the same piano, the first time we hear it. We will find some things that can be improved on when we listen to that tuning, again. And if we alter the ETD's info to match what our ears tell us, the next time we use that template, we will change less, and the third or fourth time we repeat that "massaging" of our template, the changes will be so small that we realize we are the only ones that know there has been a change. It is at this level of resolution that differences between like pianos might be seen, but once again, I have never found it of any more than academic benefit to chase that small of a target."...

Yes, I understand, perhaps it makes it easier for you, perhaps "mindless", but I think the whole question may depend on what you/we like or dislike about tuning: for instance, I love altering beats and "massaging" the whole piano and following the smallest changes my ears can detect or chase. How to explain? I like following what my ears and wrist tell me, more than having to do with a template... I don't know, a simple question of sound dimension?

..."This level of judgement is all good in a clinical world, but hard to apply to real time use, since fluctuations during a given tuning can have more effect on overall width of our triple octave than any variability of the machines'. This modeling of an ETD tuning over a broader sample can remove the variation caused by localized pitch changes we encounter in any one tuning. And after the template has been refined from numerous applications and modeling, I think it more truly reflects the ideal track through the 88 note scale. When I get a piano that is already at pitch, all across, these tunings can really express what I think a great sounding piano should be."...

I am afraid here we enter the very subjective field, and I would love to listen to one of those tunings (check aurally: 3rds, 4ths, 5ths, octaves, 10ths, 12ths, 15ths and 17ths). Even only 5ths, octaves, 12ths and 17ths, do you think you can provide a recording?

..."The modern ETD also allows a great control over stretch, giving us numbers to match what we hear. I can sell either tight or stretched bass tunings, depending on the requirements, with consistent ease, and if someone performing a concerto starts talking about "adding some sharpness for brilliance" I can deliver as much as they want, every time."...

I was never asked to add anything, for anything different from a sound and brilliant tuning. But I understand what you mean, perhaps where you leave ETDs have somehow modified the tuner/customer rapport? You can meet an extravagant customer and sell any displaied number they ask for? Why not?

..."Some of the best ears on the planet have complimented, unprompted, tunings done with an ETD, using the straight, unmodified FAC numbers. Refining beyond that is something I have done for myself, but I am under no illusions, there are very, very few people that could tell the difference between my best aural, recorded and refined, and the machine's preset idea of how a concert grand should be tuned. I have tested this theory with some really critical ears,(who had money riding on the quality of the project), and the differences seem to be academic."

Well, perhaps that's you and IMO there is nothing to be discussed. Personally, I look at customers as potential "best ears", and I feel confident to be able to rely every day on my own technical skills.

If I may ask, Ed, how do you know when... further refinement can be dismissed as "academic"?

Regards, a.c.
.

Originally Posted By: Ed Foote
Originally Posted By: alfredo capurso


..."Once we have a tuning in place, recorded on an ETD for a given piano, we have a consistent template. "...

Yes, I understand, perhaps it makes it easier for you, perhaps "mindless", but I think the whole question may depend on what you/we like or dislike about tuning: for instance, I love altering beats and "massaging" the whole piano and following the smallest changes my ears can detect or chase. How to explain? I like following what my ears and wrist tell me, more than having to do with a template... I don't know, a simple question of sound dimension?

..."This level of judgement is all good in a clinical world, When I get a piano that is already at pitch, all across, these tunings can really express what I think a great sounding piano should be."...

I am afraid here we enter the very subjective field, and I would love to listen to one of those tunings (check aurally: 3rds, 4ths, 5ths, octaves, 10ths, 12ths, 15ths and 17ths). Even only 5ths, octaves, 12ths and 17ths, do you think you can provide a recording?

..."The modern ETD also allows a great control over stretch, giving us numbers to match what we hear. I can sell either tight or stretched bass tunings, depending on the requirements, with consistent ease, and if someone performing a concerto starts talking about "adding some sharpness for brilliance" I can deliver as much as they want, every time."...

I was never asked to add anything, for anything different from a sound and brilliant tuning. But I understand what you mean, perhaps where you leave ETDs have somehow modified the tuner/customer rapport? You can meet an extravagant customer and sell any displaied number they ask for? Why not?
If I may ask, Ed, how do you know when... further refinement can be dismissed as "academic"?
Regards, a.c.



Greetings,
In reverse:

I tune as part of a whole preparation of the instrument. I don't waste time on what I consider academic, and when I reach a point in the tuning where only another tuner can tell I am changing things, I see it as academic from that point on. I have no time to waste beyond that, chasing the last 1/2 cent in my stretch, when there is constant need for regulation and voicing. Techs debating whether that last 1 cent difference in the treble makes a difference in the sound is like two highway engineers arguing about the roadway varying by 1/16 inch. It makes no discernable difference to any customers I have( and some of them are listening to these tunings in isolation rooms with VERY advanced recording equipment and monitor systems).

I work in a market of world-class musicians around here and I don't think my use of the machine has altered the expectations of artists such as B.G. Adair, Renee Fleming, Edgar Meyer, Emmanuel Ax and others. I take their feedback seriously, since they are exposed to piano technicians all over the world and are not shy about requests. Much of what I know now comes from learning what works for them.

I have now gotten CDbaby to download all three Mozart comparisons, in meantone, WT, and ET. For free. If you want to examine my tuning, that could be a place to start. Same piano, stage, equipment, just a change of temperament. The Beethoven CD is more heavily into the WT effect.

It is now mindless to find the pitches on a given piano, as I have already massaged and finessed the tuning. Having done it once, at greater length than I would ever do as a normal tuning, I don't need to do it again when there are other things like unisons to be polished. To each his own, I only wanted to invent my "wheel" once for each piano. It lets me provide a better prepared instrument.
Regards,
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 11/01/13 06:58 PM

For me 2 octave temperament is something very secure, but not going in the direction of tonality.

Tonality is defined within one octave, I do not believe a musician can envisage things differently.

The way to have a strong 2 octave temperament is to test it harmonically (arpegios, chords) , and adjust what is not coherent.

For instance I would compare Major and minor chords in the 2 octaves of the temperament.

The fact that musicians never complain about what goes on in mediums does not prove anything in my opinion. At best they accept something "neutral" and anyway there is so much power and the tone is so rich it can be a little undefined, the music will be what is heard primarily.

it is also easy to be coherent in that section, but I believe musicians would appreciate something more "free". My impression was that some tuning where following the progressions in the bottom of the long bridge and that gave some strong impression of deepness and coherence.

possibly using temperament that begin lower on the bridge may induce that, if they are the reference and not the region around A440. May be that was an old way of tuning at Hamburg.
Posted by: Ed Foote

Re: HISTORICAL ET AND MODERN ETs - 11/01/13 09:49 PM

Originally Posted By: Olek
For me 2 octave temperament is something very secure, but not going in the direction of tonality.
Tonality is defined within one octave, I do not believe a musician can envisage things differently.
The way to have a strong 2 octave temperament is to test it harmonically (arpegios, chords) , and adjust what is not coherent.
For instance I would compare Major and minor chords in the 2 octaves of the temperament.
The fact that musicians never complain about what goes on in mediums does not prove anything in my opinion. At best they accept something "neutral" and anyway there is so much power and the tone is so rich it can be a little undefined, the music will be what is heard primarily.
it is also easy to be coherent in that section, but I believe musicians would appreciate something more "free". My impression was that some tuning where following the progressions in the bottom of the long bridge and that gave some strong impression of deepness and coherence.possibly using temperament that begin lower on the bridge may induce that, if they are the reference and not the region around A440. May be that was an old way of tuning at Hamburg.


Greetings,
I have to say that I can make absolutely no sense out of this post. I think the problem is the translation of adjectives, but I don't even know where to begin. "neutral, deepness, coherence, "free", so rich it is undefined"; these are not words that I have ever heard a pianist use to describe tone, so I have no idea at all what is being described here.
Regards,
Posted by: Minnesota Marty

Re: HISTORICAL ET AND MODERN ETs - 11/01/13 10:15 PM

Well Ed,

Being a pianist, I have no clue either.
Posted by: Olek

Re: HISTORICAL ET AND MODERN ETs - 11/02/13 05:57 AM

forget it. I mean that when using 2 octaves you have more compromising and you are yet obliged to use one preference for tuning (taking in account the iH can be done different ways)

but I had in mind a 2 octave temp I have seen that used stacks of M3 as a skeleton.

if you use 2 octaves by confirming the slow beatings intervals, it gives more controls assuming the octaves are tuned consistently.


a too compromising temperament does make a little more predictable modulations and at some point it is boring to me, detracting from the music.
Now if the referent pitch are defined in a zone of the piano here the iH is not smooth, as near and above the break, you have more contrat and the break is more in tune.

ther is always a art of the tuning that consist to adapt the piano iH to the pitch of notes.

methods differ.

the temp I tried range from eb3 to e4 and created light variations in 5ths while sticking better to the break region than if pitches where defined higher in the scalr.

I can post samples but there are not so rare, tuning where the mediums are clean but uncontrasted.

Now what I have seen tuned as ET by the old techs often followed well the break region, and the discrepancies where more or less progressively smoothed higher (sometime not so much and the piano sounded with typically CF too large)

what I say is that it is unnecessary to go to extremes to provide some variations in the 5ths. following the piano plus operator mistakes is largely enough.











Posted by: E. Christensen

Re: HISTORICAL ET AND MODERN ETs - 12/02/13 12:23 AM

There is such great information on these posts, I'm glad they do not get removed. Thank you for posting some of those links to such beautiful music!
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/28/14 07:11 PM

Hi,

Tracing:

#2221724 - January 28, 2014 05:37 AM Re: Why bother? (tongue in cheek) [Re: jmw]

Originally Posted By: rxd
Originally Posted By: Minnesota Marty
Originally Posted By: rxd
Originally Posted By: Minnesota Marty
Why is the assumption being made that "concert" tuning is the same as "studio" tuning? As a pianist who has been in both situations, it seems that the tuner plays a very different role in each type of activity.

In performance, I've never been given a lunch break between the 2nd and 3rd mvts. of a concerto. The demands are totally different and shouldn't be equated.


Care to expand on both these paragraphs, Marty? Neither of them seem to be saying anything unless I'm missing some humor.

Well, it is a combined response to a number of your recent posts.

You seem to be in a situation which is unlike the vast majority of highly skilled tuners. That is why I pointed out the difference in tuning for a concert or for a recording. 'Live in Concert' recording (or tuning) is very different than studio work. I'm thinking of the quest for perfection as it relates to the concept of this thread.

In the classical world, unlike the craziness of RA Hall, piano tuners aren't pushed into rush jobs or get yelled at by a stage manager. I'm sure there are some rush jobs in unusual situations, but that is not the standard procedure for concert work or recording. I'm sorry that you work in such a frenetic environment.

Why is it that you keep stating that wind instruments go flat at the top of their range and the reverse happens at the lower end? This is simply untrue. It is the other way around. Your 'stretch theory' just doesn't cut it.

Nothing I stated was meant to be humorous.


As I suspected.

We are involved in all kinds of situations. The RAH series always gives us 3-4 seperate tuning slots on production day, 2-3 of them entirelyl to ourselves. I doubt I ever said anything different.

The experience of my former student was not with the company I work with. it happened in America, as a matter of fact. not in a major centre. That would never be tolerated here.

Everything we do here is in well defined, pre arranged, usually copious time slots.

Have you been carrying this half understood notion all this time? I categorically never said that any wind instrument played flat in the upper register and sharp in the lower. I have, however stated that the piano is stretched more than any other instruments (skilfully played, of course).

Having been a highly skilled professional wind player myself at film studio and broadcast level and in many genres with many different combinations of instruments, of course I understand their intonation. Currently, I am called upon to coach young professional ensembles and more recently, string quartets as an extension of my work with piano trios.

I have spoken of certain situations where a wind player has played the odd note or two sharper than the rest of the orchestra that has affected the piano entry. That is not to say anything about general tendencies of an instrument.

Let me clear this misunderstanding once and for all. Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played. This is easily accomodated by skilled players. They will, of course, note that it is a different experience from playing with a well tuned organ at the same nominal pitch, for example.
This is, as I'm sure you understand, the effect of inharmonicity in pianos. I am assuming an understanding of this basic characteristic of pianos. Perhaps I shouldn't.

Pianos tuned with exaggerated stretch only makes matters worse. It is the exaggerated tuning of the piano that is at fault, not the other instruments. I can't stress this enough

To say that a piano is sharp is not the same as saying that any other instrument plays flat.

Thank you for bringing this up and giving me an opportunity to clarify what I may not have said very clearly and for anybody else who may have been carrying this misunderstanding.
Hopefully I didn't create more. this partial understanding explains a lot. But it still doesn't address your post in question.

I still don't understand about "lunch between movements" or the exact nature of the distinction you make between concert and studio. Perhaps another partial understanding? What was your frame of mind when you wrote it? Strange


Hi,

I do not have much time in these days, I would like to be able to seat down for a solid time an reply properly. Instead I have to be short.

rxd, you wrote:

..."Let me clear this misunderstanding once and for all. Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played. This is easily accomodated by skilled players. They will, of course, note that it is a different experience from playing with a well tuned organ at the same nominal pitch, for example.
This is, as I'm sure you understand, the effect of inharmonicity in pianos. I am assuming an understanding of this basic characteristic of pianos. Perhaps I shouldn't."...

Perhaps you want to expand on that. When I read that, I get the feeling we come from two different planets. Please note, nothing personal and I do not think it is a question of amount_or_type_of_experience... musician, playing concerts in duo (with a piano) or more, multi-instrument player, tunings in prestigous halls, for prestigious brands etc... in fact, all this calls for a question.

Recently I have had to "learn" that the piano is the most out-of-tune instrument on the stage (BB), some colleagues still wonder about the "point of best fit", others regret that the piano cannot adjust_in_real_time, and now I learn from you that "...Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played."

Humor: Do you tune pianos sharp?

Humor: Are pianos sharp when they are not flat?

Non-humor: Have you been tuning pianos while trying to get along with other orchestra instruments and players (as I understand from your other post)? In case, do you sacrifice your "intonation"?

Humor: Gosh, all these martyrs, it looks like an army.

Regards, a.c.

P.S.: Here we wont go off-Topic.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/29/14 03:18 PM

Originally Posted By: rxd
Originally Posted By: alfredo capurso
Originally Posted By: Ed McMorrow, RPT
Perfection is like a mirage; when conditions are right you can see it is possible, but every motion towards it makes it recede from you.


For me, Perfection is like Excellence: when conditions are right I can see it possible, perhaps any wrong notion (and/or posture) may cut it down.

Beyond that, I do not think the OP was about Perfection, but scorn and indignation.


Originally Posted By: rxd
Originally Posted By: Minnesota Marty
Originally Posted By: rxd
Originally Posted By: Minnesota Marty
Why is the assumption being made that "concert" tuning is the same as "studio" tuning? As a pianist who has been in both situations, it seems that the tuner plays a very different role in each type of activity.

In performance, I've never been given a lunch break between the 2nd and 3rd mvts. of a concerto. The demands are totally different and shouldn't be equated.


Care to expand on both these paragraphs, Marty? Neither of them seem to be saying anything unless I'm missing some humor.

Well, it is a combined response to a number of your recent posts.

You seem to be in a situation which is unlike the vast majority of highly skilled tuners. That is why I pointed out the difference in tuning for a concert or for a recording. 'Live in Concert' recording (or tuning) is very different than studio work. I'm thinking of the quest for perfection as it relates to the concept of this thread.

In the classical world, unlike the craziness of RA Hall, piano tuners aren't pushed into rush jobs or get yelled at by a stage manager. I'm sure there are some rush jobs in unusual situations, but that is not the standard procedure for concert work or recording. I'm sorry that you work in such a frenetic environment.

Why is it that you keep stating that wind instruments go flat at the top of their range and the reverse happens at the lower end? This is simply untrue. It is the other way around. Your 'stretch theory' just doesn't cut it.

Nothing I stated was meant to be humorous.


As I suspected.

We are involved in all kinds of situations. The RAH series always gives us 3-4 seperate tuning slots on production day, 2-3 of them entirelyl to ourselves. I doubt I ever said anything different.

The experience of my former student was not with the company I work with. it happened in America, as a matter of fact. not in a major centre. That would never be tolerated here.

Everything we do here is in well defined, pre arranged, usually copious time slots.

Have you been carrying this half understood notion all this time? I categorically never said that any wind instrument played flat in the upper register and sharp in the lower. I have, however stated that the piano is stretched more than any other instruments (skilfully played, of course).

Having been a highly skilled professional wind player myself at film studio and broadcast level and in many genres with many different combinations of instruments, of course I understand their intonation. Currently, I am called upon to coach young professional ensembles and more recently, string quartets as an extension of my work with piano trios.

I have spoken of certain situations where a wind player has played the odd note or two sharper than the rest of the orchestra that has affected the piano entry. That is not to say anything about general tendencies of an instrument.

Let me clear this misunderstanding once and for all. Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played. This is easily accomodated by skilled players. They will, of course, note that it is a different experience from playing with a well tuned organ at the same nominal pitch, for example.
This is, as I'm sure you understand, the effect of inharmonicity in pianos. I am assuming an understanding of this basic characteristic of pianos. Perhaps I shouldn't.

Pianos tuned with exaggerated stretch only makes matters worse. It is the exaggerated tuning of the piano that is at fault, not the other instruments. I can't stress this enough

To say that a piano is sharp is not the same as saying that any other instrument plays flat.

Thank you for bringing this up and giving me an opportunity to clarify what I may not have said very clearly and for anybody else who may have been carrying this misunderstanding.
Hopefully I didn't create more. this partial understanding explains a lot. But it still doesn't address your post in question.

I still don't understand about "lunch between movements" or the exact nature of the distinction you make between concert and studio. Perhaps another partial understanding? What was your frame of mind when you wrote it? Strange


Hi,

I do not have much time in these days, I would like to be able to seat down for a solid time an reply properly. Instead I have to be short.

rxd, you wrote:

..."Let me clear this misunderstanding once and for all. Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played. This is easily accomodated by skilled players. They will, of course, note that it is a different experience from playing with a well tuned organ at the same nominal pitch, for example.
This is, as I'm sure you understand, the effect of inharmonicity in pianos. I am assuming an understanding of this basic characteristic of pianos. Perhaps I shouldn't."...

Perhaps you want to expand on that. When I read that, I get the feeling we come from two different planets. Please note, nothing personal and I do not think it is a question of amount_or_type_of_experience... musician, playing concerts in duo (with a piano) or more, multi-instrument player, tunings in prestigous halls, for prestigious brands etc... in fact, all this calls for a question.

Recently I have had to "learn" that the piano is the most out-of-tune instrument on the stage (BB), some colleagues still wonder about the "point of best fit", others regret that the piano cannot adjust_in_real_time, and now I learn from you that "...Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played."

Humor: Do you tune pianos sharp?

Humor: Are pianos sharp when they are not flat?

Non-humor: Have you been tuning pianos while trying to get along with other orchestra instruments and players (as I understand from your other post)? In case, do you sacrifice your "intonation"?

Humor: Gosh, all these martyrs, it looks like an army.

Regards, a.c.
.


I question your sobriety on this post but to answer but one of your confusion of questions.

In blending their ensemble, don't all musicians give a little in their own intonation for the common good? Sacrifice is far too vulgar a word in this instance. To not accommodate the needs of another in the intimacy of music making is somewhat akin to self pleasuring or have I lost you again?

Your grasp of the full effects of inharmonicity seem lacking. This surprises me.

Surely you heard the bleating of the piano in Bills' video in the "non vib" ensemble sections of that otherwise fine group of musicians. Didn't you hear the effects of an over stretched treble on the rest of the instruments. Or we're you, like most, only listening to the piano?
I know there are some people who enjoy the bleat of an overstretched piano. There are also those who get a similar cheap thrill from the bleat of a Mighty Wurlitzer theatre organ. you portray yourself as having higher sensibilities but you give yourself away.

I can make a trumpet bleat like a Spanish bullfighting band. Indeed, I have made a lot of money doing just that but I would not use that sound when I played under the baton of sir John Barbirolli. ( long story).. Similarly I can tune a piano so that it bleats but my default tuning is not to do that. Am I compromising the intonation of the piano when I make it bleat? Am I compromising (sacrificing?) the intonation of the piano when I use my skills to minimise that bleating?

I will minimise the bleating every time when an ensemble is to use the piano. We all heard how it compromised the ensemble sound in Bills' example. It would do the same thing in a string ensemble utilising piano.

My specialised knowledge as a musician only helps me explain this stuff. it is not the only reason I tune this way. The reason I tune this way is because all my colleagues who are involved in what is regarded as the finest tuning available for purpose tune this way.

My colleagues in NY, LA and London who I have worked alongside at different times in my life, all tune extremely similarly. There are many reasons that one piano company is used for the vast majority of top line commercial recordings by major companies and one of them is the way they are tuned by that companies' specialist staff tuners. It is also the tone regulation by those who specialise in this alone. Many of the highly regarded European record companies record in London studios, according to some of the contracts I recieve.

As I have often said, nothing beats listening to your own tuning for forty hours and continually refining it according to the standards developed over the years by generations of specialist tuners who have worked for the company who made the piano that is chosen for the highest standards demanded by the industry.

Carry on bleating.




Rxd,

You wrote:

..."In blending their ensemble, don't all musicians give a little in their own intonation for the common good? Sacrifice is far too vulgar a word in this instance. To not accommodate the needs of another in the intimacy of music making is somewhat akin to self pleasuring or have I lost you again?"...

Hope Martys reply has helped you, what can I add... As mentioned, I think we come from different experiences and cannot exclude that our sense of intonation is not that very same. What my experience tells me is that musicians, amongst themselves, can normally share good intonation, at least to a certain degree. Perhaps it is when you experience intonation as a command, as an imperative, as something that tells you when IT is right and when it is wrong, improvable or not, it is then that you can measure and compare your sense of intonation, and always a better ear is able to help the dim one.

...Your grasp of the full effects of inharmonicity seem lacking. This surprises me. ...

Yes, even now when I read ...Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played.., I cannot resist laughing.

BTW, you did not answer my humorous questions... Should I understand that a properly tuned piano can only sound sharp? Or, you hear a piano being sharp and you leave it because... that is inharmonicity? Serious, how have you ended up compromising (if not sacrificing) intonation? Any technical hint?

I hope you do not mind if we are two different musicians and technicians, and what you may want to know is that I have never compromised my intonation.

...Surely you heard the bleating of the piano in Bills' video in the "non vib" ensemble sections of that otherwise fine group of musicians. Didn't you hear the effects of an over stretched treble on the rest of the instruments. Or we're you, like most, only listening to the piano?...

Sorry, I missed that video, would you link it for me?

...I know there are some people who enjoy the bleat of an overstretched piano. There are also those who get a similar cheap thrill from the bleat of a Mighty Wurlitzer theatre organ. you portray yourself as having higher sensibilities but you give yourself away....

I do not know what you mean, is that idiomatic? In any case, why do you mention bleating? What has that to do with pianos that sound inevitably sharp... because of inharmonicity?

...I can make a trumpet bleat like a Spanish bullfighting band. Indeed, I have made a lot of money doing just that but I would not use that sound when I played under the baton of sir John Barbirolli. ( long story).....

Yes, you seem to have many long stories and to be really into sharing them. Have you thought about starting a personal thread?

...Similarly I can tune a piano so that it bleats but my default tuning is not to do that. Am I compromising the intonation of the piano when I make it bleat? Am I compromising (sacrificing?) the intonation of the piano when I use my skills to minimise that bleating?....

Well, you tell me. But, are you saying that sometimes you may as well tune a piano that will sound... sharp?

...I will minimise the bleating every time when an ensemble is to use the piano. We all heard how it compromised the ensemble sound in Bills' example. It would do the same thing in a string ensemble utilising piano....

Hmmm... See how different we are, I only have one tuning, and it is the One that, in my ears, matches my sense of intonation to the highest degree. That one, an nothing else. See, no compromise at all is (IMO) how intonation can be improved on a piano, but you need to be equipped, firm and strong, otherwise you adjust on a compromise.

...My specialised knowledge as a musician only helps me explain this stuff. it is not the only reason I tune this way. The reason I tune this way is because all my colleagues who are involved in what is regarded as the finest tuning available for purpose tune this way....

Hmmm..., Whenever, I am ready to listen to the finest tuning of yours, just tell me when.

...My colleagues in NY, LA and London who I have worked alongside at different times in my life, all tune extremely similarly....

Yes, similarly, I too think we all tune similarly.

...There are many reasons that one piano company is used for the vast majority of top line commercial recordings by major companies and one of them is the way they are tuned by that companies' specialist staff tuners. It is also the tone regulation by those who specialise in this alone. Many of the highly regarded European record companies record in London studios, according to some of the contracts I recieve.
As I have often said, nothing beats listening to your own tuning for forty hours and continually refining it according to the standards developed over the years by generations of specialist tuners who have worked for the company who made the piano that is chosen for the highest standards demanded by the industry.

Fantastic, rxd (or whatever your name is), I look forward to meeting your colleagues too.

...Carry on bleating.

?

Regards, a.c.
.
Posted by: rxd

Re: HISTORICAL ET AND MODERN ETs - 01/30/14 10:29 PM

Alfredo,

Only one question.

If you had to tune a piano and organ together, how would you minimise or even completely reconcile the differences between the way they tune?
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 01/31/14 05:49 PM

Originally Posted By: rxd
Alfredo,

Only one question.

If you had to tune a piano and organ together, how would you minimise or even completely reconcile the differences between the way they tune?


Good question, rxd, though you may already know my answer: Was it Mandrake? Sure, we might be asked to manage some uncomfortable deals, but why do you ask... Weren't we talking about "refined" and "finest tunings" and "highest standards"?

I too have only one new question: can you say when someone is singing or playing out of tune?

Of course, I would be delighted if you were to reply to my previous questions too, in order to get to the point:

Are you saying that a properly tuned piano can only sound sharp?

How do you (technically) "...accommodate the needs of another in the intimacy of music making..."?

Regards, a.c.
.
Posted by: rxd

Re: HISTORICAL ET AND MODERN ETs - 01/31/14 11:36 PM

Bingo!
You have just proven some of my earlier points.
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 02/01/14 12:08 AM

Originally Posted By: rxd
Bingo!
You have just proven some of my earlier points.


I guess anything goes in this thread.

That being said, rxd, is there any intonation problem when the organ and piano stick within C2-F6 (normal organ ambitus)?

I have played Bach Art of Fugue arranged for 2 keyboards on organ and piano (ambitus C2-C6) without problems.

Kees
Posted by: rxd

Re: HISTORICAL ET AND MODERN ETs - 02/01/14 09:57 AM

Kees,
Depending on what you mean by intonation, that word has had a couple of strange interpretations here, lately.

To the average listener, no real discrepancies would be noticed between the notes that you indicated. Maybe the odd extreme note if you were listening intently to a playback.

There is only a problem in the top 2 & lower 2 octaves or so as I'm sure you know.

An organ manufacturer had, in the '80's, three stretch settings on their larger church instruments intended to reduce this problem somewhat. So it depends on what you mean by organ. smile

I have heard some unbelievable audible piano stretching in Europe in the '60's and some brassy toned pianos in southern churches that would give problems matching just one note in the '70's so it depends on what you mean by piano. wink
Posted by: prout

Re: HISTORICAL ET AND MODERN ETs - 02/01/14 10:21 AM

I performed Flor Peters' Concerto for Organ and Piano last year. The piano was tuned with moderate stretch, but tight octaves in the treble due to so many parallel octave runs. We were unaware of major intonation issues, possibly because of the structure of the work. i didn't think about it at the time, but maybe Peters understood some of the issues discussed here and took that into consideration when writing it. Very fun piece to play.
Posted by: DoelKees

Re: HISTORICAL ET AND MODERN ETs - 02/01/14 10:57 AM

Originally Posted By: prout
I performed Flor Peters' Concerto for Organ and Piano last year. The piano was tuned with moderate stretch, but tight octaves in the treble due to so many parallel octave runs. We were unaware of major intonation issues, possibly because of the structure of the work. i didn't think about it at the time, but maybe Peters understood some of the issues discussed here and took that into consideration when writing it. Very fun piece to play.

Thanks for posting that. I was about to tell rxd there is no repertoire for piano and organ anyways so the problem is moot but I stand corrected already. I've seen some of those halleluja churches (not sure what the religion is precisely) in the southern US; I think organ-piano intonation is not on their minds at all.

Kees
Posted by: prout

Re: HISTORICAL ET AND MODERN ETs - 02/01/14 11:33 AM

Originally Posted By: DoelKees
Originally Posted By: prout
I performed Flor Peters' Concerto for Organ and Piano last year. The piano was tuned with moderate stretch, but tight octaves in the treble due to so many parallel octave runs. We were unaware of major intonation issues, possibly because of the structure of the work. i didn't think about it at the time, but maybe Peters understood some of the issues discussed here and took that into consideration when writing it. Very fun piece to play.

Thanks for posting that. I was about to tell rxd there is no repertoire for piano and organ anyways so the problem is moot but I stand corrected already. I've seen some of those halleluja churches (not sure what the religion is precisely) in the southern US; I think organ-piano intonation is not on their minds at all.

Kees


There is a reasonable amount of rep for organ piano. Here is a snippet of a work. Pretty good intonation to my ear anyway.

http://www.youtube.com/watch?v=zKntVHs2ZAY

Edit: Not my taste by the way, but still well done.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 02/01/14 02:06 PM

Hi,

Prout, Kees,

Perhaps rxd was referring to any two fixed-scale instruments, in a more general sense, that is how I understand his question. Sometime, when it comes to twin a piano and a second instrument (tuned by someone else), it could be, as I said, uncomfortable. And possibly it would be up to the tuner whether to accommodate or not. In any case, perhaps you can tell what that has to do with rxds lament on bleating pianos and pianos that sound inevitably sharp because of inharmonicity?


Originally Posted By: alfredo capurso
Originally Posted By: rxd
Originally Posted By: alfredo capurso
Originally Posted By: Ed McMorrow, RPT
Perfection is like a mirage; when conditions are right you can see it is possible, but every motion towards it makes it recede from you.


For me, Perfection is like Excellence: when conditions are right I can see it possible, perhaps any wrong notion (and/or posture) may cut it down.

Beyond that, I do not think the OP was about Perfection, but scorn and indignation.


Originally Posted By: rxd
Originally Posted By: Minnesota Marty
Originally Posted By: rxd
[quote=Minnesota Marty]Why is the assumption being made that "concert" tuning is the same as "studio" tuning? As a pianist who has been in both situations, it seems that the tuner plays a very different role in each type of activity.

In performance, I've never been given a lunch break between the 2nd and 3rd mvts. of a concerto. The demands are totally different and shouldn't be equated.


Care to expand on both these paragraphs, Marty? Neither of them seem to be saying anything unless I'm missing some humor.

Well, it is a combined response to a number of your recent posts.

You seem to be in a situation which is unlike the vast majority of highly skilled tuners. That is why I pointed out the difference in tuning for a concert or for a recording. 'Live in Concert' recording (or tuning) is very different than studio work. I'm thinking of the quest for perfection as it relates to the concept of this thread.

In the classical world, unlike the craziness of RA Hall, piano tuners aren't pushed into rush jobs or get yelled at by a stage manager. I'm sure there are some rush jobs in unusual situations, but that is not the standard procedure for concert work or recording. I'm sorry that you work in such a frenetic environment.

Why is it that you keep stating that wind instruments go flat at the top of their range and the reverse happens at the lower end? This is simply untrue. It is the other way around. Your 'stretch theory' just doesn't cut it.

Nothing I stated was meant to be humorous.


As I suspected.

We are involved in all kinds of situations. The RAH series always gives us 3-4 seperate tuning slots on production day, 2-3 of them entirelyl to ourselves. I doubt I ever said anything different.

The experience of my former student was not with the company I work with. it happened in America, as a matter of fact. not in a major centre. That would never be tolerated here.

Everything we do here is in well defined, pre arranged, usually copious time slots.

Have you been carrying this half understood notion all this time? I categorically never said that any wind instrument played flat in the upper register and sharp in the lower. I have, however stated that the piano is stretched more than any other instruments (skilfully played, of course).

Having been a highly skilled professional wind player myself at film studio and broadcast level and in many genres with many different combinations of instruments, of course I understand their intonation. Currently, I am called upon to coach young professional ensembles and more recently, string quartets as an extension of my work with piano trios.

I have spoken of certain situations where a wind player has played the odd note or two sharper than the rest of the orchestra that has affected the piano entry. That is not to say anything about general tendencies of an instrument.

Let me clear this misunderstanding once and for all. Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played. This is easily accomodated by skilled players. They will, of course, note that it is a different experience from playing with a well tuned organ at the same nominal pitch, for example.
This is, as I'm sure you understand, the effect of inharmonicity in pianos. I am assuming an understanding of this basic characteristic of pianos. Perhaps I shouldn't.

Pianos tuned with exaggerated stretch only makes matters worse. It is the exaggerated tuning of the piano that is at fault, not the other instruments. I can't stress this enough

To say that a piano is sharp is not the same as saying that any other instrument plays flat.

Thank you for bringing this up and giving me an opportunity to clarify what I may not have said very clearly and for anybody else who may have been carrying this misunderstanding.
Hopefully I didn't create more. this partial understanding explains a lot. But it still doesn't address your post in question.

I still don't understand about "lunch between movements" or the exact nature of the distinction you make between concert and studio. Perhaps another partial understanding? What was your frame of mind when you wrote it? Strange


Hi,

I do not have much time in these days, I would like to be able to seat down for a solid time an reply properly. Instead I have to be short.

rxd, you wrote:

..."Let me clear this misunderstanding once and for all. Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played. This is easily accomodated by skilled players. They will, of course, note that it is a different experience from playing with a well tuned organ at the same nominal pitch, for example.
This is, as I'm sure you understand, the effect of inharmonicity in pianos. I am assuming an understanding of this basic characteristic of pianos. Perhaps I shouldn't."...

Perhaps you want to expand on that. When I read that, I get the feeling we come from two different planets. Please note, nothing personal and I do not think it is a question of amount_or_type_of_experience... musician, playing concerts in duo (with a piano) or more, multi-instrument player, tunings in prestigous halls, for prestigious brands etc... in fact, all this calls for a question.

Recently I have had to "learn" that the piano is the most out-of-tune instrument on the stage (BB), some colleagues still wonder about the "point of best fit", others regret that the piano cannot adjust_in_real_time, and now I learn from you that "...Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played."

Humor: Do you tune pianos sharp?

Humor: Are pianos sharp when they are not flat?

Non-humor: Have you been tuning pianos while trying to get along with other orchestra instruments and players (as I understand from your other post)? In case, do you sacrifice your "intonation"?

Humor: Gosh, all these martyrs, it looks like an army.

Regards, a.c.
.


I question your sobriety on this post but to answer but one of your confusion of questions.

In blending their ensemble, don't all musicians give a little in their own intonation for the common good? Sacrifice is far too vulgar a word in this instance. To not accommodate the needs of another in the intimacy of music making is somewhat akin to self pleasuring or have I lost you again?

Your grasp of the full effects of inharmonicity seem lacking. This surprises me.

Surely you heard the bleating of the piano in Bills' video in the "non vib" ensemble sections of that otherwise fine group of musicians. Didn't you hear the effects of an over stretched treble on the rest of the instruments. Or we're you, like most, only listening to the piano?
I know there are some people who enjoy the bleat of an overstretched piano. There are also those who get a similar cheap thrill from the bleat of a Mighty Wurlitzer theatre organ. you portray yourself as having higher sensibilities but you give yourself away.

I can make a trumpet bleat like a Spanish bullfighting band. Indeed, I have made a lot of money doing just that but I would not use that sound when I played under the baton of sir John Barbirolli. ( long story).. Similarly I can tune a piano so that it bleats but my default tuning is not to do that. Am I compromising the intonation of the piano when I make it bleat? Am I compromising (sacrificing?) the intonation of the piano when I use my skills to minimise that bleating?

I will minimise the bleating every time when an ensemble is to use the piano. We all heard how it compromised the ensemble sound in Bills' example. It would do the same thing in a string ensemble utilising piano.

My specialised knowledge as a musician only helps me explain this stuff. it is not the only reason I tune this way. The reason I tune this way is because all my colleagues who are involved in what is regarded as the finest tuning available for purpose tune this way.

My colleagues in NY, LA and London who I have worked alongside at different times in my life, all tune extremely similarly. There are many reasons that one piano company is used for the vast majority of top line commercial recordings by major companies and one of them is the way they are tuned by that companies' specialist staff tuners. It is also the tone regulation by those who specialise in this alone. Many of the highly regarded European record companies record in London studios, according to some of the contracts I recieve.

As I have often said, nothing beats listening to your own tuning for forty hours and continually refining it according to the standards developed over the years by generations of specialist tuners who have worked for the company who made the piano that is chosen for the highest standards demanded by the industry.

Carry on bleating.




Originally Posted By: alfredo capurso
Rxd,

You wrote:

..."In blending their ensemble, don't all musicians give a little in their own intonation for the common good? Sacrifice is far too vulgar a word in this instance. To not accommodate the needs of another in the intimacy of music making is somewhat akin to self pleasuring or have I lost you again?"...

Hope Martys reply has helped you, what can I add... As mentioned, I think we come from different experiences and cannot exclude that our sense of intonation is not that very same. What my experience tells me is that musicians, amongst themselves, can normally share good intonation, at least to a certain degree. Perhaps it is when you experience intonation as a command, as an imperative, as something that tells you when IT is right and when it is wrong, improvable or not, it is then that you can measure and compare your sense of intonation, and always a better ear is able to help the dim one.

...Your grasp of the full effects of inharmonicity seem lacking. This surprises me. ...

Yes, even now when I read ...Pianos, when properly tuned to themselves, tend to be sharper in the treble and flatter in the bass than other instruments skilfully played.., I cannot resist laughing.

BTW, you did not answer my humorous questions... Should I understand that a properly tuned piano can only sound sharp? Or, you hear a piano being sharp and you leave it because... that is inharmonicity? Serious, how have you ended up compromising (if not sacrificing) intonation? Any technical hint?

I hope you do not mind if we are two different musicians and technicians, and what you may want to know is that I have never compromised my intonation.

...Surely you heard the bleating of the piano in Bills' video in the "non vib" ensemble sections of that otherwise fine group of musicians. Didn't you hear the effects of an over stretched treble on the rest of the instruments. Or we're you, like most, only listening to the piano?...

Sorry, I missed that video, would you link it for me?

...I know there are some people who enjoy the bleat of an overstretched piano. There are also those who get a similar cheap thrill from the bleat of a Mighty Wurlitzer theatre organ. you portray yourself as having higher sensibilities but you give yourself away....

I do not know what you mean, is that idiomatic? In any case, why do you mention bleating? What has that to do with pianos that sound inevitably sharp... because of inharmonicity?

...I can make a trumpet bleat like a Spanish bullfighting band. Indeed, I have made a lot of money doing just that but I would not use that sound when I played under the baton of sir John Barbirolli. ( long story).....

Yes, you seem to have many long stories and to be really into sharing them. Have you thought about starting a personal thread?

...Similarly I can tune a piano so that it bleats but my default tuning is not to do that. Am I compromising the intonation of the piano when I make it bleat? Am I compromising (sacrificing?) the intonation of the piano when I use my skills to minimise that bleating?....

Well, you tell me. But, are you saying that sometimes you may as well tune a piano that will sound... sharp?

...I will minimise the bleating every time when an ensemble is to use the piano. We all heard how it compromised the ensemble sound in Bills' example. It would do the same thing in a string ensemble utilising piano....

Hmmm... See how different we are, I only have one tuning, and it is the One that, in my ears, matches my sense of intonation to the highest degree. That one, an nothing else. See, no compromise at all is (IMO) how intonation can be improved on a piano, but you need to be equipped, firm and strong, otherwise you adjust on a compromise.

...My specialised knowledge as a musician only helps me explain this stuff. it is not the only reason I tune this way. The reason I tune this way is because all my colleagues who are involved in what is regarded as the finest tuning available for purpose tune this way....

Hmmm..., Whenever, I am ready to listen to the finest tuning of yours, just tell me when.

...My colleagues in NY, LA and London who I have worked alongside at different times in my life, all tune extremely similarly....

Yes, similarly, I too think we all tune similarly.

...There are many reasons that one piano company is used for the vast majority of top line commercial recordings by major companies and one of them is the way they are tuned by that companies' specialist staff tuners. It is also the tone regulation by those who specialise in this alone. Many of the highly regarded European record companies record in London studios, according to some of the contracts I recieve.
As I have often said, nothing beats listening to your own tuning for forty hours and continually refining it according to the standards developed over the years by generations of specialist tuners who have worked for the company who made the piano that is chosen for the highest standards demanded by the industry.

Fantastic, rxd (or whatever your name is), I look forward to meeting your colleagues too.

...Carry on bleating.

?

Regards, a.c.
.



Originally Posted By: rxd
Alfredo,

Only one question.

If you had to tune a piano and organ together, how would you minimise or even completely reconcile the differences between the way they tune?


Originally Posted By: alfredo capurso
Originally Posted By: rxd
Alfredo,

Only one question.

If you had to tune a piano and organ together, how would you minimise or even completely reconcile the differences between the way they tune?


Good question, rxd, though you may already know my answer: Was it Mandrake? Sure, we might be asked to manage some uncomfortable deals, but why do you ask... Weren't we talking about "refined" and "finest tunings" and "highest standards"?

I too have only one new question: can you say when someone is singing or playing out of tune?

Of course, I would be delighted if you were to reply to my previous questions too, in order to get to the point:

Are you saying that a properly tuned piano can only sound sharp?

How do you (technically) "...accommodate the needs of another in the intimacy of music making..."?

Regards, a.c.
.


Originally Posted By: rxd
Bingo!
You have just proven some of my earlier points.


rxd,

What were the points you intended to prove? Why do I get the feeling of an attempt to circumvent a few questions?

Were you saying that a properly tuned piano can only sound sharp?

How do you (technically) "..accommodate the needs of another in the intimacy of music making.."?

Regards, a.c.
.
Posted by: rxd

Re: HISTORICAL ET AND MODERN ETs - 02/01/14 06:50 PM

Dearest Alfonso,
So brill to hear from you and in such polite demeanour. That's much better. , but sweetie, you have more questions than a jealous lover!!... It's overwhelming. A positive bombardment, luvvie. I ought to be flattered but You're bored when you're adored, you're blas. To quote sir Noel who was ever so bona, even when he had no riah to zhush and his lallies were grizzled. Such an homie polone if ever there was one he could whurdle his nadgers and firtle his cordwangler round his futtocks with the best.

I can but respond to two questions darling an that's yer lot.

Don't u find that the give and take of making music with another human an intimate affair? I do. Quite possibly that turn of phrase, in partic, gains too much in translation but music making is no time to be selfish now, is it?? Thatt would b a right pain in the khyber.

The other answer, before I let you go is that of course I don't tune sharp. I would get my cards immediately and my pink slip too if I did that. Quite amazing that you think that because most others here are assuming that I must tune flat. I'm Tuning for the worlds professionals. That's no time to bugger about. Absolutely clean octaves are sacred. You work it out if that goes sharp or not. Who on earth do you think you're talking too? If my pianos could only speak, they wouldn't speak to either of us.

Just in case anybody thinks I must be on the piste or even taking the piste, I'm in fact pulling an all nighter. I can do the best part of a weeks work in no time when I have the place to myself. I was just interacting with a security guard who popped in to say hello. What he actually said was "Ey oop" because he's from my part of the world and we had some gay banter remembering Round the Horne.
They were masters of the single entendre. The writers would compose a folk song by perusing the greater, huger Oxford dictionary looking for obscure words that sounded vaguely rude but weren't. Words like "futtocks" which actually means, well, , you look it up.

If anyone thinks this should be censored, and, lord knows, my spellchecker tried, every word I used was used on "auntie Beeb" (our reference to the prudish, prim and proper BBC) fifty years ago.
Time to stop messin abart and get back to work. Except I don't call it work, they do.

They used to say that behind every successful man there's a woman....telling him he's wrong.
Posted by: accordeur

Re: HISTORICAL ET AND MODERN ETs - 02/01/14 07:11 PM

After having read that I wonder where Isaac went.
Posted by: Chris Leslie

Re: HISTORICAL ET AND MODERN ETs - 02/02/14 05:11 AM

Originally Posted By: accordeur
After having read that I wonder where Isaac went.

rxd, are you trying to be funny, or just going more insane?
Posted by: rxd

Re: HISTORICAL ET AND MODERN ETs - 02/02/14 07:13 AM

The parallel being that millions of people will know exactly what I'm talking about.
It's a closed book to all others and might even make them angry.
Posted by: alfredo capurso

Re: HISTORICAL ET AND MODERN ETs - 04/28/14 05:42 PM


Hi All,

Only this evening I learned about the 'Baldassin - Sanderson Tuning Temperament', so I went on google and found this:

http://www.youtube.com/watch?v=hs8A4B3HT34

More than ever, I think that the original problem is not the piano, but the mentor.

Regards, a.c.
.