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After the past couple of weeks of discussion, I completely get your perspective, Bill. And I share it.

Do you feel it would be appropriate to think of strict ET as a sort of baseline; a level of skill we should all be able to achieve, and from there, go on to modify it - as you do - to make it more musical? Not as an end, but a means?

For me, I like that what I'm doing is more musical, but I'd also like to think that I got there a little more than accidentally; that what I'm doing is rooted in a standard. In my way of thinking, if it's not, it's haphazard.

YMMV...

Very well said, Mr. Stopper.

Why does Bill think that this attempt is a misguided goal?

It is a fact that the modern scale is designed around equal temperament (the twelve tone divisions between octaves being the best solution below 19-TET). Modern string lengths are also designed to resonate at equal temperament frequencies (constant exponential slope on the bridge).

I see unequal temperaments as a very important and worthwhile part of musical variety and history, but the piano is not designed around them today.

Another level to this discussion is whether perfected equal temperament is considered unequal, because technically it is.

Only one partial can be tuned to equal temperament at a time, so machines that tune to the 5th partial in the midrange at the expense of 4ths and 5ths, achieve perfect 3rds and everything else is a little 'off'.

As Mr. Stopper so skillfully showed, 3rds and 6ths, which utilize primarily the first level 3rd, 4th and 5th partials, can be tuned almost perfectly on nearly any scale. To include the other parts of the spectrum, one runs into challenges.

Tenor,

I believe that you got to where you are now with an intent for ET but it was slightly colored by a good ear for music and the presence of the key signature. The latter is virtually never considered by ET only proponents but was a part of the lost art of 19th Century temperament tuning.

Tunewerk, for the answer to your question "why?" please see my most recent post in the CM3's technique topic.

Fully agreed, 12th-root-of-two (plus iH) does not result in the "...best sound".

I am sure you have noticed that severe limitation many years ago, Bill, and I understand that as the reason why you abandoned the idea of perfecting that type of tuning.

In that tuning there is nothing that could be perfected, essentially because "that ET" is wrong. I know, this seems hard to believe, but think the axiom, an aural-non-beating octave: even (or, especially) if one perfects its execution, there is no way to achieve a satisfactory tuning.

So, if we talk about 12-root-of-two-ET, I agree: "...attempts to perfect it are a misguided goal."

I guess that, being good at aural tuning and desiring a nice sounding piano, you will have tried to “get” it a fair number of times, perhaps for years as I did (and you, Bernhard?), without good results.

Sure, this of mine is only a conjecture, but I guess that for that reason, many (aural) tuners will have stopped referring to "that ET" and started to go for their own “good” tunings, no matter if aurally or with an ETD, no matter how people would have called that. To customers we would answer “Yes,... ET”, but actually it could only be a (due/so called) “variant”.

This, in my perspective, is how Piano Tuners have been left, literally in a limbo, with an ET model that could not satisfy our ear, with an unmusical axiom and few (superficial) instructions, possibly only for the first octave... wide fourths and narrow fifths. Perhaps unconfessable, but for many of us, our “good” tunings needed to be reinvented.



From my previous post, Bill: What do you think would be better, as a reference for voices?

After you recent post, how do you define "a strict ET", would it be again a "strict" 12-root-of-two-ET?

Regards, a.c.
.

Alfredo,

Those were some interesting points you made. To me, the "strict" model of ET is that which the PTG tuning exam committee makes in order to create the most perfect and humanly possible ET against which an examinee's efforts can be measured with tolerances.

That whole exercise has always intrigued me because such perfect renderings of ET are never used outside of the exam experience itself. Those records are strictly confidential and never revealed to anyone.

The only exception I know of is that one such master tuning that was done at a Community College, (where an actual tuning exam has never occurred), the technician there who participated in that master tuning uses that record to tune that piano. While he says that it works very well indeed, he does not attribute any great claims to it, only that it works well as a matter of convenience.

Also, most of those master tuning records are done at conventions where the piano is new and it comes and goes, so no one ever sees the record of that effort. One person, however, a man of a great many years experience and who teaches piano tuning at one of the most prestigious schools, was often known to take his committee far beyond the usual 4 hours to arrive at a master tuning.

One year, he was done in a remarkably short period of time, less than an hour. I asked him what the difference was that time? He replied that he had used the master tuning record from a previous year on the same make and model of piano as the preliminary tuning. There were simply far fewer errors to detect, identify and correct than there would have been otherwise.

When the exam administrator heard of that, she said it is not something that should ever be repeated because it would only mean a trend in repeating past errors. I remarked that I did not agree. I said that instead, a previous precedent that could never have been entirely perfect, was given a chance to be improved upon. There still could and would have been minute differences between the two pianos that had to be worked out, so using a previous model as a preliminary tuning was a valid idea. Otherwise, the whole process would have needed to start from the very beginning and would have been subject to all possible errors and would have taken the undue time it used to take to resolve all of them.

The only other time I have heard of a master tuning having been completed in a very remarkably short period of time, about 25 minutes, was the time when the great master and mentor of both aural and electronic tuning, Jim Coleman, Sr. had been the one to perform the preliminary tuning. In that instance, Doctor Coleman did as I suggested earlier today in another topic, to use his ETD to tune the center string of each note (which is all that is tested or considered, not the whole unison) and then to use his own very highly developed aural tuning skills to perfect that arrangement.

That left the committee with very little work to do but there were still some slight adjustments. However, I am speaking only of muted off, center strings, not whole unisons. For anyone, even the most highly skilled of technicians to ever be able to convert that arrangement into a final tuning for the whole piano would still have been a very difficult and formidable task.

Then, the question becomes whether that seemingly perfect arrangement really would sound all that good? Would it really sound all that superior to what other highly skilled technicians do in daily practice? Would the choice of 2:1 octaves in octave 7 be satisfactory to most concert and broadcast technicians? Probably not.

If not, then how much to stretch that portion of the piano? How much is too much? I have seen one self appointed expert say that it should be 0.5 beats per second. OK, how do we measure that? How do we control that? If one of those octaves is 1 full beat per second wide but another is perfectly pure, does that ruin everything?

Alfredo, I must admit that I have never fully understood your concept of CHAS. I am not even certain what those letters represent nor the meaning of them. I do not discount, however, the length that both you and Herr Stopper have gone to fully document what you do and to have such writing reviewed and vetted among parties which approve of what you say and do and how you have documented it.

But whether you two are in precise agreement or not and whether you can get the whole rest of the world to go along with it is quite another matter! Does every ETD program reproduce what you refer to as CHAS on every piano, every time? I think not. Does everyone who uses Herr Stopper's software produce a tuning on any given piano that would be identical to his? Do any two people who use any ETD program or tune aurally ever come up with exactly the same results?

I certainly agree that Herr Stopper's software is quite effective and produces superior results in the hands of a technician who is competent to use it. But it is only one idea that does not, unfortunately please everyone. It has its own effect that is undeniable. The wider the octave, the more active the RBI's within it will be.

(I consider Herr Stopper to be a personal friend and colleague and do not wish to diminish his efforts in any way, nor do I wish to do likewise to you. Herr Stopper and I have had some meetings and friendly discussions. I encourage anyone who is interested in his work, ideas and products to embrace them. I do likewise with you, Alfredo. After all, both of you have documented work which is far more scientifically credible than my own. I only write from my own experience and am not accountable to any institution or corporation, nor do I wish to be.

I am not a scholar who adheres to the standards of such that both of you do. I am merely a piano technician of long experience who has seen and embraced ideas from many different perspectives. I also have to embrace the expectations there are within my own community and those of the piano dealer who provides me with about half of my work. Those circumstances mean most often, NO ET, ANYTIME! When the rare call there may be for key signature neutral temperament, I have my own solution to that, the so called, ET via Marpurg, a Quasi Equal Temperament where all RBI's are virtually the same as in ET but 4ths & 5ths are equalized.)

If every interval is tempered equally within the kind of above arrangement (a more highly stretched central octave that results in a pure 12th), all of the RBI's beat more rapidly. While it may be a very good choice for concert instruments on stages in front of large orchestras or recording studios where the most complex kinds of music are played, there are other kinds of pianos which are used in other kinds of circumstances. A truly knowledgeable piano technician should know how to adapt to each kind of circumstance individually.

I have often mentioned the value of the key signature of which any discussion of ET is bereft, as if it should never be given any consideration. It is, in fact, my belief, the foundation upon which the "whole of Western music" is built, not ET, I am sorry to say. One actually expects for any particular key signature to sound a certain way. That cannot happen with any particular arrangement of ET, no matter what the amount of stretch in the octaves is, from a little to a lot.

To continually persist in the perfection of ET only takes away the special sound that is expected from key signature from the piano. I have heard similar arguments from the proponents of Well Temperament as I have heard from those who promote ET. Any "imbalance" is intolerable! Yet, the most perfectly well balanced Well Temperament, the Thomas Young #1 is rarely used. It has its own problems and despite how good it looks on a graph with its perfect symmetry, nearly anyone among Well Temperament proponents ever chooses it!

There are an infinite number of Well Temperaments other than that which may serve well. There are an infinite number of Mild Meantones, which by their very description violate the rules of Well Temperament. There are an infinite number of Modified Meantones which also can serve well and equally violate Well Temperament rules, and, most importantly, for the purposes of this discussion, there is an infinite possibility for Quasi Equal Temperament that follows and adheres to no rules whatsoever but satisfies the ear of both the tuner and the pianist.

Quasi Equal Temperament is what Owen Jorgensen described in his last whole book, Tuning, as "The lost art of 19th Century piano tuning". It was a time when tuners recognized that music required every key to be accessible and for there to be no greatly abrupt differences from one key to the next but still a reason and purpose for a modulation, all keeping within a very narrow range.

I possess many possibilities for effecting any number of nuances. I cannot, of course be any more perfect about any of them than I could be about ET but I can, in fact, make the piano sound pleasing to the pianist who is my client at any time. If he or she voices any displeasure with what I have done, I have a solution for it and it is never what I consider to be a perfected ET with any kind of particular stretch involved.

Should there be a standard?, Yes! I believe so and that first standard should be the adherence to A-440 pitch so that all instruments of the world can play together at any time, anywhere. Beyond that, however, the issue of temperament and octave stretch in the piano is too great to try to impose one single standard that will satisfy all. After all, the pitch of A4 tuned at exactly A-440 will have its 4th partial (A6) usually be at the same level as A-442!

None of us can change that! The best tuned piano under any circumstances will never match theoretical frequencies for ET at any time on any note except A4 measured only at its fundamental pitch! Therefore, I maintain the concept that the perfection of ET is therefore a misguided goal. I can't really say what that goal should be at this point but I know for sure that to try to attain a perfect ET is not what I should be doing or would ever want to do.

Hi Bill,

Thank you, that helps.

Thanks for your reply, Bill, possibly the whole picture is getting clearer and clearer.

On "strict ET" you wrote: ..."To me, the "strict" model of ET is that which the PTG tuning exam committee makes in order to create the most perfect and humanly possible ET against which an examinee's efforts can be measured with tolerances."...

That is good, I understand that "that ET" is still made by a human being. Please note (though), you are talking about a tuning, not a model. In a way, would you say that that works as a sort of local standard?

...SNIP..."..The only other time I have heard of a master tuning having been completed in a very remarkably short period of time, about 25 minutes, was the time when the great master and mentor of both aural and electronic tuning, Jim Coleman, Sr. had been the one to perform the preliminary tuning. In that instance, Doctor Coleman did as I suggested earlier today in another topic, to use his ETD to tune the center string of each note (which is all that is tested or considered, not the whole unison) and then to use his own very highly developed aural tuning skills to perfect that arrangement."...

I understand, first ETD, and then the arrangement is "perfected" aurally. So, perhaps by "strict ET" you mean "..the most perfect and humanly possible ET"? PTG's standard?

..."That left the committee with very little work to do but there were still some slight adjustments. However, I am speaking only of muted off, center strings, not whole unisons. For anyone, even the most highly skilled of technicians to ever be able to convert that arrangement into a final tuning for the whole piano would still have been a very difficult and formidable task."...

I understand: first the arrangement, then the "..final tuning for the whole piano".

..."Then, the question becomes whether that seemingly perfect arrangement really would sound all that good?"...

Yes, I too wonder.

..."Would it really sound all that superior to what other highly skilled technicians do in daily practice?"...

I do not know, but (please read your second paragraph) that is like asking "should that be called a strict ET"?

..."Would the choice of 2:1 octaves in octave 7 be satisfactory to most concert and broadcast technicians? Probably not."...

So, I would ask you: can that represent the final tuning of a whole piano in a "strict ET"?

..."If not, then how much to stretch that portion of the piano? How much is too much?"...

Well, unless you have a standard reference (for the whole scale) at your disposal, that would depend entirely on your sense of intonation (subjective) and/or interval beat-curves (objective). In octave 7 as well, you have fifths, octaves, 12ths, 15ths and 17ths that you can check; these intervals (all checked as part of a whole) can address both the beat-progression and your "musical ear", and reveal any possible inconsistency.

..."I have seen one self appointed expert say that it should be 0.5 beats per second. OK, how do we measure that? How do we control that? If one of those octaves is 1 full beat per second wide but another is perfectly pure, does that ruin everything?"...

Here again, whether that would ruin everything (musicality and resonance?), I would say it depends on your sense of intonation. But, if you have good sense of rhythm, you can always check all those other intervals.

Have to go /\ back tomorrow, I hope.

Regards, a.c.
.

...”Alfredo, I must admit that I have never fully understood your concept of CHAS. I am not even certain what those letters represent nor the meaning of them.”...

No problem, let’s continue our hedgehopping.

...”I do not discount, however, the length that both you and Herr Stopper have gone to fully document what you do and to have such writing reviewed and vetted among parties which approve of what you say and do and how you have documented it.
But whether you two are in precise agreement or not and whether you can get the whole rest of the world to go along with it is quite another matter! Does every ETD program reproduce what you refer to as CHAS on every piano, every time? I think not.”...

I think you are right.

...”Does everyone who uses Herr Stopper's software produce a tuning on any given piano that would be identical to his?”...

Hmmm... perhaps “identical” is a big word, I’d hope that those tunings be similar, perhaps with a bit of nuances?

...”Do any two people who use any ETD program or tune aurally ever come up with exactly the same results?”...

Certainly not, but should we preclude or negate the “artistic” side of tuning?

...”I certainly agree that Herr Stopper's software is quite effective and produces superior results in the hands of a technician who is competent to use it. But it is only one idea that does not, unfortunately please everyone. It has its own effect that is undeniable. The wider the octave, the more active the RBI's within it will be.”...

Well, perhaps you focus on active RBI’s, I look at all intervals as part of a whole. BTW, Bill, wouldn’t minor thirds get less active?

...”(I consider Herr Stopper to be a personal friend and colleague and do not wish to diminish his efforts in any way, nor do I wish to do likewise to you. Herr Stopper and I have had some meetings and friendly discussions. I encourage anyone who is interested in his work, ideas and products to embrace them. I do likewise with you, Alfredo. After all, both of you have documented work which is far more scientifically credible than my own. I only write from my own experience and am not accountable to any institution or corporation, nor do I wish to be.
I am not a scholar who adheres to the standards of such that both of you do. I am merely a piano technician of long experience who has seen and embraced ideas from many different perspectives. I also have to embrace the expectations there are within my own community and those of the piano dealer who provides me with about half of my work. Those circumstances mean most often, NO ET, ANYTIME! When the rare call there may be for key signature neutral temperament, I have my own solution to that, the so called, ET via Marpurg, a Quasi Equal Temperament where all RBI's are virtually the same as in ET but 4ths & 5ths are equalized.)”...

Hmmm..., "key neutral temperament", surely I like that better than "clinical" or "grey". Are you on WT-ET differences within the temperament area? For me the story continues when we expand.

...”If every interval is tempered equally within the kind of above arrangement (a more highly stretched central octave that results in a pure 12th), all of the RBI's beat more rapidly.”...

Also minor thirds?

...”While it may be a very good choice for concert instruments on stages in front of large orchestras or recording studios where the most complex kinds of music are played, there are other kinds of pianos which are used in other kinds of circumstances. A truly knowledgeable piano technician should know how to adapt to each kind of circumstance individually.”...

Sorry, I do not get the nexus. In any case, as far as I can say, all kinds of music, pianos and circumstances, they all call for the same issue, an instrument that sounds in tune?

...”I have often mentioned the value of the key signature of which any discussion of ET is bereft, as if it should never be given any consideration. It is, in fact, my belief, the foundation upon which the "whole of Western music" is built, not ET, I am sorry to say.”...

No doubt, Bill, we had to start somewhere, otherwise how would we know which notes to play?

...”One actually expects for any particular key signature to sound a certain way.”...

Hmmm..., if that was true we would have agreed on a kind of signature-standard long ago, and we would all be happy. My idea is that “one” expects (sound-wise) “euphony”, but I cannot exclude cases where “one” may prefer cacophony, or a “historical menu”. Denying the reason (bloodthirsty wolves) that led us where we are now... sounds a bit weird.

...”That cannot happen with any particular arrangement of ET, no matter what the amount of stretch in the octaves is, from a little to a lot.”...

Interesting that you say “...any particular arrangement of ET, no matter what the amount of stretch in the octaves is...”, as if the temperament expansion did not characterize the whole tuning even more.

Bill, I have to postpone the remaining part.

Regards, a.c.
.

Here's another attempt at progressive M3/M6/s, this time in a 1/14'+1/7' WT.

I got them just about progressive within the measurement tolerance of 0.2bps. Temperament range C#3-E4.

M3

F3A3 3.3
D3F#3 4.5
G3B3 5.2
C4E4 5.0
D#3G3 7.1
E3G#3 7.5
A#3D4 7.8
C#3F3 8.5
A3C#3 8.3
F#3A#3 9.7
G#3C4 10.3
B3D#4 11.8

M6

D3B3 5.4
F3D4 5.1
G3E4 5.6
E3C#4 8.3
C#3A#3 8.3
D#3C4 8.4
F#3D#4 10.2

Kees

Very nice Kees. It hints at Werckmeister III, with the slowest beat rates a little faster and the fastest beat rates a little slower. I like.

That is indeed impressive, Doel! A kinder and gentler temperament! I have no idea how you could combine 1/14' and 1/7' but I like it! Would you mind if I had Jason K. graph it for the sake of "modern temperament" graphs but also so I could get offset figures I or anyone could actually use to program an ETD?

This is the "kinda, sorta, pretty even" idea that I really like but adheres to key signature but seems to have no intolerable harshness in it.

The obsession with chromatic evenness for a "strict" ET is what I perceive to be the misguided goal. Yes, we want accessibility from any given key signature to the next without an emotionally disturbing contrast, yet we want and need for modulation to have a purpose that does, in fact, retain the emotional contrasts that are built into and intended in the music.

Opera Tenor's You Tube examples were an excellent example of this. The music from the opera will, of course be played by an orchestra in real performance. The orchestra and the vocalists are not tuned in, nor performing in ET! But the piano needs to be able to interpret all of these nuances for the purposes of introduction and education to the public.

I had a similar experience in 1992 when I was called upon to tune the piano for a new opera about the life of the architect, Frank Lloyd Wright. It had music in every key but each key was very specifically chosen for its color. That was the genesis for the EBVT, not a requirement for ET.

Vocal "correction" to ET is what we now often hear in pop music, instead. Any visually appealing young person who cannot really sing well has their in-the-cracks vocals helped by pitch correction software. Of course, that software is and could only be ET based. I know it as soon as I hear it!

I switch it off or ignore it when I do because it is not true musical artistry! It is what is being promoted for us to buy but I am not buying it!

A very good example of that was the Phantom of the Opera film that was produced about 9 or 10 years ago. It was great in many respects but they could have at least hired an actor for the title role who could both sing and act but the person they did hire could really do neither very well, especially sing! I went to an early screening of the film when I happened to be in Hollywood and I busted out laughing at the electronically "fixed" enhancements they had tried!

All such electronic fixes, being based upon theoretical ET and what else? Shouldn't there be a standard? Shouldn't that be it? Shouldn't we run every recorded music performance there ever was, either audio or video through such pitch correction software so that everything we ever listen to is adjusted to perfect ET values? Wouldn't that solve everything and make all music sound the way we really want it to sound?

If that ever happens, I will surely escape to Southwest Louisiana and listen only to Cajun music as produced by local artists in their own language and tuning! I might then go further South to Mexico and only listen to Folkloric music produced by local musicians in their own sense of tuning! I would want to escape the George Orwellian 1984 predictions that are now only coming true 30 years later in 2014!

Shouldn't there be a standard and shouldn't that standard be what Hermann Helmholtz defined 150 years ago and William Braide White copied in his book about 100 years ago? You better believe that there are those who are trying to impose those standards and trying to make all of us accept them!

Tuning instructions and offsets for ETD's can be found here.

Kees

I don't understand why the intervals are in this order. Why would this order be the one that should be progressive? A little different order and they would be progressive. If it is one of those WT things, you can just explain briefly. No reason to "cast your pearls before swine."

It's very simple. In UT the M3's are of unequal size, so they are not chromatically progressive. But of course you can always put them in an order where they are progressive, and every UT has a specific theoretically progressive order. In this sense there are 479001599 different UT's. The order I posted just happens to be the one for this particular temperament.

I don't want to be flaky and just settle for "better white keys" and accept anything that more or less does that, but want this precise temperament. The reason is that I used to tune a version that has P5's that are 2/13' and 1/13' narrow and EB pure instead of 1/7' and 1/14' with EB 1/14' narrow. Despite the small difference I find this one sounds noticeable better in certain keys (A major in particular).

To distinguish the 1/14' from the 1/13' version you have to be accurate.

Kees

Thanks, Kees.

Then I suppose that for some WTs the progression between some RBIs would be indistinguishable. In ET they are all about a 15:16 ratio, which seems to be the limit even for an exceptional ear. As soon as the ratio for any one RBI is even smaller, like 7:8, then others would have to be wider.

Hmmm... It is more of a challenge to get progressive RBIs in WT than in ET.

Right. If some beat rates are very close they become more like equal beating tests. You'll have to use some common sense based on the accuracy of your ear.

Kees

Hi Bill, following what you were saying:

...”To continually persist in the perfection of ET only takes away the special sound that is expected from key signature from the piano.”...

Well, we all talk about ET, but what we hear around confirms that "ET", for various reasons, is still an abstract kind of tuning. Sure, we have some kind of ETD’s variants of 12-root-of-two, but I do not have that in mind, when I mention modern ETs.

...”I have heard similar arguments from the proponents of Well Temperament as I have heard from those who promote ET. Any "imbalance" is intolerable! Yet, the most perfectly well balanced Well Temperament, the Thomas Young #1 is rarely used. It has its own problems and despite how good it looks on a graph with its perfect symmetry, nearly anyone among Well Temperament proponents ever chooses it!”...

Hmmm..., perhaps that has to do with the “..sound that is expected”? Or with the tuning execution? And, how important is “exactitude” when we execute a tuning? What will the gap be, between the model and the actual tuning? These (I suggest) are some other questions on which you might ponder.

...”There are an infinite number of Well Temperaments other than that which may serve well. There are an infinite number of Mild Meantones, which by their very description violate the rules of Well Temperament. There are an infinite number of Modified Meantones which also can serve well and equally violate Well Temperament rules, and, most importantly, for the purposes of this discussion, there is an infinite possibility for Quasi Equal Temperament that follows and adheres to no rules whatsoever but satisfies the ear of both the tuner and the pianist.”...

So, it seems that the variety of tunings that “may serve well” is infinite. But also, following what you say, it seems that you can only refer to some ETD variants of the first ET (?).

...”Quasi Equal Temperament is what Owen Jorgensen described in his last whole book, Tuning, as "The lost art of 19th Century piano tuning". It was a time when tuners recognized that music required every key to be accessible and for there to be no greatly abrupt differences from one key to the next but still a reason and purpose for a modulation, all keeping within a very narrow range.”...

Well, I haven't read that book, so I cannot comment but, perhaps, if the colleague you cite had met some colleagues from this board, he wouldn’t have come to such a pessimistic observation (if I understand correctly). Or was your mentor concerned about a trend, ETD's in place of aural tunings?

I believe that, even today, many Piano Tuners do recognize that music requires every key to be accessible and may well know the “reason and purpose for a modulation”, possibly with all keys sounding in tune. And I would make a fair distinction between what is "academic", i.e. research and ultimate accuracy, and what is ordinary/commercial tunings.

...”I possess many possibilities for effecting any number of nuances. I cannot, of course be any more perfect about any of them than I could be about ET but I can, in fact, make the piano sound pleasing to the pianist who is my client at any time.”...

Good for you, Bill. And never mind if, on top of those number of nuances, you will have to deal with a number of imperfections, that is not the point.

...”If he or she voices any displeasure with what I have done, I have a solution for it and it is never what I consider to be a perfected ET with any kind of particular stretch involved.”...

Yes, I have understood that, and that aiming at a perfect ET would be misguiding, as it would never come out perfect. So, basically, you are processing the mere idea and purpose of the first ET?

...”Should there be a standard?, Yes! I believe so and that first standard should be the adherence to A-440 pitch so that all instruments of the world can play together at any time, anywhere.”...

The one above is a different issue.

...”Beyond that, however, the issue of temperament and octave stretch in the piano is too great to try to impose one single standard that will satisfy all.”...

Well, I am afraid we have already been given an international reference model, and now the question might be whether it can be improved, in theory and in practice.

...”After all, the pitch of A4 tuned at exactly A-440 will have its 4th partial (A6) usually be at the same level as A-442!
None of us can change that! The best tuned piano under any circumstances will never match theoretical frequencies for ET at any time on any note except A4 measured only at its fundamental pitch!”...

But, doesn’t that occur to any and all “theoretical frequencies”, for any temperament? And, really, how would you expand a WT across the keyboard, by following the non-beating-octave principle?

...”Therefore, I maintain the concept that the perfection of ET is therefore a misguided goal.”...

What I understand is that you stopped tuning-and-refining “ET” long ago, say for a series of reasons.

...”I can't really say what that goal should be at this point but I know for sure that to try to attain a perfect ET is not what I should be doing or would ever want to do.”...

What you may do is perhaps go beyond your imagination and believe that both the first ET model and our tunings could be improved.

Regards, a.c.
.

Hmmm... Sometimes, when it comes to get an answer...

Hi Bill,

Have you been able to check what happens to m3, when you stretch the octave? Would you rather have calmer M3 and "more active" m3?

And, wouldn't it be impossible to rely on theoretical F-values whatsoever, no matter the temperament?

And, how do you expand a (any) WT across the keyboard? Do you do that by tuning aural-non-beating octaves?

You wrote "...I possess many possibilities for effecting any number of nuances. I cannot, of course be any more perfect about any of them than I could be about ET...".

So, why are you concerned about ET perfection? If a "perfect" ET is out of discussion, what is it that scares you?

In the post quoted above, I find your last comment superficial and alarming, as if to have a model available is tantamount to having it imposed.

Have I misunderstood?

Regards, a.c.

Hi,

Bill, perhaps you missed some posts (above)?

Regards, a.c.

As a happy proponent of ET, who is open to experimenting with HT, I have resisted for one sole reason:

You have to choose a key to be the most harmonious. This means the unrelated keys will be less harmonious. Great for creating dissonance as a piece moderates from and to the tonic.

But, what key do I choose? C major would seem to be most obvious.

But what about pieces written in other keys that did not intend to use the varying dissonance of a particular key to create intervalic dissonance?

As a composer in ET, I am happy rely on the harmonic dissonance created by tonal space, than hope the piano that my composition will be played on, will have a HT on it, and in the key I intended.

So, what is it? C major is the standard? Old music sounds better because it was composed in that temperament?

What about modern compositions in keys far from C major, that modulate away from F#, for example, designed to create more harmonic dissonance, but resulting less intervalic dissonance?

That just seems wrong and misguided, IMHO.

So, as I see it, the only people who would benefit from HT would be pianists who play classical only.

For the rest of us, ET would have to be the standard, no?