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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,

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

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.

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.
.

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.

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,

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.
.

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

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

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.)

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 )

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

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.
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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.

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

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

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?)

..."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.
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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
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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

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.