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Precisely my point - Can we really talk about a specific temperament once we start modifying the original specification of the UT in order to make it work on a piano? While I enjoy playing in UTs, my best, uneducated guess as a musician is that, from the beginning of the time that keyboards became common, people tried to make them sound good over the whole compass. We, in hindsight, look at these attempts as if they were specific recipes to make the only possible, correct sound for a particular piece of music written in that particular era. They were just trying to tune the damned thing.

I think you replied before I added my "Edit"

Edit: I suppose you could make the argument that the temperament is the same. If the ET octave tunes slightly wider than mathematical doubling of the fundamental on a modern piano because of inharmonicity, the proportions are the same and you are still in ET. If the proportions of a UT are maintained, are you still in that UT? I think you could make a very credible argument that you are.

Then again, how far do you want to carry the argument? Must it be on the same instrument the piece was originally composed on?

Edit: Or, maybe it should at least be performed on a pianoforte of that same era?

Should Bach not be performed at all on a modern piano tuned in ET?




Your interest in UTs seems to be historical performance..

Mine is different... I am interested in the effect that very mild UTs have on the resonance and character of the piano, and allowing modern musicians to take advantage of that. I see tuning HTs on a modern piano as modern representations of historic harmonization schemes. (Whatever that means lol! )

-Joe

....they were just trying to tune the damn thing.

Just thought it worth repeating. Ultimately, Aren't we all?

Thanks Mwm, you started my day with a smile.

Sounds like the way McDonalds hamburgers are made. No point asking those burger flippers for something special.

Sorry for being so disrespectful, but of course I am just joking. Or am I? Hmmm.

Kees

...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.
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Your world view from McD's is enlightening. If thats your only frame of reference, a 5 star kitchen works the same way. You would find the difference in end results startling.

I would agree with you except that each piano is listened to at each performance by the musical equivalent of a 5 star restaurant critic and all these pianos get the attention of a world class concert tech every 10 days and anybody can have the undivided attention of any one of us for as long as they can afford. Just like anywhere else. Thank you for reminding me. This is a lot more than the average concert instrument

We're talking about some of the finest and best cared for pianos in the world. A whole different class than your frame of reference.

Thank you for your interest and giving me the opportunity to clarify a couple of things I had forgotten to mention.

All Very good points. Much of my experience hearing UTs has been on period instruments, or copies of period instruments. For example, a period chamber orchestra I know, when performing works that include piano, use only the piano that was available in that country, in that day, have it rebuilt, regulated, tuned and voiced to match the conditions they think existed when the work was performed.

Yes, Bach should be played on the modern piano, and in any useful temperament. In the end, you, as a piano tuner, must ensure the listener hears the music, not the temperament.
My guess is that this is what you already do.

This is where I need help separating the math from what I hear when tuning. If, in the math of 12ET, which forms the baseline in most modern visualizations for comparing the various historical temperaments, all octaves are truly beatless, and all other intervals beat to a greater or lessor extent, then, as soon as we apply stretch to "harmonize" the whole compass of the piano, we have moved away from 12ET, since every interval has some beat to it. My ear, as a musician, doesn't really hear the errors, as it were. Now Kirnberger III, which has a number of beatless fifths and major thirds, if stretched to suit the iH of a piano (an inappropriate use of Kirnberger III I might add, but good for illustration), all intervals will have some beat and the sense of the pure, relaxed sound that would have been there without the stretch is lost.

Am I really out to lunch on this one?

I don't think you are out to lunch at all. You make a valid and important point, especially to someone like me who is formally trained to tune ET by ear, but relies heavily (but not totally) on ETD software for the HTs.

Yes, it would seem that these beatless intervals should remain beatless, regardless of stretch. But things are the way they are... You would then have to hide the error somewhere else.

But not all UTs have a similar problem. Consider the layout of the 5ths/4ths in the Moscow Equal-Beating Pythagorean Temperament. Or, consider the 1/10 Comma Meantone Temperament, where the deviations from ET are so minute that, practically, this temperament needs to be set by ETD.

-Joe

Again, excellent points. My interest in all this is due to fact that I have not, to my knowledge, played or heard a modern piano live that I knew for a fact was tuned or had attempted to be tuned to anything other than the tuner's best attempt at a harmonious sounding piano. As tuners, you and others on this forum, have an ear for the subtle vibrations of a minute deviation from some standard that simply eludes my ear when I am listening to the music. I can hear them when I tune (though it isn't helping me much yet). My sense is that all good tunings on a particular piano will ultimately converge on a single end temperament that is unique to that instrument. I know other tuners will disagree, but, as a musician, I simply hear the various temperament tuning samples posted on this forum as nice or OK, possibly as good as that piano can sound. But they, and all attempts at tuning ET, are all minor deviations from the ET baseline. Again, I am speaking only of the piano. For other instruments which exhibit less iH, strong UTs that significantly deviate from ET are wonderful.

Greetings,
The IH has little to do with the effects of tempering. It is the comma that is demanding compromise. The presence or lack of beating is not a defining characteristic of ET, since the "E" of ET is referring to a quality of equality, and this equality remains, regardless of stretch. The unequal temperaments maintain their balance, regardless of stretch.

In the Kirnberger, the quality of purity that the C-E offers extends farther from the middle of the keyboard than the human ear can discern, and the more highly tempered thirds actually begin to sound harmonious as one takes them below C3. (This is due to the critical band beginning to limit partials).
Though there are no beatless intervals on a piano, we usually accept a 4 cent M3 as pure, and a fifth that is only tempered by half doesn't sound that much different from an normal ET fifth. Thirds don't have to be totally pure to create the effect and the contrast of WT. Few people would tell the difference in the tempering of the C-E between the Young and Kirnberger. There are certain bell-like intervals on a piano in a Kirnberger, and these are the fifths of the most remote keys. I don't think this tuning on a Steinway is inappropriate, at least, not to my customers that use it, and I don't think it is nearly as inappropriate as Bach in ET (which to my WT polluted ears, sounds like a bee hive buzzing, all the time, everywhere, in the music).
Regards,

Thanks Ed for your observations. I think I begin to understand the concept of stretch as not affecting the temperament. Interesting.

Do you do concert tunings in UTs on pianos that normally have a different temperament, and then return them to the original temperament after the concert? I am thinking of the limitation on repertoire - does Prokofiev or Poulenc sound good in Valotti?

Cheers.

Mwm, I like to think of a rubber band analogy:

If a 12ET is drawn as intervals on a horizontal rubber, and the rubber is stretched, the intervals are stretched but the ET remains.

If the horizontal rubber is 8 octaves long and stretched from each end it will slightly stretch the center octave but stretch more at the extremities.

If there are more lengths of rubber attached perpendicular to the rubber for every note, like a comb, then we have an analogy for the iH for each note. If each harmonic is drawn as an interval on each perpendicular rubber then stretching those rubbers will represent the increase in frequency due to iH.

The amount of stretching for the perpendicular rubbers is fixed depending on the dimensions of the real piano strings, and varies for each string. The perpendicular rubbers at extremities stretch further.

The amount of stretching for the horizontal rubber will depend on the frequency coincidence of selected harmonics from several arbitrary perpendicular rubbers with selected harmonics from other perpendicular rubbers. There will never be perfect matching but only a best fit which depends which, and how many, perpendicular stretched rubbers are chosen.

Thanks Chris for the analogy.

Thinking further about the analogy: a UT would be represented by uneven intervals drawn on the horizontal rubber band. Stretching the rubber should widen the intervals but keep the relationship. However, since the stretch is actually variable depending on the perpendicular rubber bands, and more so at the extremities, then the UT relationship will break down towards the extremities.

I think that if a tuner balances several intervals in tuning single notes, then the extremities will converge towards equal temperament.

Don't let anyone else here at PW know what you said above. It might start a revolution!

Actually, the effects of temperament are only really discernable in the middle four octaves of a piano. above or below, and the beating of ET is too fast or slow to register as beating. The color of say, a m3 in the 6th octave, is about the same, regardless of temperament. Same goes for the first two octaves, as far as 3rds are concerned.


>>Do you do concert tunings in UTs on pianos that normally have a different temperament, and then return them to the original temperament after the concert? I am thinking of the limitation on repertoire - does Prokofiev or Poulenc sound good in Valotti?<<

I keep the concert pianos in a mild Victorian era WT, which hasn't yet caused anyone to notice it wasn't strictly equal. I don't want to change them since everyone likes the way the pianos sound, right now.
People seem to respond favorably to the slightest departure from ET, as long as that departure follows the traditional order. Unlike tuners, who suffer the occupational hazard of comparative listening, Temperament has to get fairly strong to draw musicians' attention. A 21 cent third, such as found in the Valotti or Young, might be disruptive in performing music written by composers imbued with ET from the beginning of their musical exposure. However, Debussy, for all his sweeping harmony, sounds fine and textured in a tuning that allows a range from 8 to 18 cents around the circle of fifths. Could his early imprinting have been burnished by a sense of key character? I don't know, but there are plenty of plausible routes to that conclusion.

How much tempering is optimum is like asking how much salt is needed in the soup. There is a taste component, hence, no fixed answer. Those composers who likely matured in a harmonic environment of WT could be expected to use the keys to create familiar harmonies. Those that came later possibly gave it no thought, and in their music, additional consonance and dissonance, rather than assisting in the creation of an emotional response, might cause unintended results in chord voicing, phrasing, and general overall tonal feel.
Regards,

Well stated. Thank you.

This has been discussed extensively here in the past.

What I remember is that there is no point in keeping the UT structure outside the midrange, and the temperament morphs outside there. (No music uses M3's in the bass.) This is possible because there is no unique P8 on the piano because of IH and opens the possibility of an UT on 88 notes, rather than 12.

Interesting stuff!

Kees

Hi All,

Yes, interesting stuff, at least for me (as an aural piano tuner); beyond general discussions, I would really like to come to some logical conclusions, to some steady and shareable points that may better explain "voice intonation" as well as "taste", UTs and modern ETs properties.

Would you please let me know if one of you is (really) interested in this kind of analysis?

Regards, a.c.
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