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Greetings,
That is not the way it works, at least, not here at Vanderbilt.

Last point first: string players have often commented on how easy it was to play with a Coleman 11, one well known violinist on tour specifically told me that it was the first time he could remember of that "all the overtones lined up perfectly". He did not know the piano was tuned in any particular way, he and his pianist simply chose it out of the line-up, leaving behind a perfectly good ET and a subtle Victorian era quasi ET (Moore and Co.) The performance was of Carl Maria Von Weber's concerto for piano and violin, all sorts of key changes, modulations, etc.

Unfettered by expectations, his musical sense took control and I listened to it,(not being a real fan of violins, I was half expecting to snooze, until I noticed that they had chosen the Coleman), with a new appreciation of control. In a number of places, he and the piano took turns heading up or down the scale, and the intonation between the two was impeccable. I heard comments in the hall, afterwards to that effect, so I wasn't deluding myself in this single-blind event.

Rene Fleming, without knowing anything was "abnormal", specifically told the Dean that she just loved rehearsing and performing with the piano, saying how comfortable it was to sing with.

A full Young temperament, with its 21 cent F#, went in front of the Vandy orchestra for a concerto (Beethoven's III). The artist, Enid Katahn. The conductor, and the head of the brass dept. told me later that they had never heard the kids play so in-tune.
Audra McDonald performed here with the Moore and Co. behind her and I was told was "well pleased" with the piano.

Any of these could be discounted as an anomaly, but the pattern speaks for itself. None of these were tuners, they were all musicians, and none of them had been told that the pianos were not in ET. It makes me wonder why an ear has trouble with a 18 cent third, when the needs of the music call for that tonality, and much music does. I wouldn't want every third to be that wide, I don't like meantone, where they are all pure, but I have come to recognize that the width of the third is a musical value, and different musical "meanings" can best be expressed in this or that level of color.

There is also the psycho-physiological aspect of contrast, I mentioned it earlier. When every third is the same, the brain no longer processes it as a factor in response, there is no new information and our conscious mind becomes inured to the dissonance. When that width is a variable, there is a part of the pitch processing center that is stimulated to cause responses, such as changes in heart rate, pupil dilation, etc. There is more brain activity involved in dealing with contrasting values than there is in hearing only one. It is not unlike the stone mason that ,while build a natural stone wall, is dealing with complexity that a brick layer doesn't have to bother with.
It is like a composer making decisions on how to modulate, and where the home key is, and how to leave it and come back to it in small enough steps so that the listener's emotional state isn't interrupted, but, rather, manipulated into as high a degree of involvement as possible. In ET, there need be no consideration of step size, making it easier to make music. If simplicity is the goal, ET is the answer.

Using ET for everything composed on the piano, though is, imho, a mistake, since I am one of those that feels that ET does more damage to Bach, Beethoven, etal., that a WT does to Debussy, Rachmaninoff, etc.

The twelfth root of two is not a compromise, it is a number. But if we take into account inharmonicity, the resulting stretch can be a compromise, but need not be. Pure twelfths can be used to avoid any compromise whatsoever. But some people like prints rather than plaids. That is what we are really talking about here, preference.

Exactly.

If I may digress for a moment.

Why did the art and science of piano tuning arrive at such a widely accepted temperament to begin with - one that has stood an exceedingly long test of time? There may be several reasons, but the only one that really "adds up" is this: For the typical family, it provided an agreeable basis for all of their music. Dad played Bach; Mom, Beethoven; Junior, Brahms; Little Sally, a little bit of everything. Piano teachers? Ditto.
One piano accommodating a wide range of interests.


I don't know about the rest of the tuners that post here, but this arena generated most of my "tuning income." Inasmuch as I had neither the time nor working capital to change tradition, I went with what worked the best for the most.

For many reasons - growing interest in period instruments, et al. - variety in temperaments have gained in popularity in certain quarters. Times change. Needs change. This is perfectly fine. Such has certainly found a niche. To one degree or another, some techs desire to be in that niche. This is perfectly fine as well.

There is really no "right" or "wrong" here. Different temperaments are meeting the needs of different "temperaments."
As stated above: "But some people like prints rather than plaids. That is what we are really talking about here, preference. "

Ed,
You write well and passionately about how it is possible to marry the sound of a piano well with other instruments by using carefully chosen UTs. Thanks for that insight. I hope to hear live someday an example, and I may force my wife to allow me to move our piano to Young, or do you think Coleman 11 would be less jarring for her singing work? The problem is that she does a large amount of late 19th C through modern song as well as the standard vocal rep.
Thanks again for your thoughts.

I guess we will have to agree to disagree. The twelth root of two is a compromise choice, made by tuners using math, to divide up the notes on a 12 tone keyboard. Those pitches do not match the natural harmonic series that arise from a plucked string or blown pipe. Listen to a natural trumpet. Just intonation is the only non compromise. Tune ET on pianos if you want - I do - and I hate it.

The plucked string and blown pipe are subject to a number of other effects that make them diverge from the theoretical natural harmonic series, some of which can be controlled, and some cannot.

You are correct, but as an ideal (thought experiment), given total constraints on the other variables (tension shift with plucking, wind pressure variation with pitch changes), they do produce pure harmonic structures, which the piano cannot, being limited by 12 notes per octave and iH.

Greetings,
I think the first step should be the least alteration. Big thirds 15 cents or under.

It seems that the step between ET and the mildest UT is the biggest step of all. Something about leaving a specific "sound" behind. When it loses that seamless texture, the sound "feels" differently. Even though pianists have listened around the tuning, they rarely can point to anything that they hear as changed, but they do say that the instrument certainly has a new feel. It isn't a pitch thing, it is a relationship thing.

The distance from that to the next stronger temperament might be greater, numerically and harmonically, but emotionally, it will have lost the newness, that first kiss is usually the most memorable one, (and the first slap, as well). A pianist familiar with these tunings has said, flatly, that "you can play it harshly or you can play it expressively". The pianist can make more use of the texture if they understand what it does to the harmonic qualities, but we don't throw babies in the deep end, first, so i think it is better to leave the familiar in the smaller steps.

The Young has a 21 cent third at the F#, that is the historical limit to most of the UT's I have seen or heard, as such, it is the extreme. Keep that particular spice for a later introduction.

All normal UT's have about the same shape, just varied steps and evenness of progression. As the tempering gets more and more "colorful", we all reach a point where it calls attention to itself. It is this point that I use to define "out of tune". When the listener becomes more aware of the tuning than the music, even for a split second, the piano is out of tune. This means Dr. John's piano can have well-tempered unisons and I wouldn't notice. His music is, with the help of that loose piano, taking control of my full attention. Listening to a Brahms intermezzo, I don't wanna hear no meowing unisons, at all!
Regards,

The natural harmonic series is not the least bit theoretical. Hence the term "natural." On fixed pitch instruments, tunings are based on the theory of what sounds best when confronted by a mathematical impossibility.

Is ET based on a theory of what sounds best or is it just the generally accepted compromise?

All temperaments are a compromise.

Sure, but what is a good example of a theory of what sounds best?

Even it was just a form of words, it would be interesting to know what you had in mind.

You get ET if you take the view that all notes are created equal but I am not so sure the notes themselves are always happy with that sort of democracy.

Bottome line is that even musician's ears have grown accustomed to the equal temperment. It's what's acceptable. It is tried and proven.

Monkeying around with equal temperment seems poinless is all I'm saying

I erred when I said plucked string. I meant to say bowed string.

Thanks Ed. My wife (a singer) and I have performed French lute songs on clavichord at 392 using 1/4 comma meantone, and Jacquet de la Guerre on harpsichord at 415 using Kirnberger. Wonderful resonance. I agree a gentle UT on the piano shift first would be wise. I just would eventually like to try Young.

Listen to The King's Singers, or a good barbershop quartet. They sing in just intonation. THAT is what tuning should be. It is IMPOSSIBLE, on an acoustic piano (it is on a digital piano) to achieve just intonation. Every tuning of a piano is a compromise from just intonation. You need to understand that just intonation means that the interval CE in Cmajor sounds different from the interval CE in Fmajor.

Ian, it is not a form of words, it is a fact. You don't get a tidy, whole number (not a fraction) of pitch Hz, when you try to divvy up the "space" into 11 subdivisions between a perfect octave.

Let me say, again, all temperaments are unequal due to the laws of physics. Even though one carries the title of ET, it doesn't mean that it is. "Temperaments" are nothing but names which are applied to the many solutions of the quandary of how to tune a fixed pitch instrument in a 12 tone scale.

Our tonal structure (Western) is derived from the formalized singing of chant. The ear perceives in what we label as Just Intonation, and that is the basis of the structure as we define it. Most music historians/musicologists believe that plain song, at the infancy of polyphony, was the ear perceiving harmonic structure due to echo/resonance. A huge event was the codification of the major and minor third. To this day, it is the anguish of piano tuners. (Blame it on the Renaissance.)

Have you ever noticed, at a ball game during the singing of the National Anthem, thousands of untrained singers will sing in parallel fifths? Hmmm. The eardrum responds to the natural laws of physics and we recreate them with voice. We learn to "identify" consonance, dissonance and what we term as perfect intervals. The un-schooled ear will often confuse octaves and fifths. We identify a lack of dissonance quite naturally.

As far as temperaments, to the ear, it is nothing more than preference. To a tuner, it is what they have been trained to do and what is the most comfortable for them to recreate with consistency.

So, what do I prefer? A superb tuning in whichever temperament is selected. My own pianos are not tuned in ET, though they differ from each other in their "non-equality." That is due to my tuners being able to "listen" to what works best on each of the pianos.

Uniformity seems to be one of the hallmarks of our times.

Plucked or bowed makes no difference. They still follow the laws of physics. Temperaments are theoretical, physical properties are not. The first law of physics is that there is always an exception due to interactive and combinative physical properties.

Whereas on instruments which are not fixed pitch, tunings are based on whatever pitch the player is able to make them play at the moment. That, in turn, makes the temperament arbitrary.