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We already have a thousand posts about this, so what will one more hurt?

I have a love-hate relationship with ET. The tech in me sees the practicality of it, but the pianist in me hates it. For me, music should sound musical; not practical.

Give me the shades, colors, and textures of the different keys.

I didn't realize that the term "musical" had only one narrow definition. Equal temperament allows full versatility to play in any key with aproximately the same amount of "un-musical" quality. Every other non ET is a compromise. If one is playing pieces that uses keys which have more favourable musical qualities, there would obviously be some small benefits.

Unfortuanately, I have yet to open a fake book or classical music book that has "All pieces in the key of Db" written on it.

Key word being "un-musical."

One key or another does not mean anything to me. but that is not so with those with absolute pitch. I have to suspect that those with AP tend to have a preference for UT.

But before I understood what ET really was, I used to wonder why the F and especially the Eb brass instruments couldn't play in tune while us Bb brass instruments could. And I also wondered why pieces with flats sounded sooo much better than pieces with sharps. I had a band director encourage us to try playing with the 12 note strob-o-scope to work on our intonation. There were some notes where this just didn't work, I would run out of "lip". It was much easier for woodwinds. I understand this all now.

It is ET which is the compromise. You seem to need a lesson in the history of Western music.

Careful now. Every temperament on a 12 tone per octave keyboard is a compromise of some kind versus just intonation.

The inference in the posting was the ET was not a compromise. ET is a temperament based on a compromise, which is based on a compromise, and yet another compromise, ad infinitum.

To think that ET is not a compromise begs the study of music history and musicology.

Alex McDonald, a competitor in the recent Cliburn Competition, made a comment in an interview about the piano choices available. He observed that a piano is an instrument which is, and can never be, in tune with itself. Yet the common feeling in this forum is that pianists can't tell if a piano is in tune or not. I always beg to differ.

Marty,

You are correct about the compromise of a compromise of a compromise...

I am not so sure about pianists knowing when a piano is as tuned as it can be. Now that I tune my own piano, I am starting to hear the tuning qualities of all the pianos I hear, and I hate that it is interfering with my enjoyment of the music. Until I started tuning, I was blissfully unaware of the subtle variations in the structure of a tuning. I just performed the music and the piano was the vehicle. It is different from the awareness of the tuning of an organ or harpsichord, which are inherently cleaner sounding.

Loren,
You want the shades, colors,..., but using which UT?

I have a feeling ET is here to stay. People just like to be able to play in every key!(playing f# chord should sound as good/bad as playing C chord)

Playing a F# chord should every bit as good as a C chord, but it should sound different other than just a difference in pitch.

There is no reason why you can't play any fixed pitch instrument with a non-ET tuning in every key! It just sounds better.

(Flame suit on)

I like EBVT. Love it, actually.

I use ET 'cause it has only two letters and is first alphabetically bufur UT!

I use ET because I like sterile environments...

Oh yeah, and octave stretching is for sissies!

Of course you can! It is done all the time. 99+% of all tunings on a piano, by the time the tuner has left, are non-ET. And, if you really want key colour, tune your piano in 1/4 comma meantone, founded on C, and play all your pieces one half step higher or lower than written. Or better yet, for those people who don't transpose at sight, base your fundamental pitch on F#. Then you can play all the pieces as written.

Just read about it à la Hebrew. Then you'll love it - Trust me!

I use ET because it's out of this world(!)where wolves roam not.

I agree with what I think you are saying.

I understand completely! One of the reasons I became a piano technician was so I would be in the yellow pages between Physicians and Pizza.

On a good day I tune ET. If I mess up? Hey, its ... UT! Yay!

I have pitch memory (prefer not to call it "absolute", because I can be 1 or 2 Hz off at A440) - certainly recognize keys immediately if the instrument is between about -50 cents and +20 cents. But I certainly prefer ET. To me, C major is C major, with no need for an overly sweet M3. And F# major is F# major, with no need for an overly sour M3.
I might be an exception to your rule/suspicion, but there you have it.



I submit that you can't have both "every bit as good" and "different other than just pitch". I see one of two cases:

1) F# sounds every bit as good as C, in which case
... a) you have ET or
... b) you have UT but don't care about the widths of M3s or can't distinguish them,

or

2) it sounds different, in which case you have UT and can actually distinguish between close and remote keys. But amongst musicians who can distinguish M3s of different widths, I've never found one person who likes a 17 cent M3 just as much as a 14 cent or 10 cent M3. They all prefer the closer keys.

So, if you tune/use UT and can distinguish between M3s of different widths, then F# does not sound "every bit as good" as C. (That's the whole idea, I've been told.)

Here's a question for the ET folks out there...

You say that C is the same (every bit as good) as F#, or any other triad (in a real ET) - how is that REALLY possible with the thirds all beating at different speeds from each other? Or do you mean something else?

[/quote] Playing a F# chord should every bit as good as a C chord, but it should sound different other than just a difference in pitch.

I submit that you can't have both "every bit as good" and "different other than just pitch". I see one of two cases:
1) F# sounds every bit as good as C, in which case
... a) you have ET or
... b) you have UT but don't care about the widths of M3s or can't distinguish them,

or

2) it sounds different, in which case you have UT and can actually distinguish between close and remote keys. But amongst musicians who can distinguish M3s of different widths, I've never found one person who likes a 17 cent M3 just as much as a 14 cent or 10 cent M3. They all prefer the closer keys.<<

So, if you tune/use UT and can distinguish between M3s of different widths, then F# does not sound "every bit as good" as C. (That's the whole idea, I've been told.)[/quote]

Greetings,
So, it appears that the value judgement has been placed="good" equal consonance? Thus, dissonance is "bad"? If so, why would anyone want to accept all the thirds being so dissonant? 14 cents is pretty far away from consonant. I think it is more a question of contrasts.

I have found that the ET advocates consider sameness to be good, even if it is dissonant, and inequality is bad, even if it reduces the overall dissonance in piano music. ( The only way that a UT creates dissonance on a par with ET is if the use of all 12 keys is totally democratic, and this is not the case in piano music.)

The greater decision is whether a listener is more emotionally moved by one or the other, and science has proven that emotional response varies with the level of dissonance. This alteration of response occurs involuntarily, and is virtually universal. So, while the resolutions in classical music are obviously intended to relax, having them accompanied by a reduction in tempering increases the effect, and we find that classical composers don't resolve to a key with a higher level of tempering, they always resolve to a calmer place. In the absence of contrast, emotional responses are forced to rely on intellectual response, which many of us have found to be a weaker, watered-down, effect.

I love the effect of F# in a strong UT when it indicates a very deep emotional turmoil. I love the pure calmness of the closer keys. What I find most disturbing about ET is the boring sameness when there is no difference other than pitch, and the busy-ness of tempering in passages that would be so much more beautiful if they were closer to pure. I like my classical music as complex as it can be, and ET, with its reduction of harmonic effect to a mathematically determined value, is the antithesis of this. Once understood, the UT casts a new light on phrasing......

And to the statement " I've never found one person who likes a 17 cent M3 just as much as a 14 cent or 10 cent M3. They all prefer the closer keys." I can only say that I must have run into all of them that do, because I have a majority of customers that will never go back to ET. If so many people like the 'closer keys', there must be something repulsive about dissonance, and the only way to accept ET, with its ever-present beating, is to stop listening to the tempering completely, (which is what happens).
Regards,

Hi Ron,
I think the explanation is that we hear the beating in logarithmic terms and pitch determines the effect, i.e. the C-E in the 4th octave, though beating twice as fast as the C-E an octave lower, is registered by the ear as the same tempering because the pitch is twice as high.
Regards,

This is turning into a really good discussion. Good question, Ron. And Ed, excellent post.

That is because you think/hear as a tuner and not as a musician. It is exactly the difference in intervals, such as thirds, which create the tonal colors of each individual key. I prefer to hear a distinction between C-minor and C#-minor. If memory serves, composers seem to choose from all keys. Why not just compose everything in C-Major or minor if ET is the best solution?

As an aside, I performed the Beethoven Concerto No. 4 in Prague on a Petrof P-282. The piano immediately brought forth incredible vibrancy. Unlike the USA, rehearsals are accorded much more time and the tuner is included in discussions with the pianist and conductor. I had time to pick the brain of the tuner to find out what was going on.

With an orchestra, he centers the temperament octave on A, rather than C. He used EBVT-III as the foundation temperament and then "listens to what the piano wants." What this created was an identification that G-Major was not a clone of C-Major in ET, merely at a higher pitch. He indicated that for a Wind Ensemble, he sets his temperament octave from Bb.

Keep in mind, I'm not a tuner. But, I am a pianist with an interest in non-ET tunings. If I have messed up the terminology, I apologize in advance.

You would seem to need a lesson in distinguishing between an inferances/observation and also the meanings of statements within greater context. When quoting a snippet of someones posting and leaving out its context, it is also appropriate to precede and follow the quote with 3 dots.

My statement stands, and relates to the versatilitya musician has to explore every key signature they come across without wondering if the piece will be more, or less musical for lack of unequalness.

As an analogy, I have 4 or 5 different eye glasses I wear that have various coatings, filters, prescriptions and tints on them. I do both day and night driving, competitive shooting in both bright sunlight and overcast conditions and numerous other tasks with varying conditions that would benefit from wearing one over the other. If I wore a bright amber high contrast lens on a bright day I would lose much of what I want to see in the same way as if I wore dark grey sunglasses at night. An UT basically does the same thing musically with pieces/key signatures that do not favour what it was intended to help. I would never dream of permanently having implant lenses in my eyes that addressed one condition, nor would I tune my home piano to address specific period pieces and have it muck up and cloud over the musical qualities of all the otherrs.

Emmery - Are you saying that ET is not a compromise?

--- I am quite familiar with the use of ellipses. Your sentence was quoted in its entirety and did not require an ellipsis or ellipses. It was not taken out of context, it was a complete statement and the source and additional text is available for all to read.

You should search for glasses which are tempered to adapt to all conditions. One doesn't need to change pianos when the instrument is tuned in a non-ET, and the point is, that on the same piano, key color is evident.

[quote=Emmery
As an analogy, I have 4 or 5 different eye glasses I wear that have various coatings, filters, prescriptions and tints on them. I do both day and night driving, competitive shooting in both bright sunlight and overcast conditions and numerous other tasks with varying conditions that would benefit from wearing one over the other. If I wore a bright amber high contrast lens on a bright day I would lose much of what I want to see in the same way as if I wore dark grey sunglasses at night. An UT basically does the same thing musically with pieces/key signatures that do not favour what it was intended to help. I would never dream of permanently having implant lenses in my eyes that addressed one condition, nor would I tune my home piano to address specific period pieces and have it muck up and cloud over the musical qualities of all the otherrs.
[/quote]

Greetings,
I think you have rebutted your own argument. On the one hand, you state that there is no universal pair of glasses that will do it all, yet attempt to say that ET will cover all the bases. One pair of glasses will not satisfy all your visual needs, why would one size third be optimum for all your musical needs?

Composers used different keys for different effects. You will never hear a funeral dirge composed in the key of C, nor a calm idyll composed in F#. Just like your lenses, the various keys are best suited for different musical expression, (see WTC). The UT is a harmonic tool box, offering various resources to the sensitive composer that knows how to best present a musical experience. It is far easier to compose with ET, since modulations don't make any difference other than pitch. Easier because of simplicity.

Using ET for everything is the equivalent of using a Crescent wrench instead of the individual sizes of tools. It works for everything but is optimum for nothing. Its use is for convenience, and that is all. It comes down to the difference between how music sounds and how music feels. Those of us that rely on the intellect pay more attention to the former, those that seek the emotional perspective will pay more attention to the latter.
Regards,

Greetings,
I think you have rebutted your own argument. On the one hand, you state that there is no universal pair of glasses that will do it all, yet attempt to say that ET will cover all the bases. One pair of glasses will not satisfy all your visual needs, why would one size third be optimum for all your musical needs?

Composers used different keys for different effects. You will never hear a funeral dirge composed in the key of C, nor a calm idyll composed in F#. Just like your lenses, the various keys are best suited for different musical expression, (see WTC). The UT is a harmonic tool box, offering various resources to the sensitive composer that knows how to best present a musical experience. It is far easier to compose with ET, since modulations don't make any difference other than pitch. Easier because of simplicity.

Using ET for everything is the equivalent of using a Crescent wrench instead of the individual sizes of tools. It works for everything but is optimum for nothing. Its use is for convenience, and that is all. It comes down to the difference between how music sounds and how music feels. Those of us that rely on the intellect pay more attention to the former, those that seek the emotional perspective will pay more attention to the latter.
Regards, [/quote]

Greetings Ed,
I would agree with your comparison of an adjustable wrench to a specific box end wrench, but you skirt around a very important point....a 3/8" box end wrench will not work at all on any other nut than the 3/8" one it was made for. Every piece written in a different key signature is a different sized nut, so to speak. An UT is not a complete set of box end wrenches, it is the same having a full set of wrenches, and most of them missing.

I have a pair of clear prescription glasses that will work universally in all conditions, this is the equivelant of ET. The other glasses I have to address certain conditions can easily be switched out in seconds. A temperament and tuning on a piano cannot be switched so easily on a moments notice. An UT is a pair of handcuffs that ties a musician to appropriate pieces the UT favours. UT's are simply not practical for musicians who do not want doors shut in their face when fully exploring all the keys the piano has to offer.

To put it in a nutshell, no self respecting mechanic has an incomplete set of box end wrenches in their tool box....and to the same degree, no self respecting musician has a temperament on their piano that does not address all the keys available to him on the piano.

To Ed Foote:

If it comes down to that: yes, I find dissonance "bad". In fact, I don't find even the ET M3 particularly beautiful. I agree with you, it's actually quite dissonant. What I dislike, is having to listen to M3s that are even wider than ET. What I like, is a tuning where such dissonance has been minimized.



Assume all you want, but you haven't a clue how I think/hear. My dislike of overly wide M3s, as I described to Ed above, is much, much older than any tuning I've ever done. I've only tuned some 20-odd pianos since I started in 2010, and one harpsichord in earlier years. In contrast, I've been making music in various degrees of (mostly im-)perfection since 1974, been aware of my pitch memory since about 1978 (but probably had it more or less from birth), been acutely aware of interval tempering and whether I like it or not since about 1984.

My value judgement on dissonance does not stem from any form of "tuner's hearing". To the contrary, I've made my tuning decisions (of recent years) based on my musical hearing preferences (developed over 30 years or more). Yes, I've tried EBVT-3, amongst others, but when I heard Ab major, I didn't want to continue playing. (Not to mention my favorite Christmas Chorale by JS Bach, in b minor, with its prominent F# dominant. To me, it was spoiled.)

UTs on instruments with little or no iH work very well. Bach's WTC in a common UT of the time has wonderful variations in tension and relaxation according to the key. But, on the piano, keys far from the base key really start to scream when the iH is added.

Well, you may believe that, but the facts in front of me prove this statement totally wrong. I have numerous professional musicians in my clientele, (including 2 Steinway artists), that have been profoundly influenced by an introduction to WT. These musicians have little use for ET, other than 20th century music. These jazz, country, and classical pianists have found all sorts of improvement in the sound and response of their pianos when I have shifted them out of ET. If you want to argue for a toolbox of all the same size wrenches, go ahead, but it has little pertinence to the world I live in.

For many, there is a great difference between unequal and restrictive, but since it is an esthetic difference, some listeners will not realize it. The fact is that the size of an ET third was derived by dividing an octave into an easy to handle number of notes, (a number determined by the number of fingers we have), not by its musical quality.
Regards,

How many fingers do you have? I have 10. I admit my knowledge of musical history and anatomy is limited.

Ed, I'm thinking that yourself and these artists have mangaged to convince yourselves that there is some kind of parallel temperment dimension out there which does not follow the fixed rules of the science of sound. Those of us in the know on this understand that within the fixed confine points of an octave, you cannot venture away from ET tuning to better favour an interval, without the opposite effect on other interval(s) connected to that adjusted note. It is possible to split the bias of it amongst more intervals but then the UT becomes more and more restrictive in freedom to venture to other keys. Its a lose/lose situation for 99.9% of technicians and musicians out there, and that is the reality of UT's. The arguement stands that if the adjustment is not so much that it makes the one unacceptably/noticably worse, then the adjustment is not enough to make the other acceptably/noticably better.

Incidently, I was discussing with an otchestra conductor the other day the issue of the pianos tuning not precisely matching a fixed pitch instrument when one ventures away from A440. All I could say is be thankfull that ET minimizes this....imagine if its tuned in EBVT3 and you played C4, you would have the pianos unusual tuning working against you and then add almost 4 cents difference on top of that.

Emmery,

Please ask that conductor if he believes that his orchestra plays in ET. Have you ever heard one that does? Have you ever had the opportunity to hear a vocal ensemble singing in ET?

It just doesn't happen.

BTW - Orchestral instruments and the voice are not fixed pitch instruments.

Non keyboard Instrumentalists and singers pull their pitches into just intonation. In general, they hate, but accept, as a necessary evil of the job, playing closer to ET in order to match a piano.

I know that. You know that. I'm sure Emmery's conductor knows it too. Does Emmery?

Even though I am a huge advocate of UTs, I am not convinced about its utility on a piano, simply because I have not experienced it and my wife doesn't want me to change our piano into something like EBVT III because of all the transposed pieces of her students.

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.

Yes, that is the point. C and F take a different view of what sounds best and would tune the other notes differently. ET based on the twelfth root of two, or the nineteenth root of three to allow for inharmonicity, may be least likely to offend with some dissonant interval or other. That principle makes ET generally acceptable, but it is scarcely a good enough theory of what sounds best to persuade C and F to agree on that compromise.

If I were C or F, I'd be pragmatic and go along with a tuning such as Marty describes:

I'm not sure what "first law of physics" you're referring to, but in my years of studying physics (including acoustics, harmonic and non-harmonic oscillators) at university, I've never heard of such a statement - least of all under the guise of "the first law of physics".

I wonder if pianos have not yet enough tendency to just intonation since the iH level is enough, so if that is the goal he problem would be more to avoid overpassing it than the opposite.

Now one can make a tuning without any correction of frequencies but it will not sound very nice.

It is the issue of inharmonicity that has caused me to ask so many questions here at PW on temperaments and UTs versus ETs. When tuning other instruments with no iH or that have short sustain, UTs sound much better than ET, since the purity of the intervals in the close keys sound so wonderful. But with the very long sustain on the piano, it seems that any temperament the tuner chooses to use will be heavily modified by his/her attempts to align the partials in a manner that makes a nice sound.

Greetings,
It depends on what you call "nice". If we oversimplify it to "consonance is good, dissonance is bad", we are either going to be disappointed by any piano tuning, or we are going to have to stop listening to what is really there. There is no way to tune a piano without dissonance, so all we can do is handle it in different ways. I think of it as salt, some like none, others put it on everything, while others, yet, prefer its tang to be selectively applied, leaving opportunity for both sweetness and edge. Great cuisine often mixes dissimilar tastes, why not great composition?

Purity is beautiful, but I, for one, lose interest when everything is consonant. As Plutarch said, "Music, to create harmony, must investigate discord". Meantone is attractive, but without some contrast or color, the music begins to lose its grip on my attention. It is so sedative that I begin to zone out. The same effect comes from ET, to me. There is no consonance, and it is stimulative, everywhere, all the time. Ear fatigue follows. This is why I like a tuning that encompasses some of both. Judging from the music, I think composers did, too.

There are classical passages where the quiver in the melodic line is more expressive than it would be if rendered purely. Perhaps it is the 10th, or 17th in a highly tempered key that gives that vocal vibrato effect. I can't quote the pieces, but I hear this in numerous places when listening to Brahms, or Schubert. Beethoven likes to crash contrasts together, etc. The right key, in the right temperament, can present this musical quality in a way that it would not otherwise be heard. Resolving from a very tense triad to a very consonant one creates a sense of resolution that isn't obtainable without harmonic contrast. I hear evidence that the composers thought so , too.

Dissonance has its place; anytime we hear composers writing minor 2nds, we can be assured that they were seeking a dissonant quality to their sound. What was Bach doing in the Tocatta in D? Regardless of temperament, huge smears of dissonance were there for a reason. So, composers were not afraid of it, and, I think, made use of it.

I also don't think that the presence of inharmonicity is of much importance in the choice of temperament, since the difference between ET and UT dwarfs any effect that inharmonicity has on the overall sound. Particularly with the larger pianos. I have stretched and compressed these tunings to slight comment from artists, but the alteration of the temperament is much more profound.
Regards,

I was being entirely facetious for those who always find an exception to any rule. They are rife at PW.

Ed,
I agree that playing only in useable meantone keys is a bit too relaxing. I think Bach, in his WTC, was probably using a just barely non-wolf WT that allowed him to find huge variation in key colour. The way in which he wrote the different preludes, in particular, seems to indicate he was enjoying exploring the tensions of the traditionally remote keys.

Thanks for your comments on the small effect of iH on the various temperaments. I have increased hopes of trying a UT soon.

Cheers

Ah, yet another humor failure on my part. Apologies!
(In bed with unequally tempered tonsils.)

Yes. I'd like to lock the QP Box and throw away the key.

The nineteenth root of three is purely arbitrary, and has nothing to do with inharmonicity, which varies from note to note. If you are allowing for inharmonicity, equal temperament is based on a relationship of intervals, not on any mathematical ratio.

Quite so, but I'd note that a temperament based on twelfths must build in some stretch as the nineteenth root of three (1.059526) is slightly greater than the twelfth root of two (1.059463).

I dont know, iH is low enough in mediums to allow all kind of temperaments, but as soon as the treble is met , the piano seem to allow for some "double" pitch.

SO there is a clear tendency to enlarged intervals that do not beat, where on an organ they would be unaudible.

Anyway, before any of those enlightements the managment of the attack and the one of the decay are necessary.
They give by themselves so much musicality, that looking for specific temperaments seem to be unnecessary at that point.
I simply follow the piano and tune musically.

Some methods allow to work the partials match more preciselty ; other seem to regulate the beats created by partial match in a smooth progression.

I seem to believe that a 3d way exists, if you mostly consider energy and activity of the intervals, the tuning take in account voicing, and probably the tempering is installed by itself.

That last "organic" method allow to tune quietely, diorectly in the musical result.
Of course one may have a good pattern to follow, and know well the lower and higher limit allowed in intervals managment.

I have not enough experience in UT to talk about them on pianos, I heard some light UT that where sounding well, not better than a standard tuning, somply well.

Also tuning with the tone so much under developed that harmony loose meaning anyway. That is what made me cautious about that UT "movement" initially and make me unable to appreciate them (while I had fun with samples at the organ and harpsichord and readings on the subject)

If the piano have to be tuned as if it was a barocco era instrument, better use directly the original one, in my opinion.

That is numerology, not science.

Dividing a P12 into 19 equal parts (e.g. Stopper's OnlyPure) is just as much an ET as dividing a P8 into 12 equal parts. It's just that the former (19 equal semitones in a pure 12th) is a little more stretched than the latter (12 equal semitones in a pure octave).

Whence the assertion that this is numerology, not science?

All of which brings us back full circle to:

After all of the various convolutions, my statement remains that all temperaments applied to fixed pitch instruments are compromises and the named Equal T isn't equal at all.