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Having been involved in major recordings of piano trios I find the string players rarely precisely match the pitches of the piano. Nor is it necessary or even desirable within limits. They are on a differing tonal plane, somehow. the tone of each is so different. the same thing happens with singers. That inherent flexibility pf tone is part of what makes a fine piano such an ideal collaborative instrument. That is a fine piano. A poor toned piano can create problems where they needn't exist. A fine pianist capable of grading the tone color to allow others in the ensemble this freedom is another essential.
That may be why equal temperament continues to be be found ideal or at least eminently workable.

That's one of the glories of the medium. A violin or cello can soar in their own continuous ribbons of string intonation that doesn't necessarily have to totally agree with the pianos' succession of notes which is more like a row of pearls, if I may wax somewhat poetic, there is lots of musical room between them.

Greetings,
I wonder how many string players have actually had experience with the intonational landscape provided by a well-tempered piano. The ones I encounter have a far easier time playing "in tune" with a palette of increasing thirds than they do with strict ET. I consider ignorance to be the prime motivator, as very, very, few string players could give you a definition of temperament or why we have to have it.

I have also noticed that when there is a piano involved with a string quartet, the intonation goes out the window as soon as the piano begins playing. The players tell me that playing with a piano requires they forget about what each other is doing and try to match to the piano. A mild WT seems to allow them more room for expression, and their harmony amongst themselves is more accurate.

As a professional singer (hence the user ID), RXD is correct. Just intonation maybe the tendency, but we never really get there on our own.

All of our lives, our pitch reference has almost exclusively been a piano, and while some believe there's such a thing as "perfect pitch," it is in reality pitch memory. Some of us have a more refined sense of it than others, and what we remember is what we hear - primarily from a piano.

For a vocalist, I believe that is probably true. Introduction to singing is often in a choral tradition, accompanied by a fixed pitch, keyboard instrument.

But, instrumentalists are trained and 'grow up' without the influence of a fixed pitch instrument. Being accompanied by a piano is a very minor experience compared to being in a band or orchestra. The major influence affecting the concept of intonation is developed through the means of ensemble, rather than tempering intonation to a fixed pitch instrument.

It's unfortunate, Ed, that most piano quintets are made up of a star pianist and a star string quartet. For that reason, I don't think I've ever heard a truly successful colaboration, mainly, I suppose because I avoid them, particularly when the quartet takes its name from the name of the first violinist.

A committed string quartet will have their own intonation patterns, often with a shifting pitch base It is too much to ask them to relinquish this highly developed quality in favour of any fixed intonation. Nor should we ask this of them. A mentor of mine when I was a teenager was a violinist who was instructed as a student at the Royal. College of m over 100 years ago now, never to play with piano accompaniment if he wanted to become a successful string quartet player.

Conversely a piano trio is usually also a self contained unit and it's musicians well used to listening with a piano constantly in the context. This makes a huge difference. That plus the pianist gets to choose his piano from a bank of pianos that have been already preselected for their qualities for concert use. They know I will be able to do things with the tuning of such a piano and still stay within the law since I must also think of string players' tendencies in melodic intonation.

For me, while the piano trio is a flexible format, the piano quintet and even quartet seems unwieldy to me, perhaps from hearing too much of the situation I just described in the first paragraph.

Have string quartet cellists where you are all developed the fetish of leaving strings ringing like they do here? Fiddlers can get away with it but cello strings ring 3-4 times longer. Can be effective but mostly not. I must have come into contact with 6-7 string quartets so far this year and they all do the same. must be something in the water.

Schubert writes well for piano quintet. Trout in particular. The way the piano part is often written like another single line instrument in octaves contributes to its cohesiveness. That plus using a viol is more coherent with piano sound somehow and lends a binding effect when it's tone is present anywhere in the texture.

So very true, Marty. The local band I was brought up in had a championship professional euphonium player as conductor. He would often play when conducting was unnecessary and instil in us all a sense of good tone quality and intonation. I noticed for some time now that too many band directors no longer play and so students don't get a good example set before them.

I don't remember anybody teaching us or even speaking about intonation. We just, as you say, "grew up with it".

You weren't hammered with "listen, listen, listen?" WOW !!!

Playing in tune was stressed, in band, all the time. It's the whole concept of Bb tuning. Temperament, or "a temperament" was an unknown concept. In tune was the goal! Though, even to our developing sense of intonation, we could surely tell when a piano was out of tune. That unison thing, ya know. Aargh!

Bb was the center of our universe. Life deviated from the great and cosmic center of our lives!

Ah, such fond memories.

Yes, I remember now. This was a village under a mountain. The BBC radio antenna was atop this mountain so they had no radio and no television reception. They still spoke King James' bible style English. So the word I heard there was "Harken".

There were only 2-3 of us 10-12 year olds in a band of adults so most of what we learned was by osmosis. We got paid the same as the rest of the band for all engagements so we were the richest kids on the block.

personally I was trained to sing the A 440 once a day at last, during lunch ! control at the piano .

I developed a good pitch memory automatically except it was at A=457 old band pitch, a throwback to some old mitary pitch that the instruments were built in
When I switched to 440 i Iost that questionable skill.

rxd,

Wasn't that the instrument that John Phillip Sousa wrote his masterpiece opera Die Zauberalpenhorn?

Pythagorean and Just Intonation are musical tunings which correspond to naturally occurring harmonic series.


Wow, no, I can't begin to tell you how wrong that statement is. But, in a way, it might explain why many in this thread have a hard time understanding why any a cappella choir will gravitate to Just Intonation.

Just Intonation is not one tuning or scale. Just Intonation is a system of tunings, all of which correspond to a harmonic series. That is to say, for a particular Just Intonation tuning, every note in that tuning correspond to the same harmonic series.

Mathematically, we can construct a particular Just Intonation tuning by using integer ratios of (small) prime multiples. Since there are many ways we can arrange ratios of these numbers, there are many ways we can construct Just Intonation tunings.

The Pythagorean tuning, for example, is a Just Intonation tuning where the largest prime (N) is limited to 3. So the N=3 ratios in the Pythagorean system are based on powers of 2 and 3.

Another way to construct a (different) Just Intonation tuning is to use primes up to 5 (so the N=5 ratios are powers of 2, 3 and 5). The Ptolemy's Sequence is one example of a N=5 Just Intonation scale (there are many others).

Of course we can construct Just Intonation tunings based on higher prime limits, e.g., M=7, M=11, M=13, etc. Additionally there are also many tunings not based on 12-note scales.

For singers to sing in harmony, sooner or later they will converge on a harmonic series (if not accompanied by a tempered instrument). This is why there is always a pull to Just Intonation, since by definition a collection of notes from a harmonic series forms a Just Intonation tuning.

I can see the reason for a strict standard of tuning for certain situations; those where multiple techs are rotated to take care of the same piano. It just seems that it would be easier on both the techs and the piano if the same targets were always used...

In fact, being in a large metro area, there are a few of us that follow each other as different performing groups hire the tuner at the same venue.

There is this one aural tech I follow that I can always tell it was him before me... You might think that I'm going to use an example of how far off from ET he tunes, but it is just the opposite. He must tune with near zero margin for error - just playing chromatic triads, the consistent busyness sticks out from the other ET techs that I follow. (I think the consistency is felt through the ratio of the major thirds beating to the minor thirds beating in a triad - no matter where on the keyboard, the ratio should be the same in ET - tricky to accomplish!)

Last time he followed up on me, he made a point to find me and say "hey, you left it in ET this time for me!" He knows I usually use a really mild WT, but it never is a cause for concern - our seasonal (sometimes weekly) fluctuations are far greater than any few cents difference in the temperament!

Ron Koval

My comment was in response to peekay's post regarding singers and just intonation. Sure, it's different with regards to instrumentalists.

Then why is it that they don't?
Have you listened closely to anything yet?
Is this your own work or what you understand from someone else's work?
There's a lot missing.

Try this;

Write a 3 part progression that goes from Cmajor directly to a chord of E major by means of 2 voices moving in opposite directions by a small minor second and the third voice staying still and then works back to C through a series of dominants. Does your hypothetical choir end up flat, sharp, or in tune? And by how much? Then work it out with the opening progression moving by large minor seconds. How do the results differ? Then do it all again in a minor key. (c# minor to A minor as the opening progression).

You can play with it more by using progressions of just thirds alternating with Pythagorean thirds (is a Pythagorean third a natural interval in and of itself? how would I construct one if I were to sing one?). The combinations are endless.

Then get it sung by real people. 10 seperate groups of 3 people with the random smattering of those with or without what is commonly known as perfect or absolute pitch. That should produce enough variety. What did they eventually gravitate to? Which of your theoretical findings did it agree with?

All fascinating stuff. Have fun with it.

How absurd. I'm not about to hire world class singers, and strand them in a deserted island for a few weeks to demonstrate what is already known: a convergence to just intonation.

It's easy to be a denier, without zero evidence and only anecdotal observations.

Stating bizarre things like "just is just" doesn't make it right and only shows lack of knowledge.

However, there is ample scientific evidence saying otherwise. The following references came from the last paper, maybe you care to refute all of them?

As the saying goes: "Have fun with it".


Alldahl, Per-Gunnar. 2004. Intonation i kör-sång (Stockholm: Gehrmans Musikförlag)
Backus, John. 1969. The acoustical foundations of music (New York: W.W. Norton & Company Inc.)
Barbour, James Murray. 1951. Tuning and temperament: a historical survey (Mineola, NY: Dover Publications Inc.)

Bohrer, Jocelei Cirilo Soares. 2002. Intonational Strategies in Ensemble Singing (London: Ph.D. dissertation, City University)
Brown, Oren. 1996. Discover your voice (San Diego, CA: Singular publishing group)

Butler, David. 1992. The Musician’s Guide to Perception and Cognition (New York: Schirmer Books)

Covey-Crump, Rogers. 1992. ‘Vocal Consort Style and Tuning’ in Companion to Contemporary Musical Thought, II, ed. by J. Paynter and others (London and New York: Routledge Reference)

Devaney, Johanna. 2006. ‘A methodology for the study and modeling of choral intonation practices’, Conference proceeding of the 2006 International Conference on Music Perception and Cognition (Alma Mater Studiorum University of Bologna)
Devaney, Johanna and Daniel P. W. Ellis. 2008. ‘An Empirical Approach to Studying Intonation Tendencies in Polyphonic Vocal Performances’ in Journal of interdisciplinary music studies, 2/1&2
Duffin, Ross W.. 2007. How equal temperament ruined harmony (and why you should care) (New York: W.W. Norton & Co. Inc.)
Goebl, Werner and Caroline Palmer. 2009. ‘Synchronization of timing and motion among performing musicians’ in Music Perception, 26/5, (CA: University of California Press), pp. 427-38

Hagerman B. and J. Sundberg. 1980. ‘Fundamental frequency adjustment in barbershop singing’ in Speech Transmission Laboratory Quarterly Progress and Status Report (STL-QPSR 21-1/1980), pp. 28-42
Helmholtz, Herman L. F.. 1954. On the Sensations of tone as a physiological basis for the theory of music, 2nd edition of the 4th German ed. of 1877 (New York: Dover Publications Inc.)
Larson, Steve. 2004. ‘Musical Forces and Melodic Expectations: Comparing Computer Models and Experimental Results’ in Music Perception, 21/4 (CA: University of California Press), pp. 457-99
Lerdahl, Fred. 2001. Tonal Pitch Space (New York: Oxford University Press)

Lerdahl, F. and C. L. Krumhansl. 2007. ‘Modelling tonal tension’ in Music Perception, 24/4 (CA: University of California Press), pp. 329-66
Loosen, Franz. 1995. ‘The Effect of Musical Experience on the Conception of Accurate Tuning’ in Music Perception, 12/3 (CA: University of California Press), pp. 291-306
Mandelbaum, Joel. 1974. ‘Review: Toward the Expansion of Our Concepts of Intonation’ in Perspectives of New Music, 13/1 (Seattle, WA: University of Washington), pp. 216-26
MacClintock, Carol. 1979. Readings in the history of music in performance (Bloomington and London: Indiana university press)
Morley, Thomas. 1597. A plain & easy introduction to practical music, ed. by R. Alec Harman (New York: W. W. Norton Company)
Norden, Norris Lindsay. 1936. ‘A new theory of Untempered Music’ in The Musical Quarterly, XXII, pp. 217-36

Plomp, Reinier. 1976. Aspects of Tone Sensation (London: Academic Press)

Tosi, Pier Francesco. 1747. Observations on the Florid Song; or, Sentiments on the Ancient and Modern Singers, translated by Mr. Galliard (London: J. Wilcox)
Schön, Donald. 1987. Educating the reflective practitioner (San-Francisco, CA: Jossey-Bass)
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Sundberg, Johan. 2001. The Science of the singing voice (Stockholm: Proprius förlag)

Vurma, A. and J. Ross. 2006. ‘Production and perception of musical intervals’ in Music Perception, 23/4 (CA: University of California Press) pp. 331-44

Here' my argument for why ET is the logical standard for tuning. Using the analogy of a target, consider the following:
We have 12 targets to represent the 12 notes of our temperament.
-Imagine each tuned note represents an arrow on its target.
-For the sake of this argument let's assume that if a note is on the target it will be basically unnoticeable to a client. Perhaps if they are a connoisseur they may recognize the tuning as not being ET, but there will be no wolfs.
-If we tune a strict equal temperament the arrows will all be in the bulls eye area of the target.

Here's the problem with the well tunings: Some of those arrows will be closer to the edges of the target. Humidity change and use will cause some of those arrows to drift. Once they drift off the target they become noticeable to the client as being out of tune.

With ET the notes will stay on target for longer. With changes in weather, the tuning will change, but it will sort of morph into some sort of well-tuning before it becomes noticeably out.

In other words with ET you get some of both worlds - the balanced, symmetrical sound of ET, which naturally evolves into a WT before deteriorating into just plain out of tune.

With UT, you will never experience the ET sound, and with humidity change the tuning will become noticeably off sooner.

As a professional tuner, one of my main concerns is stability. Since ET is arguable more stable than UT, it is a more logical choice for the standard tuning.

Peekay,
The whole world says so is not an answer.
The OP asked If there should be a standard.
The standard is currently ET
Why?
The whole world says so.
Many of us here do not accept that as an answer. Particularly those of us who listen intently.

I don't think it absurd to ask you for your own personal listening experience. To rely on the opinion of others is living vicariously, don't you think?

The reference to a desert island is your invention. Reduction ad absurdam is, among other cheap arguing techniques, often exposed in this forum for what it is. Getting a bunch of singers together locally should not be difficult for someone of your apparent experience and worldliness nor should the mathematics be beyond you. The exercise I gave you was based on something that occurred on a broadcast some years ago that has intrigued me for many years.

Ryan, I totally agree.
However, one of the points of WT is that the harmony becomes closer to acoustically in tune as the home key is approached. That WT's become further from the commonly accepted ideals of melodic intonation as the home keys are approached is being conveniently ignored here for the time being.
The seemingly random nature of ET going out of tune would make it a mere UT.

I agree that the finer the tuning is of any temperament, the more almost constant attention to keep it there.

Peekay, I'm afraid the mathematics of this is quite beyond me.

When it comes to setting a standard for tuning a piano, are you saying that ET is unsuitable because it is not a musical tuning which corresponds to a naturally occurring harmonic series?

Are there any such series that could be used as a practical basis for piano tunings?