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I was talking to Antony Pay (the clarinettist, copied here) the other day, and he described an interesting psychoacoustical problem.  I can think of ways to approach it with tests, but as always with such questions my first recourse is to run it past you in case you say “This is a well-known effect, it’s in my book….

Sometimes, he has experienced frustrating difficulties trying to play in tune with other woodwind players.  He has explored this enough that he has reduced it to quite a stark example: trying to play a single note, accurately in unison with one other instrument.  He reports that sometimes he can adjust his pitch from something that is clearly too sharp, all the way through to something that is clearly too flat, without finding anywhere in between that does not strike the ears of a professional musician (such as the conductor) as “out of tune.”

One might have thought that a steady woodwind note would be quite accurately periodic, with exact harmonics, and that makes it seem quite surprising that there isn’t a natural point where all the beats vanish, and everyone agrees that they are in tune. My suggestion for an initial test is to see if the phenomenon can be reproduced with a synthesised steady note in place of the other player.  That would give no ambiguity about periodicity, and would give control over the waveform and harmonic content of the reference sound.  Perhaps he is describing an effect where sounds with sufficiently different spectra never “blend” in a satisfactory way, and this is perceived by musicians as a tuning problem?

Any thoughts?

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It might be helpful to say that the difficulty often occurs high up in the range of the instrument; that it can sometimes be minimised by choosing a different fingering, often one using a lower harmonic of a shorter tube; and that it is particularly a problem of period instruments, which of course often need to use acoustically less than optimal fingerings.

I myself thought about 20 years ago that the explanation might lie in anharmonicity of ‘crappy’ notes – some high stuff 'getting through' the tube unmodified? – but a small investigation with Jim and Michael McIntyre failed to show any evidence of that, as you say is the case.  We didn’t look at very high frequencies, though.

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Even within one instrument, the pitch conveyed by the higher harmonics (if they were heard alone) might differ from the pitch conveyed by the lower harmonics (if heard alone), and this combination might make the overall pitch somewhat indistinct and ambiguous.

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I don’t understand how this squares with your previous statement that "woodwind notes are strictly periodic."  Surely if that were true, the pitch conveyed by the higher harmonics would necessarily coincide with the pitch conveyed by the lower harmonics?

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Pitch is defined in terms of WHAT IS HEARD. It is distinct from the physical periodicity of a sound. For example, the pitch of the fundamental component of a musical note may differ slightly from the pitch of the sound as a whole, even when all harmonics are exactly in tune.

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What is the easiest place to read the details of this?  Now is the moment for you to say "It's in my book..."  Tony and I should probably do a bit of homework, then perhaps talk to you again.

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Some related effects are discussed in the sixth edition of my book (An Introduction to the Psychology of Hearing, Brian C J Moore) on pages 213-214.

Some relevant papers are:

Terhardt, E. (1975). "The influence of intensity on the pitch of complex tones," Acustica 33, 344-348.
Terhardt, E., and Grubert, A. (1987). "Factors affecting pitch judgments as a function of spectral composition," Percept. Psychophys. 42, 511-514.

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I was thinking about the discussion we had about pitch and probably came to the conclusion you tried to explain to me. I tried to explain it as simply as possible and came up with this. Please let me know if this makes sense to you.

We perceive the sound at a different pitch than it is physically, depending on the balance of the harmonics; when different harmonics are more or less strong in a given sound; we hear the pitch of the main note changing although physically it's the same.

You experienced some notes where it's never "in tune" even if you clearly covered the pitch area where it should have sounded in tune. Therefore, at the point in your experiment where we would have perceive the two sounds at the same pitch, the harmonics wouldn't align. And at the point where the physical pitch was the same, the perceived sound (and therefore the perceived harmonics as they come together) wouldn't align.