Klarinet Archive - Posting 001219.txt from 1998/12

From: Martin Pergler <pergler@-----.edu>
Subj: RE: [kl] re:Intonation training
Date: Thu, 31 Dec 1998 11:08:04 -0500

On Wed, 30 Dec 1998, Kevin Fay (LCA) wrote:

> Bill Hausmann noted:
> <<<Piano is pretty hard to tune to because of the richness in harmonics and
> decaying tone as the note is held. There is nothing much you can do about
> drummers!>>>
> My (admittedly dim) understanding of piano acoustics--gleaned over a beer or
> several with a piano-tuner friend--is that you can simultaneously be in and
> out of tune with a piano. The pitch of a piano string is apparently not
> constant during a note, and there are usually 3 strings vibrating away for
> each note! The fluctuation in pitch is supposed to be a factor in the
> "richness" of the sound.

My even dimmer understanding concurs. The 3 strings are even
(sometimes?) tuned slightly differently.

Another issue here is the following: we identify the pitch of a
note by a complicated process involving analyzing the spacing of
peaks in the harmonic spectrum (the basilar membrane in the inner
ear is actually a spectrum analyzer), not just the frequency of the
"first" peak. In an acoustically "perfect" world, all these peaks
would be at integer multiples of the base frequency, which would be
the pitch. But in real instruments, the peaks are only approximately
distributed in this way, and the brain must do its best to assign
a pitch (when it is too difficult to do so we get multiphonics).

"Out-of-tune-ness" between 2 instruments can be caused not only by
mismatched fundamental frequencies or percieved pitch whan playing
alone, but even between higher peaks. For instance, an overly
simplified ex:

Inst A with peaks at freq 440 879 1320
Inst B with peaks at freq 440 881 1320
both have fund freq 440 and peaks at almost 2x440, 3x440, so
perceived pitch at 440 Hz.
But, if they play together, get 440 and 1320 but also 879 and 881.
Ouch. 2 beats per second!
If A adjusts by sharpening slightly by a factor of 881/879 to have
peaks at approx 441 881 1323 and now we have interference elsewhere.

I think Tony Pay (or someone else, can't remember right now) said
situations can arise where Inst B=piano, Inst A=clar, and the
interference gets *better* if the clar deliberately does play
sharper or flatter, ie. would be perceived as out of tune if played
after or before piano rather than together. I talk about this
a bit at http://www.math.uchicago.edu/~pergler/intune.html

Martin

Oh yeah...the piano connection. I believe that piano tuners
deliberately tune "out-of-tune" on some notes so that this higher
order interference is better, so that the instrument as a whole
sounds "better".

--
Martin Pergler pergler@-----.edu
Grad student, Mathematics http://www.math.uchicago.edu/~pergler
Univ. of Chicago

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