Klarinet Archive - Posting 000430.txt from 1995/03

From: Jonathan Cohler <cohler@-----.NET>
Subj: Re: Flatness when loud (J. Cohler, E. Lacy, et al.)
Date: Wed, 15 Mar 1995 10:26:21 -0500

Edwin Lacy wrote:

>The problem with it, as I see it is this: The Pythagorean 5th is 702
>cents, compared with 500 cents for the equally tempered 5th. (Cent =
>hundredth of a semi-tone.) So, the 3rd, 6th and 12th partials will be
>flat. Naturally, the 6th and 12th are negligible in the spectrum of the
>harmonic structure of the clarinet tone, and so will have no perceptible
>effect on the perceived pitch. But, the 3rd is the strongest overtone in
>the clarinet spectrum, so we are dealing with a frequency which should
>cause the perceived pitch to be sharp.

Pythagorean partials do not apply to the clarinet. The clarinet is not an
idealized physical system. All of the partials on the clarinet are flat
relative to the integral multiple harmonics. See my previous posting on
the physics of the clarinet.

>I do think that the concept
>of "perceived pitch" as opposed to "frequency" is one that has gotten far
>too little attention.

There are several models of pitch perception:

1. Pitch is the frequency of the lowest partial
2. Periodicity Pitch - a measure of how often the signal repeats
itself each second.
3. Residue Model
4. Template Model
5. Pattern Recognition
6. And various combinations of the above

There is a brief explanation of these models on page 100 of "Music, Speech,
Audio" by William J. Strong and George R. Plitnik, published by Soundprint
of Provo, Utah. There are also many references in the bibliography to the
book.

---------------

Jonathan Cohler
cohler@-----.net