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Re: pitch and psychophysics

I wrote:
>A piano uses long, thin wires under tremendous tension in order to minimize
>the contributions of these elastic effects -- but even then elasticity
>contributes enough to require the stretching of octaves as discussed back
>in November.

And in response at 08:23 AM 1/23/00 -0800, Leigh Palmer wrote:

I think you are ignoring the psychophysics of the situation here.

I'm not.

The mechanics of the basilar membrane in the cochlea have at least
as much influence on what is perceived as an octave as the mechanics
of a stiff string.

That's true, but it does not detract from the correctness of my
statement. In particular, why does the basilar membrane not require the
stretching of octaves on a pipe organ? I stand by my assertion that the
stiffness of the piano strings is significant.

There's been a ton of work on this by various characters including Max
Mathews and John Pierce. I've personally participated in some experiments
in this area. The most obvious hypothesis is that the ear contains
nonlinearities that result in synchronous detection of coincidences between
partials. This is not quite right, as can be shown by playing one note in
one ear and another note in the other ear. The second-most obvious
hypothesis is that the *brain* performs such detection. This doesn't quite
explain all the data, but it explains quite a lot.

We physicists should not construct explanations
based solely on our knowledge of physics when evidence in other
realms is to the contrary.

You have not presented any contrary evidence that I consider even
marginally relevant.

An octave on any instrument is determined
by an auditor, not by a frequency ratio.

I know what you mean, and don't disagree with the meaning .... but be aware
that many authorities *define* an octave to be a factor of two. They would
say that the standard piano tuning requires more than an octave -- a
*stretched* octave -- between C3 and C4.

Streched octaves are a matter of taste, not physics.

To first order, that's wrong. Practically everybody agrees that stretching
is required, to first order. To higher order, there are dilemmas for which
there is no good solution, and the choice of solution becomes a matter of
taste. Even so the point remains that if we could get rid of the
elasticity and other nonidealities, there would be far fewer dilemmas.