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pitch and psychophysics



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.

I think you are ignoring the psychophysics of the situation here.
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. We physicists should not construct explanations
based solely on our knowledge of physics when evidence in other
realms is to the contrary. An octave on any instrument is determined
by an auditor, not by a frequency ratio. The pitch of a note in the
middle of the audible frequency range may be quite different for a
singer than it is for an auditor, and singers must often consciously
compensate for this effect. There is a graph of perceived pitch vs.
loudness in, I think, Olson (op. cit.). Pitch is not solely related
to frequency much more than color is solely related to wavelength.

Streched octaves are a matter of taste, not physics. De gustibus...

Leigh