Ice - You're right; now it was I who was imprecise.  It's a theorem that
a periodic function is harmonic.  I guess what I meant was that
"musical" sounds are not only periodic but tend to have the power
concentrated in not-too-high multiples of the fundamental. (But, as
we've said before, "music" may have important "nonmusical" transients
as well as sustained "musical" tones.)

I don't really know the physics of bells, if that is what you are
asking.  I gather that by virtue of their shape they must be able to
vibrate in modes other than the relatively simply related ones of a
string or the column of air in an organ pipe, which produces sounds
that are not perceived as having a definite pitch.  Obviously this is
more true of a gong than of a tubular bell.

So, leaving the electronics out altogether, my hypothesis is that if
anything would sound different from the front and the back, in an
anechoic chamber, it might be a gong (which is a nice dipolar radiator,
too, isn't it?)

As for listening - no, I haven't.  I'm a professional mathematician but
at my age I can scarcely hear thunder, which makes the accusation of
"know-it-all," if he meant me, perhaps on target; though if ever there
were a case of the pot and the kettle ...


-- 
tom permutt
------------------------------------------------------------------------
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