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non-linear phenomena?

susan moreland smorelan at MAGNUS.ACS.OHIO-STATE.EDU
Mon Aug 28 12:15:32 EST 1995

>Another important non-linearity is in the ear. Perceived pitch depends 
>on amplitude. Low tones get flatter as they get louder, and high tones 
>get sharper (the crossover is at 2 kHz). I don't know if this 
>phenomenon has a name. Anyone? 
>(I'm cross-posting this to bionet.audiology as they may know there.
>Follow-ups to a.s.p.a)
>			Cheers,
>				Douglas Nunn

>In a related issue, the mel scale also strongly contradicts the musical
scale's treatment of octaves.  In the musical scale an octave is a 2:1
ratio, with a note in a higher octave being twice as high in frequency as
the same note in the octave immediately below it.  In higher frequencies,
when people are asked to dial a variable tone to one octave above it, there
is a tendency for "octave stretch" to occur (is that what you were looking
for?).  In other words, the dialed frequency is liable to be slightly more
than one octave above the standard.  However in the mel scale, the size of
an octave in high frequencies can be as much as six times the size of one in
the lower frequencies.  This shows that the ratio changes dramatically for
the subjective octave -- much more so that it does in the musical scale.  In
the musical scale the octave is, in fact, used as an invariant in musical
patterns. Incidentally, Stevens stated that the mel scale was only
applicable to pure tones, and since musical instruments produce complex
tones, his theory should not be applied to music.

I'm not at all sure that this is what you were looking for, but i pulled it
out of a paper i wrote some time ago. For what it's worth...


we stroll together silently,
just the two of us -- my wolf and me...

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