Re: [Phys-l] Exotic harmonies

[Brian Whatcott <betwys1@sbcglobal.net>]

At 08:48 AM 5/31/2006, John D., you wrote:
> ...
> Now let's consider the human voice.  The collision between the vocal chords
> is hugely nonlinear.  It can be represented by a delta function.  The
> Fourier transform of a delta function contains all frequencies (integer
> ratio frequences as well as others).   However, a sequence of equally-
> spaced delta functions -- a Dirac comb -- contains only the integer ratio
> frequencies.  The Fourier transform of a Dirac comb is another Dirac comb.
> In this case it is not 100% clear we can apply Floquet's theorem with
> confidence, because there is some coupling between the air column and the
> vocal chords.  However, I suspect the coupling doesn't distort the Dirac
> comb very much, and I suspect the coupling is non-systematic, stretching
> some intervals and shrinking others, unlike the systematic stretching we
> see in the piano.
> ...


I enjoyed BC's provocative post of the Clockmaker's question, and
I have been waiting for the human voice to make its entrance - but this
 paragraph from John D., is not it.

An audible characteristic of vocal performance is vibrato.
It's not there by accident.   It takes effort to form sustained &
 pleasant vibrato. The Fourier transform of a voiced tone is modified
 by the vibrato. Now there's a spectral line  broadener!



Brian Whatcott    Altus OK    Eureka!