To Paul Erlich et alia-tuneia:

Hi Paul. You are, indeed a "tough customer," but the confusion in my
paragraphs could also be the result of my limited memory of acoustics. I
did study acoustics with John Clough at the Univ. Michigan, but I have
forgotten much of it by now -- although I still refer to the John Backus
book...

Your "original" objection as I understood it (you may have more by now,
possibly) had to do with the fact that I mentioned simple harmonic ratios
as a property of any enclosed vibrating space. I thought that was your
basic objection, whereas such simple ratios ONLY apply to the partials
created by the vocal cords. You will note (I'm not going to quote it again
to save space), that I have ELIMINATED any reference to these simple ratios
in the paragraph on the enclosed space -- but saved my mention of the
simple ratios for the second paragraph, the vocal cord section.

If I am understanding this correctly -- and THIS is where I need your
help... any enclosed space that is set to vibrate (like a wind column) has
a given potential resonating fundamental and overtones which may OR MAY NOT
be in integer multiples of the fundamental. (Is that much right??)

When the shape of the enclosed space is changed to reinforce ONE harmonic
of the vibrating space [and that harmonic may or MAY NOT be an integer
multiple of a possible vibrating fundamental of the enclosed space], and
that harmonic ALSO happens to coincide with ONE simple integer harmonic
partial of the vocal chords, the "whistling effect" takes place.

(???) Oui? or wee-wee?

When I finally get this, I will rewrite the paragraphs again and send them
along. It might be nice if I could finally get this right!

Thanks!

Joseph Pehrson

>If I am understanding this correctly -- and THIS is where I need your
>help... any enclosed space that is set to vibrate (like a wind column) has
>a given potential resonating fundamental and overtones which may OR MAY NOT
>be in integer multiples of the fundamental. (Is that much right??)

True, the resonant frequencies may or may not form a harmonic series, if
they don't, it may be meaningless to talk about a "fundamental" resonance,
and, in your statement below, a "harmonic of the vibrating space." The vocal
cavity is certainly in this category.

>When the shape of the enclosed space is changed to reinforce ONE harmonic
>of the vibrating space [and that harmonic may or MAY NOT be an integer
>multiple of a possible vibrating fundamental of the enclosed space], and
>that harmonic ALSO happens to coincide with ONE simple integer harmonic
>partial of the vocal chords, the "whistling effect" takes place.

What also often happens in throat singing is that two or more resonances
from different parts of the vocal cavity are brought into alignment at an
overtone of the vocal cord vibrations, and then you get a really pronounced
whistling effect.

>(???) Oui? or wee-wee?

Seems like a oui.