throat singing

John Starrett wrote,

>If ordinary
>vowels are strange attractors of the vocal chords, then controlling a
>period two imbedded in the attractor would result in a true subharmonic.
>Is it possible that throat singers use this technique?

I would say ordinary vowels represent period-one behavior, and throat
singers use the period-two regime.

Paul H. Erlich [TD223.15]

>John Starrett wrote,
>>If ordinary
>>vowels are strange attractors of the vocal chords, then controlling a
>>period two imbedded in the attractor would result in a true subharmonic.
>>Is it possible that throat singers use this technique?

>I would say ordinary vowels represent period-one behavior, and throat
>singers use the period-two regime.

Paul, it is not clear to me what you mean here. Please explain?

I wonder what the standard research says about the vowel frequency
relationships. My own analysis is that every person has a fundamental
frequency in their voice, which changes when they sing or try to change
it or when stressed. Each vowel has a cycle of some number of this
other cycle (with the wave sizes varying over this cycle) with that
number varying from 2 to about 7. That left one number (6 I think)
unused but I found that I could make that extra vowel by attempting to
make a sound between the other two vowels.

Is this what you are referring to as period 1 and period 2?
If not, does it have any relationship to it?

I have no idea to what extent other people have studied all this stuff.
I just study many things without checking what has gone before because I
don't know what it is called in many cases. Sometimes I find that my
research has been done before and other times that it hasn't.

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John Starrett wrote,

>>>If ordinary
>>>vowels are strange attractors of the vocal chords, then controlling a
>>>period two imbedded in the attractor would result in a true subharmonic.
>>>Is it possible that throat singers use this technique?

I wrote,

>>I would say ordinary vowels represent period-one behavior, and throat
>>singers use the period-two regime.

Ray Tomes wrote,

>Paul, it is not clear to me what you mean here. Please explain?

This is exactly the same thing I've been saying before regarding chaos theory.
I just thought John Starrett could have put it more clearly, so I clarified.

>I wonder what the standard research says about the vowel frequency
>relationships. My own analysis is that every person has a fundamental
>frequency in their voice, which changes when they sing or try to change
>it or when stressed. Each vowel has a cycle of some number of this
>other cycle (with the wave sizes varying over this cycle) with that
>number varying from 2 to about 7. That left one number (6 I think)
>unused but I found that I could make that extra vowel by attempting to
>make a sound between the other two vowels.

The nature of vowel sounds is actually understood in much greater detail
and has to do with the absolute frequency of the "formants" or resonant
peaks. See Hall's _Musical Acoustics_ for a full exposition.