reply to John Starrett

I wrote,

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

John Starrett wrote,

>Actually, I am saying that perhaps vowels are (in some cases) represented
>by a strange attractor, in which case true subharmonics could be generated
>by controlling one of the embedded periodic orbits. There are attractors
>that are "close to" their embedded period one orbits in the sense that the
>chaos is a chaotic variation around the period one. The usual method of
>chaos control requires only small perturbations of some parameter (chord
>tightness?) to switch between the embedded periodic orbits. Of course this
>is just speculation, but the fact that at least one study has found
>a strange attractor in a human vowel vocalization,

Can you point me to this study?

>and the fact that
>controlling chaos is quite easy leads me to wonder about the possibility.

Do you think we are agreeing or offering two distinct possibilities? I
honestly can't tell, but it seems like we might be saying exactly the same
thing.