Re: Digest Number 221

Ray Tomes said
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> Right. One reason that I have been a bit slow responding is that I was
> taken aback when someone (sorry I forget who) said that I was wrong and
> that chaos frequency doubling does add lower frequencies. Now that I
> think about it the mathematical cases of chaos do in fact do that, so I
> was wrong to say that was not so. However I will have another go at
> putting my foot in it and say that I think that real world, continuous
> systems do show frequency doubling and not frequency halving behaviours
> - which is presumably why they call it frequency doubling.
>
I'm not sure what you are referring to, but I thought Paul E. was talking
about period doubling behavior (therefore frequency halving). Certainly
coutinuous chaotic systems exhibit period doubling and period halving
depending on the way the parameter is being twiddled. I had a neat paper,
which of course I cannot now locate, using template analysis on vocalized
vowels to exhibit natural strange attractors in normal speech. 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 like to make a recording of this phenomenon and send it to whomever on this list
> >is interested in listening to it, analyzing, etc. I guess cassette is the easiest for me
> >to make. I am really interested to get your feedback on these sounds - any takers?
I would love to have such a recording. Is it possible to send me a wave
file as an attachment?
> Yes please. I am in New Zealand, so sending a WAV file might be
> easiest, but if you want to use post my address is:
> Ray Tomes, 59 Maritime Tce, Birkenhead, Auckland, New Zealand.
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