We should take this discussion offline, but here's a little of the musically relevant stuff:
>>>It's unlikely that a period 3 cascade could be picked out from a chaotic >>>region with one parameter. > >>Not unlikely at all, I've done it with my vocal cords.
>Well done! How did you perform this experiment?
I'm not at all a skilled throat singer, but I do occasionally get a subharmonic a perfect twelfth below the note I'd be singing if I weren't going for the "throat" effect. I have almost no control over which subharmonic I get; often I get something very unmusical-sounding (presumably chaos).