period tripling and a microtonal pendulum

All-
Just a small clarification and I will shut up. I mentioned
period tripling in maps of the real interval- all the cases that I know of
are discontinuous and rather contrived, and probably don't apply to music.

Musically speaking, we have a driven pendulum experiment whose
angular position is determined by decoding square wave pulses from an
optical shaft encoder. In addition to decoding the absolute position, I
also feed the output to a speaker. The angular velocity of the pendulum
manifests itself as a pitch, and the bifurcations of the system are
heard as subtle changes in melody. I am trying to get my student to hear
these subtleties so he can recognize when something interesting is
happening by sound alone as we sweep through parameter space. You really can
distinguish very small pitch changes when the bifurcations take place.

John Starrett
http://www-math.cudenver.edu/~jstarret