source file: m1410.txt
Date: Sat, 9 May 1998 08:52:40 -0600 (MDT)

Subject: Re: period tripling and a microtonal pendulum

From: John Starrett <jstarret@tiger.cudenver.edu>

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