"If we sample a moment from music and analyze it in terms of its fundamental frequency and associated harmonics, and then apply that sample to, say, a circular

"If we sample a moment from music and analyze it in terms of its fundamental frequency and associated harmonics, and then apply that sample to, say, a circular latex membrane of known elasticity, known diameter and fixed edge, present mathematical techniques cannot predict what pattern will form on the membrane." If you knew the resonate frequency of the membrane I wouldn't think this would be that hard to figure out using Fourier analysis http://en.wikipedia.org/wiki/Fourier_analysis http://en.wikipedia.org/wiki/Fourier_analysis