On Dec 16, 2012, at 9:05 AM, music-dsp-requ...@music.columbia.edu wrote: > In a synthetic system (say a feedback network of waveguides) a > non-linear element (say a static waveshaper) can be used to disperse > energy accross the spectrum. I'm wondering whether anything similar > happens in physical media? > > Am I correct to assume that in most cases resonating acoustic objects > will only resonate at a mode if you put energy into the system at that > mode? This seems to be the basis of commuted waveguide techniques. Are > there exceptions/counterexamples?
One important nonlinearity is tension modulation in strings and membranes. The wave speed of these objects changes with the overall energy, and so as energy is lost after an excitation, all modes get shifted downward and we hear the pitch falling. When strings are very tense, this effect is less audible, and that is probably why commuted synthesis of the piano (playing the body through the strings) works OK. I guess there may be problems with low notes. I don't think a banjo would work well at all. Thin shells (like cymbals) have profound nonlinearities due to their geometry. If you imagine radial cross sections of a cymbal, you have a kind of bent spring where the force/displacement curve is different in one direction than the other. So the decay is not simple harmonic oscillation, and when this effect dominates you get all the wonderful mode transfers and chaos. Scott Van Duyne came up with a clever way to add this kind of effect to a waveguide, presented in Pierce. J. R. and S. A. Van Duyne. (1997). "A Passive Nonlinear Digital Filter Design Which Facilitates Physics-Based Sound Synthesis of Highly Nonlinear Musical Instruments." Journal of the Acoustical Society of America, 101 (2): 1120-1126. In general, adding nonlinearities to a physical model while insuring stability is difficult. I would recommend Stefan Bilbao's recent "Numerical Sound Synthesis" very highly. -Randy -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
