Stability/Instability of Periodic Solutions and Chaos in Physical Modles of Musical Instruments
Xavier Rodet · University of Michigan Library Repository · 1994
We study multiple solutions and chaos in simple physical models and their stabilities. A path toward a unique solution can be based upon the low pass character of the linear element. Chaotic signals are shown to cover a large space ranging from a sound perceived as harmonic without noise up to an essentially noisy sound. This is a very important feature for sound synthesis since the synthesis of noise and irregularities of traditional instruments has always been difficult and unsatisfactory. Methods are proposed to find the solutions and their stabilities, and to obtain controllable systems with periodic and chaotic behaviors.