Nonlinearity, transients and spectra

Abstract

The role of nonlinearity in generating the steady spectrum and· defining the transient behaviour of musical instruments is discussed. A simple theory for analysing, in the time domain, a multimode inharmonic system driven by a nonlinear self-excited generator is presented and it is shown that this can lead to a mode-locked hantlonic regime, a multiphonic regime, or even chaotic oscillation. The theory is applied to discuss the steady state and transients in bowed-string, woodwind and brass instruments. Brief reference is made to impulsively excited instruments.