Routes to Chaos in a Non-Linear Musical Instrument Model
A simple physical model of a single reed woodwind instrument involves the coupling of a linear resonator (the bore) wit a nonlinear resistive element (the reed). We will examine the results of a real-time digital music synthesis system based on this physical model. As a result of variations in a single external input parameter, corresponding to mouthpiece blowing pressure, the system will exhibit harmonic, subharmonic, quasiperiodic, and nonperiodic or chaotic responses. Nonperiodic responses from simple deterministic systems have been the subject of intense investigation in the physics and circuit theory of the past decade. We will provide an introductory discussion of this class of system, as well as a mapping of the behavior in the time domain and frequency domain of the simple woodwind model. Special emphasis will be placed on the transient response of the system as well as the transitions from one mode of oscillation to another. It is hoped that models of this kind may form the basis for a new class of synthesis techniques, providing complex dynamic response not available with other methods.
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