Models of musical instruments from Chua's circuit with time delay

Abstract

We study a new version of Chua's circuit where the linear elements are replaced by a delay line. We show that this circuit is a model of an interesting class of musical instruments, namely, those, like the clarinet, consisting of a massless reed coupled to a passive linear system. The properties and behaviors of this circuit are studied with or without a filter in the feedback loop. In particular, the oscillation conditions are determined, and the respective role of the nonlinearity and of the linear elements are explained. Real-time simulations of the time-delayed Chua's circuit on a digital workstation makes possible easy experimentation with signals and sounds. A surprisingly rich and novel family of periodic and chaotic musical sounds has been obtained. The audification of the local properties of the parameter space permits easy determination of very complex structures that could not be computed analytically and would be difficult to determine by other methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>