ASA 124th Meeting New Orleans 1992 October

4aMU2. Time-delayed nonlinear dynamical systems as musical instruments.

Xavier Rodet


University Paris-6, Paris, France

Boris Doval

University Paris-6, Paris, France

In many physical models of musical instruments, the instrument itself is represented by a passive linear system coupled to a nonlinear dynamical system (NDS) [M. E. McIntyre et al., ``On the Oscillations of Musical Instruments,'' J. Acoust. Soc. Am. 74, 1325--1345 (1983)]. Modeling the excitation process is one of the key points for music synthesis [Proc. Colloquium on Phys. Model., ACROE, Grenoble, France (Oct. 1990)]. It would allow the design of synthetic instruments with as much flexibility and expressivity as natural ones and hopefully with high sound quality. Some classical NDS and the various forms they have in musical instruments such as voice, trumpet, clarinet, or strings are presented. A clarinet-like basic model is designed taking as a starting point the sound requirements. Conditions of periodic oscillation are studied. Properties of the sound are related to the characteristic of the nonlinearity. Other typical behaviors such as period doubling or chaotic regime result in interesting sound effects. A real-time implementation allows for easy experiments and tests of the parameter values. Sound results are demonstrated and discussed. [sup a)]Presently on sabbatical at Ctr. for New Music and Audio Technol. (CNMAT), Univ. of California at Berkeley, 1750 Arch St., Berkeley, CA 94709.