Ircam - Centre Georges-Pompidou Equipe Analyse/Synthèse

Physical Models of Trumpet-like Instruments, Detailed Behavior and Model Improvements

Xavier Rodet, Christophe Vergez

Proceedings of the International Computer Music Conference (ICMC'96), Clear Water Bay, Hong-Kong, August 1996.

Abstract

The behavior of a model of instrument has to be foreseeable in order to be used by musicians. We are working in this way. We first develop a basic model of a real instrument to capture its main principle. Then its behavior is studied and some properties are settled about its different ways of working: periodic, quasiperiodic, or chaotic trajectories. Finally we try to improve our model without loosing any information about its behavior.
We are studying four models of instruments with sustained sounds : clarinet like, flute like, violin like, and trumpet like instruments. These models have the same basic structure:a non linear time delay system. But each classe of instruments has its own specifications. For instance, the flute model includes a second delay loop. In the same way, the linear feedback loop of the violin model is composed of two interleaved loops with delays, and the force exerted by the bow on the string is an instantaneous nonlinear function of the bow's velocity. Our model of trumpet like instruments is rather more complicated. In fact, since the mass of the vibrating lip can't be neglected, the hypothesis of an instantaneous nonlinearity can't stand. The nonlinear function has then two inputs.

The behavior of the four previous systems shall be studied, in order to control the models efficiently. A further step is to consider more elaborate models. Their behavior is also precised to avoid loosing some control abilities. Furthermore the effects of each improvement will have to be analyticaly weighed up to consider how closely the model's behavior matches that of the associated acoustic instrument. For instance, we could include in our basic trumpet, a more realistic reflexion function, taking into account the effects of both the mouthpiece and the bell. This could be done either by identifying parameters of a measured reflexion function, or by using truncated cones with fractional delays. Another way of improving the model could be to describe more precisely the wave travelling into the bore. Then, viscothermal losses and nonlinear propagation in the waveguide should be considered.
Our work should lead to the best model, in terms of a compromise between realism and computational complexity.