Conclusions

An overview of recent results in music synthesis based on physical models has been presented. Basic ``distributed'' building blocks such as vibrating strings and resonating bores are modeled very effectively using the digital waveguide approach. Additionally, ``lumped'' systems such as Helmholtz resonators and mass-spring-damper combinations are easily modeled using second-order digital filter sections. However, many special details of various instruments such as mouthpieces, reeds, radiation load, and nonlinearities require further research. In general, we hope that all such components can be modeled effectively using low-order digital filters, nonlinear polynomials/table-lookups, and in some cases filtered noise injection. Promising preliminary results have been obtained along these lines. Finally, there remains much research to be done into estimating model parameters such as filter and polynomial coefficients from measured data. As these methods evolve, virtual musical instruments based on physical models will become easier to devise, like ``wavetable voices'' based on sampled sound. In fact, the physical models can be seen as a form of ``structured sampling synthesis'' in which deeper physical parameters are sampled in place of the simple air pressure fluctuations recorded in traditional sampling synthesis.