Introduction

A musical instrument should be ``alive'' in the hands of the performer. A performance is naturally an interaction between the player and the instrument. While the main attributes of each note are predictable from a score, for example, many subtle qualities are not, contributing to the delight of the player and audience. Recently, commercial music synthesizers have been progressing toward more interactive, model-based instruments, and there seems to be growing interest in them among performing musicians. A new breed of ``virtual acoustic'' synthesizer is now on the market, and there has been a resurgence of interest in ``virtual analog'' synthesis. One can even hear former leaders of the development of wavetable (``sampling'') synthesizers claiming that, for the future, ``ROM is dead.''

The principal source of ``life'' in most acoustic instruments (aside from the performer) is resonance of one kind or another. For example, in a cello, the strings resonate to provide pitched notes, and the whole body resonates to provide subtle variations in the tone. Resonance gives memory and variable character to the sound. The player interacts with body resonances in unpredictable ways, sometimes reinforcing, sometimes partially canceling or beating against the accumulated resonating state.