Perhaps the simplest possible signal ``model'' is a recording of the desired sound indexed by the controller state used to produce it. In other words, for each possible input condition (such as a key-press on a keyboard, pedal press, etc.) we record the sound produced in the desired acoustic space (which itself can be a recording parameter). Such a procedure is called instrument sampling [#!MassieMohonkBook!#]. Sampling is of course highly laborious, but it is actually the current common practice for electronic musical instruments, such as ``sampled pianos''.2.2
A problem with sample-based synthesizers, aside from the enormous recording effort required, is that the dimensions of expressive performance are invariably limited. While impressive results have been obtained for struck-string instruments such as the piano, continuously-controlled instruments such as bowed-string, wind, and brass instruments are reduced to highly oversimplified shadows of themselves. This can be appreciated by considering that the only non-pedal control parameters for the piano are key-number and key-velocity, while for bowed-string and wind instruments, the player manages multiple continuous dimensions of control. Skilled performers do not wish to give up these dimensions.
Another source of sonic richness routinely given up by sampling synthesis is the interaction between the performer and the instrument. For example, in a long-sustaining electric guitar performance, there is significant interaction between a ringing string and its subsequent re-excitation. Such effects are also audible (though subtle) on a piano when restriking a ringing string (with the sustain pedal down).
While sample-based sound synthesis can be frustrating (or at best constraining) for the performing musician, its best feature is the high quality of the ultimate sound to the listener. The sound quality is limited only by the quality of the original recordings and subsequent signal processing.
A major advantage of physical models, especially relative to sample-based signal models, is that the internal state is automatically maintained. That is, sample-based models should in principle index each acoustic2.3recording by not only the input state, but also by the internal state of the instrument (which is prohibitive and rarely done). Physical models, in contrast, propagate some kind of simulation of the internal state, so that realistic interactions between the external inputs and the internal state are provided ``for free''.