Different musical situations will bring different requirements, but several criteria appear likely to recur in work of this sort, perhaps at varying levels of importance. Some of these are:
Perceptibility. Changes in input timbre should be clearly heard as changes in output timbre. This is desirable so that gestures made by the musician will be clearly audible, in some way, in the output.
Robustness. A slight change in the input should not result in a huge change in the perceived output. For example, one should not map loudness to pitch, because the pitch would then always be wavering up and down in a way that the player could not control accurately enough.
Continuity. The synthesis parameters should not jump precipitately if the input sound is changing smoothly.
Correspondence. When a change in playing makes an audible change in the synthetic sound, the two should move in compatible directions. For example, a softer performed sound should not translate into a louder synthetic one.
Fast response. The output should depend on the current, or very recent, input, not on time averages or past gestures, so that the musician can get quickly to any desired sound output.
These criteria may sometimes be traded off against each other. For example, optimizing for `fast response' will often require compromising `continuity'.