It depends on the instrument. 128 positions is well enough for piano. From other instruments, drums is the one I know best, and there single parameter is just n

It depends on the instrument. 128 positions is well enough for piano. From other instruments, drums is the one I know best, and there single parameter is just not enough: the result depends on velocity, the position where the stick hits drum head, for non round tip sticks the stick angle. For cymbals, in addition to hitting different parts of the cymbal, stick tip, shaft and shoulder give different sounds. And so on... There's a good reason why loops sampled from acoustic drums are used even though drum synths exist.