Physical modelling synthesis
Synthesis that simulates the instrument itself — the string, the tube, the body — rather than imitating the sound it makes.
Instead of describing a tone as waveforms, the model computes what happens when a hammer sets a string vibrating or an airflow drives a tube into resonance. The Karplus–Strong algorithm of 1983 showed how cheap this could be: a short burst of noise circulating through a delay line with a simple low-pass filter sounds uncannily like a plucked string. Julius O. Smith at Stanford's CCRMA generalised the idea into digital waveguides.
Yamaha licensed the work and released the VL1 in 1994, a synth that could breathe, overblow and squeak like a saxophone but managed only two voices and was priced accordingly. The payoff is expressiveness: the model responds to how you play, not just which key. Pianoteq, launched in 2006, renders an entire piano without a single sample, and the install fits in a few tens of megabytes.