Commuted Piano Synthesis
Julius O. Smith, Scott A. Van Duyne · 1995
The #commuted piano synthesis" algorithm is described, based on a simpli#ed acoustic model of the piano. The model includes multiple coupled strings, a nonlinear hammer, and an arbitrarily large soundboard and enclosure. Simpli#cations are employed which greatly reduce computational complexity. Most of the simpli#cations are made possible by the commutativity of linear, time-invariant systems. Special care is given to the felt-covered hammer which is highly nonlinear and therefore does not commute with other components. In its present form, a complete, two-key piano can be synthesized in real time on a single 25MHz Motorola DSP56001 signal processing chip.