On the Nonlinear Commuted Synthesis of the Piano
In this paper a novel method is presented for the physics-based sound synthesis of the piano, based on digital waveguides. The approach combines the advantages of the commuted synthesis technique and the methods using a nonlinear hammer model. The interaction force of the hammer-string contact is computed by an auxiliary digital waveguide connected to a nonlinear hammer model. This force signal is used as a target impulse response for designing a low-order digital filter real-time. The piano sound is calculated by filtering the soundboard response with the hammer filter and feeding this signal to a synthesizer digital waveguide. A new method is presented for separating the contribution of the interaction force and the soundboard in measured piano tones. For modeling beating, a new technique is proposed based on a simplified pitch-shift effect. Considerations on modeling the effect of sustain pedal are also given. It is shown that the technique of designing the hammer filter real-time is not only useful for digital waveguide modeling, but it can be combined with sampling synthesis too.