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.

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In this paper a mixed-paradigm piano model is presented. The major development is the ability of modeling longitudinal string vibrations. Longitudinal string motion is the reason for the metallic sound of low piano notes, therefore its modeling greatly improves the perceptual quality of synthesized piano sound. In this novel approach the transversal displacement of the string is computed by a finite-difference string model and the longitudinal motion is calculated by a set of second-order resonators, which are nonlinearly excited by the transversal vibration. The soundboard is modeled by a multi-rate filter based on measurements of real pianos. The piano model is able to produce high-quality piano sounds in real-time with about 5–10 note polyphony on an average personal computer.

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