Two-Polarisation Physical Model of Bowed Strings with Nonlinear Contact and Friction Forces, and Application to Gesture-Based Sound Synthesis

Abstract

Recent bowed string sound synthesis has relied on physical modelling techniques; the achievable realism and flexibility of gestural control are appealing, and the heavier computational cost becomes less significant as technology improves. A bowed string sound synthesis algorithm is designed, by simulating two-polarisation string motion, discretising the partial differential equations governing the string’s behaviour with the finite difference method. A globally energy balanced scheme is used, as a guarantee of numerical stability under highly nonlinear conditions. In one polarisation, a nonlinear contact model is used for the normal forces exerted by the dynamic bow hair, left hand fingers, and fingerboard. In the other polarisation, a force-velocity friction curve is used for the resulting tangential forces. The scheme update requires the solution of two nonlinear vector equations. The dynamic input parameters allow for simulating a wide range of gestures; some typical bow and left hand gestures are presented, along with synthetic sound and video demonstrations.

Keywords

• computer generated music
• finite difference
• musical acoustics
• signal synthesis
• nonlinear systems
• energy balanced scheme
• instrument simulation