Physical modelling of the bowed string and applications to sound synthesis

This work outlines the design and implementation of an algorithm to simulate two-polarisation bowed string motion, for the purpose of realistic sound synthesis. The algorithm is based on a physical model of a linear string, coupled with a bow, stopping fi ngers, and a rigid, distributed fingerboard. In one polarisation, the normal interaction forces are based on a nonlinear impact model. In the other polarisation, the tangential forces between the string and the bow, fingers, and fingerboard are based on a force-velocity friction curve model, also nonlinear. The linear string model includes accurate time-domain reproduction of frequency-dependent decay times. The equations of motion for the full system are discretised with an energy-balanced finite difference scheme, and integrated in the discrete time domain. Control parameters are dynamically updated, allowing for the simulation of a wide range of bowed string gestures. The playability range of the proposed algorithm is explored, and example synthesised gestures are demonstrated

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

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