Physical modelling of the bowed string and applications to sound synthesis

Abstract

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.