Efficient synthesis model for bowed strings using a nonlinear bow–string interaction model

Abstract

A digital simulation method for bowed strings was developed which combines features of preexisting ‘‘digital waveguide’’ and ‘‘commuted synthesis’’ methods. In both methods, sampled acoustic traveling waves are explicitly modeled in the string, and string losses are lumped at one or two points along the string for computational efficiency. In the digital waveguide case, the bow–string interaction model is based on the theory of McIntyre, Schmacher, and Woodhouse [J. Acoust. Soc. Am. 74 (1983)]. The commuted synthesis model [J. Smith, Int. Computer Music Conf., pp. 64–71 (1993)] interchanges the order of the string and body (assumed linear and time invariant), and therefore cannot support a nonlinear bow–string interaction model. However, according to theory and measurement of bow–string interaction, disturbances sent out by the stick–slip process along the string are fundamentally impulsive in nature. The proposed method consists of a full nonlinear dynamic model for the bow and string, without body, followed by an ‘‘impulse prioritizer,’’ which detects the most important impulsive events reaching the bridge, followed by a commuted synthesis model which drives a second string model with body impulse-responses initiated at the time and amplitude of each high-priority pulse.