Towards reproducing bowed-string instrument transients using physical modeling

Abstract

Physical models of bowed-string instruments can forecast various aspects of bow-string interaction. However, accurately replicating transient waveforms of string oscillations remains a challenge. In this work, measured transient behavior of the bowed string is compared with predictions from a simulation model. Fixed boundary conditions are assumed and a finite-width bow, bow-hair compliance, torsional string motion, and an elasto-plastic friction model are incorporated. The latter links relative velocity and friction force through a differential equation, and therefore, exhibits hysteresis behavior. Simulated Guettler diagrams are then compared to measured ones obtained from a robot bowing a monochord. The general shape of the playability region is successfully predicted, but some details in the measured time-domain waveforms are not reproduced by the model. Employing inverse modeling, parameter values for the elasto-plastic friction model are derived, demonstrating the ability to generate reliable reconstructions of the measured transient signals. These results emphasize the need to account for variable friction coefficients in order to reproduce measured signals. This observation aligns with prior findings indicating that static and dynamic friction coefficients vary with bow force and bow acceleration. [Work funded in whole or in part by the Austrian Science Fund (FWF) (P34852-N).]