Off-line Physics-based Sound Synthesis

To simulate the function of bowed-string instruments, one must model the frictional interaction between the bow hair and the vibrating string. Several models have been proposed to capture this interaction; however, it remains difficult to accurately resynthesise experimentally obtained waveforms. This work employs an elasto-plastic friction model capable of reproducing experimental data recorded with a monochord setup. A numerical scheme is derived that considers the energy balance of the underlying continuous model, resulting in numerically stable simulations. The resulting model involves an implicit update requiring an iterative solution at each time step. While this is suitable for off-line sound synthesis and analysis, real-time capability (e.g., during a live performance) is not guaranteed. This is due to the unknown number of Newton iterations required to solve the nonlinear equations of the implicit scheme. However, the implicit nature of the schemes allows for an accurate approximation of the nonlinear interaction between the bow and string. Recent attempts to find explicit solvers for nonlinear bow-string interaction still lack this level of accuracy.

Matlab code: https://doi.org/10.5281/zenodo.15341818

Sound example:

References

• Matusiak, Ewa; Van Walstijn, Maarten and Chatziioannou, Vasileios (2025) "Numerical modelling of elasto-plastic friction in bow–string interaction with guaranteed passivity," Frontiers in Signal Processing 5. DOI↗
• Matusiak, Ewa and Chatziioannou, Vasileios (2024) "Elasto-plastic friction modeling toward reconstructing measured bowed-string transients," The Journal of the Acoustical Society of America 156(2), 1135-1147. DOI↗