String Sound Synthesizer on GPU-accelerated Finite Difference Scheme

TL;DR

This work addresses the challenge of high-fidelity nonlinear string synthesis by introducing a GPU-accelerated finite-difference time-domain (FDTD) model of planar strings with cross-mode coupling between transverse and longitudinal motions. The approach combines a nonlinear string formulation, a mixed-transverse/longitudinal FDTD scheme, stiffness and dissipation extensions, and excitations for pluck, bow, and hammer, all implemented in a PyTorch-based CPU/GPU framework. Key contributions include an open-source nonlinear string synthesizer with stochastic parameterization, a matrix-vector formulation amenable to parallelization, and a dataset-generation capability for neural audio synthesis. Empirical analysis demonstrates stiffness-induced detuning, phantom partials arising from nonlinearity, and GPU-accelerated performance trends, highlighting batching benefits and the dominant cost of temporal recurrence. The work provides a practical, high-fidelity tool for physical modeling and a scalable data generator that can support neural-synthesis research and reproducible experimentation.

Abstract

This paper introduces a nonlinear string sound synthesizer, based on a finite difference simulation of the dynamic behavior of strings under various excitations. The presented synthesizer features a versatile string simulation engine capable of stochastic parameterization, encompassing fundamental frequency modulation, stiffness, tension, frequency-dependent loss, and excitation control. This open-source physical model simulator not only benefits the audio signal processing community but also contributes to the burgeoning field of neural network-based audio synthesis by serving as a novel dataset construction tool. Implemented in PyTorch, this synthesizer offers flexibility, facilitating both CPU and GPU utilization, thereby enhancing its applicability as a simulator. GPU utilization expedites computation by parallelizing operations across spatial and batch dimensions, further enhancing its utility as a data generator.

Figures (6)

• Figure 1: String coordinate system at the deflected () state is shown along with the equilibrium () state for the reference.
• Figure 2: Log-magnitude spectrum of plucked $u$ and $\zeta$ in dB scale.
• Figure 3: $\varphi$ curves for various $a$, $\epsilon$.
• Figure 4: Spectrograms of simulated lossy and nonlinear stiff strings. From the 2/3rd point onwards, the bowing force is deliberately adjusted to zero. The overlays of white lines indicate: input $f_0$ (), estimated $f_0^{(\tt est)}$ (), and modes $\hat{f_p}$ (, $p=0,1,\cdots,9$).
• Figure 5: Detune in Hz.