Abstract

This paper presents a linear mathematical model of bass guitar string vibration with experimentally identified, frequency- and fret-dependent modal damping, aimed at high-fidelity generative sound synthesis. To identify the string damping parameters across various frets and configurations, an experimental framework was developed to benchmark four structural identification methods: half-power bandwidth, I. Yoshida’s method, Discrete Fourier Transform Interpolation, and Hilbert-transform envelope approximation. Experiments were systematically conducted on Cort C4H, Ibanez RB 630, and Yamaha bass guitars. Based on the extracted parameter space, two audio generation strategies are formulated: a spectrum-driven harmonic reconstruction method (Method 1) and a physical modeling approach utilizing spatial wave equations (Method 2). The proposed linear approximation framework effectively captures the inverse relationship between the damping factor and fret numbers specifically on the E-string, while mapping linear increases on the G and D-strings. Quantitative verification using Sobolev norm differences demonstrates good agreement between the synthesized and original signals for the spectrum-driven method (Q = 0.031–0.057) and moderate agreement for the physics-based wave equation method (Q = 0.058–0.153). This reflects a trade-off in which the former achieves tighter spectral convergence, while the latter better preserves the physical, time-domain waveform structure. As both synthesis strategies are closed-form and computationally lightweight, the model is suitable for real-time implementation and the dynamic control of playing techniques (e.g., plucking location and, in principle, slap-type excitation), without relying on heavy, multi-gigabyte audio sample libraries.

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