Modeling of tension-modulated strings using finite difference and digital waveguide techniques

Tension modulation is a nonlinear phenomenon where large-amplitude string vibrations cause the tension of the string to vary. This results in an initial pitch glide and energy coupling between modes, causing for example the generation of missing harmonics. The presentation discusses two methods for numerical simulation of the tension modulation nonlinearity from the sound synthesis point of view. The tension modulation is assumed to propagate instantaneously along the string. In the digital waveguide approach, spatially distributed fractional delay filters are used in modulating the string length during run time. Energy-preserving techniques can be used in implementing the fractional delays. In the finite difference approach, time-domain interpolation is used to artificially modulate the wave propagation velocity. The generation of missing harmonics is implemented in the finite difference model by creating an additional excitation point at the string termination. In the waveguide model, the same effect can be obtained by using suitable approximations in the string elongation calculation. Synthesis results for both techniques are presented. Also, a brief comparison of the models with a discussion on stability issues is provided. [This research has been funded by the Academy of Finland (Project No. 104934), S3TK graduate school, and Tekniikan edistamissaatio.]