Plucked-String Synthesis Algorithms with Tension Modulation Nonlinearity

Vesa Välimäki, Tero Tolonen, and Matti Karjalainen

Helsinki University of Technology, Laboratory of Acoustics and Audio Signal Processing, P.O. Box 3000, FIN-02015 HUT, Espoo, Finland


Digital waveguide modeling of a nonlinear vibrating string is investigated when the nonlinearity is essentially caused by tension modulation. We derive synthesis models where the nonlinearity is implemented with a time-varying fractional delay filter. Also, conversion from a dual-delay-line physical model into a single-delay-loop model is explained. Realistic synthetic tones with nonlinear effects are obtained by introducing minor amendments to a linear string synthesis algorithm. It is shown how synthetic plucked-string tones are modified as a consequence of tension modulation. Examples of synthesized tones are available at

Keywords: time-varying fractional delay filter, musical acoustics, physical modeling of musical instruments, sound synthesis, vibrating string

This paper was published in the Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'99), vol. 2, pp. 977-980, Phoenix, Arizona, March 15-19, 1999.

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Last modified: 14 April, 1999
Authors: Vesa Välimäki and Tero Tolonen