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 http://www.acoustics.hut.fi/~ttolonen/sounddemos/tmstr/.

**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.

- Complete paper in PostScript format (410 kB)
- Complete paper in PDF format (67 kB)
- Slides of the presentation given at ICASSP'99 (120 kB)
- Sound example 1:
listen to the change of timbre caused by variation of the
*a*_{p}parameter of filter*I*(*z*) (loop filter parameters:*g*= 0.992 and*a*= -0.005; delay-line length 2*L*_{nom}= 90, plucking point = 1/3)- Linear plucked-string synthesis model (
*g*_{p}= 0) - Tension modulation model:
*a*_{p}= -0.999 - Tension modulation model:
*a*_{p}= -0.990 - Tension modulation model:
*a*_{p}= -0.970 - Linear plucked-string synthesis model (
*g*_{p}= 0)

- Linear plucked-string synthesis model (
- Sound example 2:
listen to the change in fundamental frequency caused by variation
of the
*g*_{p}parameter of filter*I*(*z*) (*a*_{p}= -0.990, other parameters as in Example 1)- Linear plucked-string synthesis model (
*g*_{p}= 0) - Tension modulation model:
*g*_{p}= 200 - Tension modulation model:
*g*_{p}= 1000 - Tension modulation model:
*g*_{p}= 10000 - Linear plucked-string synthesis model (
*g*_{p}= 0)

- Linear plucked-string synthesis model (
- Sound example 3:
listen how much (or little) the sound is affected when only every
*M*th squared sum is computed (*g*_{p}= 1000, other parameters as in Example 1)- Tension modulation model:
*M*= 1 (full implementation) - Tension modulation model:
*M*= 6 - Tension modulation model:
*M*= 12 - Tension modulation model:
*M*= 24 - Tension modulation model:
*M*= 1 (full implementation)

- Tension modulation model:
- Some more sound examples

This
URL: *http://www.acoustics.hut.fi/~vpv/publications/icassp99-tm.htm
*Last modified: