Two-polarisation finite difference model of bowed strings with nonlinear contact and friction forces

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Abstract

Bowed string sound synthesis has long relied on physical modelling techniques; the achievable realism and flexibility of gestural control are appealing, and computational cost is increasingly manageable as technology has improved. A bowed string is simulated in two polarisations by numerically solving the partial differential equations governing its behaviour, using the finite difference method; a globally energy balanced scheme is used, as a guarantee of numerical stability under highly nonlinear conditions. In the vertical polarisation, a nonlinear contact model is used for the normal forces exerted by the bow hair, left hand fingers, and fingerboard. In the horizontal polarisation, a force-velocity friction curve is used for the resulting tangential forces in the other polarisation. The scheme update requires the solution of two nonlinear vector equations; iterative methods (in this case, the Newton-Raphson method) are employed. Sound examples and video demonstrations are presented.
Original languageEnglish
Title of host publicationProceedings of the 18th International Conference on Digital Audio Effects
Place of PublicationTrondheim, Norway
Number of pages8
Publication statusPublished - 30 Nov 2015

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