Computational modelling of string–body interaction for the violin family and simulation of wolf notes

Most theoretical studies of bowed-string instruments deal with isolated strings, pinned on fixed supports. In others, the instrument body dynamics have been accounted by using extremely simplified models of the string–body interaction through the instrument bridge. Such models have, nevertheless, been instrumental to the understanding of a very common and musically undesirable phenomenon known as the wolf note—a strong beating interplay between string and body vibrations. Cellos, bad and good, are particularly prone to this problem.In previous work, a computational method that allows efficient time-domain modelling of bowed strings based on a modal approach has been introduced. This has been extended to incorporate the complex dynamics of real-life instrument bodies, and their coupling to the string motions, using experimental dynamical body data. The string is modelled using its unconstrained modes, assuming pinned–pinned boundary conditions at the tailpiece and the nut. At the intermediary bridge location, the string–body coupling is enforced using the body impulse-response or modal data, as measured at the instrument bridge.In the present paper, this computational approach is applied to a specific cello, which provided experimental wolf-behaviour data under several bowing conditions, as well as laboratory measurements of the bridge impulse responses on which the numerical simulations were based. Interesting aspects of the string–body dynamical responses are highlighted by numerical simulations and the corresponding sounds and animations produced. Finally, a qualitative (and, when possible, quantitative) comparison of the experimental and numerical results is presented.