Modeling the nonlinear string body coupled dynamics of bowed musical instruments
Octávio Inácio, José V. Antunes · The Journal of the Acoustical Society of America · 2004
Most theoretical papers on bowed-string instruments deal with isolated strings, pinned on fixed supports. In addition, the instrument body dynamics has not been accounted at all, or else by using extremely simplified models of the string/body interaction at the bridge. Such models have, nevertheless, been instrumental to the understanding of a very common and musically undesirable phenomenon—the ‘‘wolf note’’—a strong beating interplay between string and body vibrations. Cellos, bad and good, are prone to this problem. In previous work we developed a modal method to deal with friction-excited strings, enabling effective simulations of such systems in which the strings were assumed decoupled from the instrument body. In the present paper our computational method is extended to incorporate the complex dynamics of real-life instrument bodies, coupled to the string motions. In this approach, the string is coupled with experimental body data—body modes or impulse response at the bridge. Our computational method is illustrated through extensive parametric computations performed on a bowed cello. These numerical simulations show some light on interesting and less-known features of wolf notes, in particular concerning the ranges of bowing-parameters leading to their emergence, as well as the dependence of the beating frequency on the playing.