Physics-Based Methods for Modeling Nonlinear Vibrating Strings

Nonlinearity in the vibration of a string is responsible for interesting acoustical features in many plucked string instruments, resulting in a characteristic and easily recognizable tone. For this reason, synthesis models have to be capable of modeling this nonlinear behavior, when high quality results are desired. This study presents two novel physical modeling algorithms for simulating the tension modulation nonlinearity in vibrating strings in a spatially distributed manner. The first method uses fractional delay filters within a digital waveguide structure, allowing the length of the string to be modulated during run time. The second method uses a nonlinear finite difference approach, where the string state is approximated between sampling instants using similar fractional delay elements, thus allowing run-time modulation of the temporal sampling location. The magnitude of the tension modulation is evaluated from the elongation of the string at every time step in both cases. Simulation results of the two models are presented and compared. Real-time sound synthesis of the kantele, a traditional Finnish plucked-string instrument with strong effect of tension modulation, has been implemented using the nonlinear digital waveguide algorithm.