Simulation of Distributed Contact in String Instruments: a Modal Expansion Approach

Impactive contact between a vibrating string and a barrier is a strongly nonlinear phenomenon that presents several challenges in the design of numerical models for simulation and sound synthesis of musical string instruments. These are addressed here by applying Hamiltonian methods to incorporate distributed contact forces into a modal framework for discrete-time simulation of the dynamics of a stiff, damped string. The resulting algorithms have spectral accuracy, are unconditionally stable, and require solving a multivariate nonlinear equation that is guaranteed to have a unique solution. Exemplifying results are presented and discussed in terms of accuracy, convergence, and spurious high-frequency oscillations.

Towards a Virtual-Acoustic String Instrument

In acoustic instruments, the controller and the sound producing system often are one and the same object. If virtualacoustic instruments are to be designed to not only simulate the vibrational behaviour of a real-world counterpart but also to inherit much of its interface dynamics, it would make sense that the physical form of the controller is similar to that of the emulated instrument. The specific physical model configuration discussed here reconnects a (silent) string controller with a modal synthesis string resonator across the real and virtual domains by direct routing of excitation signals and model parameters. The excitation signals are estimated in their original force-like form via careful calibration of the sensor, making use of adaptive filtering techniques to design an appropriate inverse filter. In addition, the excitation position is estimated from sensors mounted under the legs of the bridges on either end of the prototype string controller. The proposed methodology is explained and exemplified with preliminary results obtained with a number of off-line experiments.