A Real-Time Synthesis Oriented Tanpura Model

Physics-based synthesis of tanpura drones requires accurate simulation of stiff, lossy string vibrations while incorporating sustained contact with the bridge and a cotton thread. Several challenges arise from this when seeking efficient and stable algorithms for real-time sound synthesis. The approach proposed here to address these combines modal expansion of the string dynamics with strategic simplifications regarding the string-bridge and string-thread contact, resulting in an efficient and provably stable time-stepping scheme with exact modal parameters. Attention is given also to the physical characterisation of the system, including string damping behaviour, body radiation characteristics, and determination of appropriate contact parameters. Simulation results are presented exemplifying the key features of the model.

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.