Download Efficient Simulation of the Bowed String in Modal Form The motion of a bowed string is a typical nonlinear phenomenon resulting from a friction force via interaction with the bow. The system can be described using suitable differential equations. Implicit numerical discretisation methods are known to yield energy consistent algorithms, essential to ensure stability of the timestepping schemes. However, reliance on iterative nonlinear root finders carries significant implementation issues. This paper explores a method recently developed which allows nonlinear systems of ordinary differential equations to be solved non-iteratively. Case studies of a mass-spring system and an ideal string coupled with a bow are investigated. Finally, a stiff string with loss is also considered. Combining semi-discretisation and a modal approach results in an algorithm yielding faster than real-time simulation of typical musical strings.
Download Real-Time Implementation of the Dynamic Stiff String Using Finite-Difference Time-Domain Methods and the Dynamic Grid Digital musical instruments based on physical modelling have gained increased popularity over the past years. This is partly due to recent advances in computational power, which allow for their real-time implementation. One of the great potentials for digital musical instruments based on physical models, is that one can go beyond what is physically possible and change properties of the instruments which are static in real life. This paper presents a real-time implementation of the dynamic stiff string using finitedifference time-domain (FDTD) methods. The defining parameters of the string can be varied in real time and change the underlying grid that these methods rely on based on the recently developed dynamic grid method. For most settings, parameter changes are nearly instantaneous and do not cause noticeable artefacts due to changes in the grid. A reliable way to prevent artefacts for all settings is under development.