Mass-Spring Networks for Sound Synthesis - Morgan, Don (My University, 2008)
Physical sound synthesis produces sound by modelling the physics of musical instruments. One way to do this is to model the musical instrument as a network of masses, springs and dampers. This is known as a mass-spring system.
The goal of this thesis is to determine the stability and accuracy of the numerical methods commonly used to implement mass-spring systems for sound synthesis and determine if there are alternate methods that might provide superior results.
We show that the standard method used in mass-spring systems, when used on undamped systems, has no numerical damping, but does have frequency warping and is unstable at frequencies above 1/π times the sampling rate. As well, we find that for lightly damped systems the damping is accurate, but large damping can cause instability even at low frequencies. We present an algorithm to implement mass-spring systems using implicit numerical methods and show how a mass-spring system can be implemented using a wave digital filter. We compare the standard method implementing mass-spring systems with two higher order numerical methods: the fourth order Runge-Kutta, and the VEFRL algorithm, a fourth order symplectic algorithm. We find that the VEFRL algorithm is much more accurate than the standard method, but that this increase in accuracy does not noticeably affect the quality of the sound produced by the mass-spring system when used to simulate a vibrating string. The increased accuracy of the VEFRL method may, however, be useful for mass-spring spring systems used in physics or engineering requiring high accuracy.
Title: Mass-Spring Networks for Sound Synthesis, Author: Don Morgan, Location: Thode