Accuracy and stability in mass-spring systems for sound synthesis

ABSTRACT

This paper examines the stability and accuracy of mass-spring systems used in sound synthesis. We show that the standard method used in mass-spring systems has no numerical damping, but does have frequency warping and is unstable at frequencies above 1/π times the sampling rate. We compare the standard method 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.

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INDEX TERMS

Primary Classification:
  H. Information Systems
  H.5 INFORMATION INTERFACES AND PRESENTATION (I.7)
      H.5.5 Sound and Music Computing

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Finite difference methods; Error analysis

General Terms:
Reliability

Keywords:
mass-spring system, symplectic Euler method