Antoine J. Chaigne
Signal Dept., Telecom Paris, 46 rue Barrault, 75634 Paris Cedex 13, France
The tones of existing instruments are simulated in the time domain by means of standard finite difference methods. The string model previously applied to the guitar [A. Chaigne, J. Acoust. Soc. Am. Suppl. 1 88, S188 (1990)] and more recently to the piano [A. Chaigne, A. Askenfelt, and E. Jansson, J. Acoust. Soc. Am. 89, 1878(A) (1991)] has been extended to the violin, the xylophone bars, and tympani membranes. The general procedure, which is similar for each type of instrument, will be presented. It consists first in deriving a numerical scheme from the continuous differential equations governing the motion of the vibrating systems including the interaction with an exciter (hammer, bow, mallets,...). In a second step, the mathematical properties of these discrete approximations are evaluated with special emphasis laid on stability, accuracy, and dispersion problems. Simulated waveforms are computed with realistic values of the parameters derived from measurements on existing instruments. These waveforms as well as their spectral contents are then systematically compared with those of real tones. This time-domain approach is used in order to test the influence of various physical parameters on the transients of strings and percussive sounds in which the nonlinear effects are essential. The paper will be illustrated by sound synthesis examples of various instruments obtained with this technique.