Numerical Study on Multi-Stable Oscillations of Woodwind Single-Reed Instruments

Abstract

Single reed instruments with cylindrical and conical bores were studied numerically, focusing on the dependence of the acoustic mechanism on the bore geometry. As experimentally demonstrated by Idogawa et al. [J. Acoust. Soc. Am., Vol.98, p.540 (1993)], reed instruments can be characterized as multi-attractor systems, which exhibit multi-stable oscillations and hysteretic transitions among oscillating states with change of a control parameter, such as blowing pressure in the mouth. We numerically analyzed dynamical models of single reed instruments to clarify differences in the acoustic mechanisms between cylindrical and conical bore instruments. We analyzed a dynamical model of a cylindrical pipe fitted with a clarinet mouthpiece(CPCM), as a simplified model of the clarinet, and a dynamical model of a truncated cone with a clarinet mouthpiece (TCCM), as a model of conical-bore instruments, together with intermediately shaped models. We found a clear difference in the global structure of transition diagrams (i.e., the overall picture showing the transitions among all the excited states with change of the blowing pressure) between CPCM and TCCM, together with interesting structural changes of the transition diagrams in the intermediate models.