Dept. of Music, Ohio State Univ., Columbus, OH 43210
Using results obtained from prior investigations into the biology, chemistry, and physics of the clarinet reed [D. Casadonte, J. Acoust. Soc. Am. 90, 2351(A) (1991)], a realistic computer simulation using the ANSYS finite-element program has been developed. Using this simulation, modal frequencies and shapes were isolated for those modes below 20 000 Hz, as well as stress maps of the reed structure, etc. The simulation is flexible enough to allow for the inclusion of any type of ligature, embouchure, air column pressure spectrum, mouthpiece, and variations in reed material properties and biology during any stage of the life cycle of the reed. This allows for most questions of practical importance in reed science to be examined (including those of historical reed shapes). Specifically, the problem of reed resonance [S. C. Thompson, J. Acoust. Soc. Am. 66, 1299--1307 (1979)] is investigated. It is shown that a good reed is one ``tuned'' to maximize statistically the power output from the overtones of the air column. This tuning is gradually lost as the reed ages. Finally, the reverse procedure of designing a reed shape and material that will maximize the resonance for a typical clarinet air column is studied.