| Résumé |
Previous studies (Mooney Benade, Hoekje) confirm musicians' opinions that the vocal tract affects both timbre and pitch. Jhnston, Troup and Clinch modelled the tract as a one peak resonator, which, if tuned tuned to the fundamental f0 of the clarinet, gives a playing frequency of f0. But this result depends upon their particular tract impedance Z, which is small and real ar harmonics of f0. In general, the playing frequency is shifted. We relate the flow and the pressure difference at the reed by the usual non linear Bernouilli' equation in the time domain, simplified as a third order polynomial. In the frequency domain, the impedances of the clarinet and the vocal tract are in series. To obtain an analytical result for the frequency shift, we expand about the threshold oscillation. We compare this result with numerical results from the harmonic balance method. Finally, impedance spectra measured on an artificial VT with a discrete but variable area function are used in this theoretical study. We suggest that tuning the vocal tract to f0 may be rare and unnecessary. |
