Caractérisation objective de la qualité de justesse, de timbre et d ...

Abstract.___________________________________________________________________________TITLEObjective characterisation of pitch, timber and ease of playing qualities for single reedwoodwind instruments.ABSTRACTTwo methods for characterising the acoustic features (pitch, timber, easiness of playing) ofsingle reed woodwind instruments are developed and tested. On one hand, we study theresonator, and on the other hand we make a numerical simulation of the auto-oscillationsresulting from the coupling between the resonator (supposed linear) and the excitator(supposed to be a non linearity at the mouthpiece input). The studied physical variables are thefundamental frequency and the spectrum of the pressure in the mouthpiece. In all the study,these variables represent respectively the pitch and the timber. In order to test the twomethods, we compare these variables with variables measured in the mouthpiece of realinstruments. These are played with the help of a blowing machine that we built to reproducethe musician embouchure accurately.We begin with a historical background and choose a physical model. The analysis of thesolutions resulting from the model enables to show that the fundamental frequency can bededuced from resonance frequencies for the linear threshold. This is possible by means of acorrective term, called the length correction. This term represents the effect of theembouchure and does not depend on the frequency.The discrete solutions of the model are calculated with the help of the measured inputimpedance and embouchure characteristics. We choose the sampling frequency values withrespect to the resonator input impedance. This enables to minimise numerical errors on thediscrete reflection function. Since the simulation uses measured input impedance, samplingfrequency values are small with respect to the reed resonance frequency. We chose thecompensated bilinear transformation which gives a "discrete" reed whose properties are nearfrom those of the "analog" reed.Input impedance and fundamental frequencies of the pressure in mouthpiece are measured forall the fingerings of the two first registers of a clarinet and an alto saxophone. The resonancefrequencies and the fundamental frequencies are compared for each fingering. For eachregister, we evaluate a length correction, due to the embouchure. Comparisons betweenmeasured and calculated pressures in a clarinet mouthpiece for some fingerings show that thesimulation detects "difficult fingerings" if low blowing pressures are used in the model. Thebending of the reed against the curved lay of the mouthpiece is not taken into account in themodel and seems to be the major reason for this discrepancy. A first theoretical approach ofthis mechanical phenomenon is proposed in appendix A.KEYWORDMusical acoustics, woodwind instrument, numerical simulation, input impedance, resonancefrequency.