| Résumé |
In this paper, we consider a class of simplified smooth bores of wind instruments which are composed of a mouthpiece, a cylindrical or conical pipe and a bell. The acoustic model under consideration is based on a standard matrix formalism in the Laplace-Fourier domain for which analytic formula are available. The mouthpiece can be modeled by the beginning of the bore, or more simply, by a volume to be connected to the bore. The acoustic transfer functions of the bore are derived from the smooth connection of a few lossy acoustic pipes with constant-flared profiles (governed by a refined curvilinear 1D horn equation) concatenated with a radiation load model, which is consistent with spherical wavefronts. These models have proved to be relevant, based on a comparison with measurements on a trombone bell. Then, the geometric parameters of the complete model are optimized according to a constrained objective function. This function is specially designed in order to optimize acoustic targets. A special care is devoted to the tuning of the first resonances according to an ideal harmonic sequence. Results are presented for some typical cylindrical and conical chambers, corresponding to a few sketched instruments without fingerings, that could correspond to some idealized clarinets, trombones, oboes, saxophones or horns. This work is part of the ANR project CAGIMA. |
