Acoustical modeling of the saxophone mouthpiece as a transfer matrix

Abstract

This paper proposes an acoustic model of the saxophone mouthpiece as a transfer matrix (TM). The acoustical influence of the mouthpiece is investigated, and the TM mouthpiece model is compared to previously reported mouthpiece representations, including cylindrical and lumped models. A finite element mouthpiece model is first developed, from which the TM model is derived, and both models are validated by input impedance measurements. The comparison of acoustic properties among different mouthpiece models shows that the TM mouthpiece is more accurate than the other two models, especially in preserving the high-frequency acoustic characteristics. The TM model also produces the best overall tuning of the first several impedance peaks when coupled to a measured saxophone impedance. The internal and radiated sound pressure are synthesized for an alto saxophone connected to different mouthpiece models by jointly modeling the input impedance and the radiation transfer function using recursive parallel filters. Differences are found among mouthpiece models in terms of oscillation thresholds, playing frequencies, spectral centroids, pressure waveforms, and bifurcation delays, which can be partially explained by differences in the tuning and high-frequency characteristics.