Inverse problem to estimate lips parameters values of outward-striking trumpet model for successive playing registers

The objective of this work is to estimate by inverse problem lip parameters values of trumpet model so that the oscillation thresholds for successive playing registers occur for the same blowing pressure as the one measured on several trumpet players. The lips vibration is modeled through an oscillator including unknown parameters such as resonance frequency, quality factor, surface mass, stiffness, and opening at rest of the lips. The oscillation threshold is calculated through linear stability analysis of the outward-striking model including the nonlinear coupling with the bore of the trumpet. It appears that many combinations of parameter values are suitable to obtain the same blowing pressure at threshold as in the experiments. According to the analysis of the possible parameter values, some hypotheses are formulated about the playing strategies used by the trumpeter to select the different registers of the instrument. In addition to the resonance frequency of the lips, controlling the lips opening at rest appears to be a viable strategy to match experimental oscillation thresholds in terms of blowing pressure. Numerical values for the lips parameters are given and through sound synthesis, allow the successive registers of the trumpet to be played.

Characterization of open woodwind toneholes by the tube reversed method

Woodwind tonehole's linear behavior is characterized by two complex quantities: the series and shunt acoustic impedances. A method to determine experimentally these two quantities is presented for the case of open toneholes. It is based on two input impedance measurements. The method can be applied to clarinet-like instruments, and can be used for undercut toneholes as well as toneholes with pads above their output, under the condition that a symmetry axis exists. The robustness of the method proposed is explored numerically through the simulation of the experiment when considering geometrical and measurement uncertainties. Experimental results confirm the relevance of the method proposed to estimate the shunt impedance. Even the effect of small changes in the hole's geometry, such as those induced by undercutting, are characterized experimentally. The main effect of undercutting is shown to be a decrease in the tonehole's acoustic mass, in agreement with theoretical considerations based on the shape of the tonehole. Investigation on the effects of pads will be studied in a further work. Experimental results also reveal that losses in toneholes are significantly higher than those predicted by the theory. Therefore, the method is suitable for the experimental determination of the shunt impedance, but it is not convenient for the characterization of the series impedance.

Sound production on a "coaxial saxophone"

Sound production on a "coaxial saxophone" is investigated experimentally. The coaxial saxophone is a variant of the cylindrical saxophone made up of two tubes mounted in parallel, which can be seen as a low-frequency analogy of a truncated conical resonator with a mouthpiece. Initially developed for the purposes of theoretical analysis, an experimental verification of the analogy between conical and cylindrical saxophones has never been reported. The present paper explains why the volume of the cylindrical saxophone mouthpiece limits the achievement of a good playability. To limit the mouthpiece volume, a coaxial alignment of pipes is proposed and a prototype of coaxial saxophone is built. An impedance model of coaxial resonator is proposed and validated by comparison with experimental data. Sound production is also studied through experiments with a blowing machine. The playability of the prototype is then assessed and proven for several values of the blowing pressure, of the embouchure parameter, and of the instrument's geometrical parameters.