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International audience; The system formed by a trumpet player and his/her instrument can be seen as a non-linear dynamical system, and modeled by physical equations. Numerical tools can then be used to study these models and clarify the influence of the model parameters. The acoustic input impedance, for instance, is strongly dependent on the geometry of the air column and is therefore of primary interest for a musical instrument maker. In this study, a method of continuation of periodic solutions based on the combination of the Harmonic Balance Method (HBM) and the Asymptotic Numerical Method (ANM), is applied to a physical model of brass instruments. It allows the study of the evolution of the system where one parameter of the model (static mouth pressure) varies. This method is used to compare different B trumpets on the basis of two descriptors (hysteresis behavior and dynamic range) computed from the continuation outputs. Results show that this methodology enables to differentiate instruments in the space of the calculated descriptors. Calculations for different values of the lip parameters are also performed to confirm that the obtained categorization is independent of variations of lip parameters.

International audience; 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.

Several factors explain the difference between the resonance frequencies of the resonator of reed instruments and their playing frequency: the flow rate due to the reed displacement, the reed dynamics, the resonator inharmonicity, and the temperature gradient. For conical instruments, the truncation of the cone entails non-negligible inharmonicity effects. This is true even if the inharmonicity is reduced by a proper choice of the mouthpiece volume. The playing frequency was calculated by using a minimum, ab initio model of self-sustained oscillations, and compared to analytical results. Furthermore, the “reactive power rule” (Boutillon, 1989) provides a link between the pressure spectrum and inharmonicity. Compared to the natural frequency of the complete cone, which is a well known approximation, the playing frequency is slightly higher: typical discrepancies are 50 cents for short truncated cones (higher notes) and 10 cents for long truncated cones (lower notes). This discrepancy, due to inharmonicity,...

Using an artificial mouth with an accurate pressure control, the onset of the pressure oscillations inside the mouthpiece of a simplified clarinet is studied experimentally. Two time profiles are used for the blowing pressure: in a first set of experiments the pressure is increased at constant rates, then decreased at the same rate. In a second set of experiments the pressure rises at a constant rate and is then kept constant for an arbitrary period of time. In both cases the experiments are repeated for different increase rates. Numerical simulations using a simplified clarinet model blown with a constantly increasing mouth pressure are compared to the oscillating pressure obtained inside the mouthpiece. Both show that the beginning of the oscillations appears at a higher pressure values than the theoretical static threshold pressure, a manifestation of bifurcation delay. Experiments performed using an interrupted increase in mouth pressure show that the beginning of the oscillation occurs close to the stop in the increase of the pressure. Experimental results also highlight that the speed of the onset transient of the sound is roughly the same, independently of the duration of the increase phase of the blowing pressure., Comment: 14 pages

Some aspects of sound production by wind musical instruments are rather well understood. A minimum model for reed cylindrical instruments was proposed in 1983 by Mc Intyre et al. When the reed dynamics and resonator losses are ignored, the mouthpiece pressure is a square signal. Three primary parameters are necessary: (i) the mouth pressure; (ii) the “valve” parameter (based on the reed opening and its stiffness); (iii) the length of the cylinder. The model gives a simplified shape of the waveform; the playing frequency and the amplitude are rather well predicted. For further spectrum details, it is necessary to add losses, therefore a secondary parameter, the radius. Furthermore other parameters influence the spectrum: reed dynamics, toneholes, vocal tract.... What happens for conical reed instruments? Considering the waveform of the mouthpiece pressure, a fourth primary parameter is the length of the missing part of the truncated cone. Similarly to cylindrical instruments, a secondary parameter is relat...

Measurements of the quasistatic nonlinear characteristic curve for double reeds show systematic deviations from an elementary model of a reed instrument based on a spring model associated to a Bernoulli flow input into the reed. These deviations were previously explained by the pressure recovered by the flow as it expands in the conically divergent output duct of the reed. We will show measurements of the pressure recovery inside the reed as well as detailed flow profiles that can explain the different regimes observed for the pressure recovery (laminar and turbulent). An extension of these measurements to oscillating regimes allows us to observe some qualitative differences in the flow, suggesting an important influence of the dynamic terms in the Navier‐Stokes equation in these kinds of regimes.

When air pressure is low enough, wave propagation in a pipe can be considered linear to a reasonable degree. When the pressure level increases, this simplification becomes more and more inaccurate since high pressure values travel faster than low pressure values. The speed of propagation is thus a function of the pressure level. A new time‐domain approach is proposed to simulate nonlinear propagation of a sound wave in a tube of any shape. This constraint‐based algorithm does not prevent the derivative of the signal from breaking, as it happens when a shock wave occurs. Moreover, the algorithm allows the carrying out of nonlinear propagation even once a shock has occured. Thus, as expected the distorsion of a sinusoidal wave into a N‐wave of progressively decreasing amplitude was observed. Moreover, without any additional computational cost, this technique provides fractional delay variation as needed for continuous tube’s variations in length. The nonlinear propagation algorithm is included in the real‐time high‐quality physical model of trumpetlike instruments. Simulation shows a great improvement in the sound quality since this algorithm allows subtle nuances in the timbre as well as hard brassy effects.