Joël Gilbert

Shock waves in trombones

Based on physical models of musical instruments and of the human voice, a new generation of sound synthesizers is born: virtual instruments. The models used for wind instruments are simple feedback loops in which a nonlinear sound source drives a linear filter representing the pipe of the instrument. While very rewarding musical sounds have been obtained with these models, it has become obvious that some essential phenomena escape such a description. In particular the brightness of the sound generated by trombones is expected to be due to the essential nonlinearity of the wave propagation in the pipe. At fortissimo levels this leads to shock wave formation observed in our experiments both from pressure measurements and flow visualization. A modest modification of the physical model could already take this phenomenon into account. The key idea is that the nonlinear effect is essential for the transfer of sound from the source toward the listener, but can be ignored in a model of the generation of the pipe ...

Nonlinear characteristics of single-reed instruments: quasistatic volume flow and reed opening measurements.

A wind instrument can be described as a closed feedback loop made up of a linear passive element-the resonator-and a lumped nonlinear element-the mouthpiece. A method for measuring the nonlinear characteristics of the mouthpiece-nonlinear flow relationship-in static condition is given. An artificial mouth is used in which the volume flow is deduced from the pressure difference between both sides of a constriction (orifice) which takes place in the resonator. The orifice also plays the role of a nonlinear absorber, thwarting possible reed oscillations. This allows the measurement of the complete characteristics. In addition, the reed opening is measured using an optical device. Results are compared to a model in which the reed is reduced to its stiffness and the flow is governed by the Bernoulli equation. It is shown that the reed stiffness and the ratio of the effective surface of the jet and the reed opening are constant in a large range of openings. Standard range values of embouchure parameters are given.

Calculation of the steady‐state oscillations of a clarinet using the harmonic balance technique

The harmonic balance technique is known as a time‐frequency simulation technique used for the study of large signal regimes of microwave circuits driven in forced oscillation. The technique can be adapted to self‐sustained oscillations, especially for wind musical instruments such as clarinets. The resonator (i.e., the instrument body) is the linear part, treated in the frequency domain, while the driving system (the reed) is the nonlinear part, treated in the time domain. The harmonic balance method is shown to connect the results of two known methods, so‐called weakly nonlinear (in frequency domain) and strongly nonlinear (in time domain). The advantages and disadvantages of the method are discussed.

An analytical prediction of the oscillation and extinction thresholds of a clarinet

This paper investigates the dynamic range of the clarinet from the oscillation threshold to the extinction at high pressure level. The use of an elementary model for the reed-mouthpiece valve effect combined with a simplified model of the pipe assuming frequency independent losses (Ramans model) allows an analytical calculation of the oscillations and their stability analysis. The different thresholds are shown to depend on parameters related to embouchure parameters and to the absorption coefficient in the pipe. Their values determine the dynamic range of the fundamental oscillations and the bifurcation scheme at the extinction.

Some aspects of tuning and clean intonation in reed instruments

Abstract The influence of the first and second resonance frequencies on tuning, timbre (or tone colour) and ease of playing is investigated for reed instruments, such as the clarinet, alto saxophone and oboe. Theoretical analyses of the effects of the reed and the player embouchure (i.e. lip position and pressure on the reed) are reviewed, as well as the consequences of inharmonicity in the resonance frequencies. This review allows us to present interesting interpretations of the numerous experiments reported here. Three kinds of results are given: (1) comparison of playing frequencies and first resonance frequencies, for several fingerings with or without open register hole, leading to the definition of a frequency independent length correction for the embouchure; (2) examination of the effect of inharmonicity of the two first resonance frequencies on both tone colour and ease of playing, the causes coming from either the player embouchure or the instrument construction; (3) comparison between theory and experiment for the inharmonicity produced by the changes in conicity in oboes, leading to an interpretation of the maker s choices. The results show how judicious use of simple tools, such as calculations or measurements of input impedance or playing data obtained using an artificial mouth, can be of help to the understanding of instrument construction and to the instrument designer.

A simulation tool for brassiness studies

A frequency-domain numerical model of brass instrument sound production is proposed as a tool to predict their brassiness, defined as the rate of spectral enrichment with increasing dynamic level. It is based on generalized Burgers equations dedicated to weakly nonlinear wave propagation in nonuniform ducts, and is an extension of previous work by Menguy and Gilbert [Acta Acustica 86, 798-810 (2000)], initially limited to short cylindrical tubes. The relevance of the present tool is evaluated by carrying out simulations over distances longer than typical shock formation distances, and by doing preliminary simulations of periodic regimes in a typical brass trombone bore geometry.

Investigation of non-linear acoustic losses at the open end of a tube

At high acoustic level, non-linear losses at the end of a tube are usually interpreted as the consequence of a jet formation at the tube end resulting in annular vortices dissipating part of the acoustic energy. Previous work has shown that two different regimes may occur. The present work, using particle image velocimetry visualization, lattice Boltzmann method simulation in 2D, and an analytical model, shows that the two different regimes correspond to situations for which the annular vortices remain attached to the tube (low acoustic particle velocity) or detached (high acoustic particle velocity).

On the reflection functions associated with discontinuities in conical bores

The decomposition of reflections by finite tubes into successive elementary reflections by the input, discontinuities, and output of the tubes is interesting for its physical reasoning and for calculations using multiconvolution. In the case of tubes with conical bores, Martinez and Agullo [J. Martinez and J. Agullo, J. Acoust. Soc. Am. 84, 1613–1619 (1988)] have stated that in certain cases, the elementary reflection functions can be growing (causal) exponentials. Although such functions do not have Fourier transforms, Agullo et al. have assumed that they are inverse Fourier transforms of functions of frequency. It is shown that this assumption is erroneous. but by using a Laplace transform (i.e., by introducing losses through a complex frequency), we have also shown that for a general class of physically feasible systems, the decomposition into growing exponentials is valid.

Evidence of biphonation and source–filter interactions in the bugles of male North American wapiti (Cervus canadensis)

ABSTRACT With an average male body mass of 320 kg, the wapiti, Cervus canadensis, is the largest extant species of Old World deer (Cervinae). Despite this large body size, male wapiti produce whistle-like sexual calls called bugles characterised by an extremely high fundamental frequency. Investigations of the biometry and physiology of the male wapitis relatively large larynx have so far failed to account for the production of such a high fundamental frequency. Our examination of spectrograms of male bugles suggested that the complex harmonic structure is best explained by a dual-source model (biphonation), with one source oscillating at a mean of 145 Hz (F0) and the other oscillating independently at an average of 1426 Hz (G0). A combination of anatomical investigations and acoustical modelling indicated that the F0 of male bugles is consistent with the vocal fold dimensions reported in this species, whereas the secondary, much higher source at G0 is more consistent with an aerodynamic whistle produced as air flows rapidly through a narrow supraglottic constriction. We also report a possible interaction between the higher frequency G0 and vocal tract resonances, as G0 transiently locks onto individual formants as the vocal tract is extended. We speculate that male wapiti have evolved such a dual-source phonation to advertise body size at close range (with a relatively low-frequency F0 providing a dense spectrum to highlight size-related information contained in formants) while simultaneously advertising their presence over greater distances using the very high-amplitude G0 whistle component. Highlighted Article: North American wapitis produce extremely high-pitched bugles that are incompatible with the dimensions of their vocal folds. Anatomical and acoustic investigations suggest plausible mechanisms responsible for the production of this extraordinary vocalisation.

Influence of wall vibrations on the behavior of a simplified wind instrument

The issue of the influence of wall vibrations on the behavior of wind instruments is still under debate. The mechanisms of vibroacoustic couplings involved in these vibrations are difficult to investigate, as fluid-structure interactions are weak. Among these vibroacoustic interactions, the present study is focused on the coupling between the internal acoustic field and the mechanical behavior of the duct. For this purpose, a simplified single reed instrument consisting of a brass tube connected to a clarinet mouthpiece has been studied. A theoretical model of coupling between the plane inner acoustic wave and mechanical modes is developed and suggests that in order to obtain measurable effects of wall vibrations, the geometrical parameters of the studied tube have to be unusual compared to that of real instruments. For a slightly oval-shaped and very thin brass tube, it is shown theoretically and experimentally that a coupling between the inner plane acoustic wave and ovalling mechanical modes occurs and results in disturbances of the input impedance, which can slightly affect the tone color of the sound produced. It is concluded that the reported effects are unlikely to occur in real instruments except for some organ pipes.