De l'utilisation de la décomposition modale pour la synthèse sonore temps réel : écueils et solutions

National audienceUn algorithme de synthèse compatible temps-réel, utilisant une décomposition modale ajustée sur les pics d'impédance d'entrée d'un instrument de type clarinette, est proposé. La comparaison avec la résolution effectuée hors temps-réel par un solveur à pas de temps adaptatif met en lumière une très bonne adéquation entre les méthodes en régime permanent. Une influence significative du nombre de modes pris en compte est observée pour les deux méthodes, imputable à la troncature des décompositions modales. Celle-ci a trois effets : un premier effet lié à la représentation d'un système propagatif par une somme finie de sous-systèmes à réponses instantanées, un deuxième concernant la valeur des pics d'admittance qui a donc une influence sur le taux d'harmoniques pairs de la pression interne, et un troisième effet lié à la valeur à haute fréquence de l'impédance modale tronquée qui tend par construction vers zéro donc vers un système non dissipatif. Plutôt qu'une augmentation du nombre de modes (peu intéressant d'un point de vue du coût de calcul), il est proposé d'ajouter un terme correctif permettant de simultanément rétablir une hauteur correcte des pics d'admittance en dessous de la fréquence de la troncature de la décomposition modale et d'assurer la décroissance à l'infini du coefficient de réflexion et l'absence de réflexion instantanée de la fonction de réflexion associés à la décomposition modale tronquée

The logical clarinet: numerical optimization of the geometry of woodwind instruments

The tone hole geometry of a clarinet is optimized numerically. The instrument is modeled as a network of one dimensional transmission line elements. For each (non-fork) fingering, we first calculate the resonance frequencies of the input impedance peaks, and compare them with the frequencies of a mathematically even chromatic scale (equal temperament). A least square algorithm is then used to minimize the differences and to derive the geometry of the instrument. Various situations are studied, with and without dedicated register hole and/or enlargement of the bore. With a dedicated register hole, the differences can remain less than 10 musical cents throughout the whole usual range of a clarinet. The positions, diameters and lengths of the chimneys vary regularly over the whole length of the instrument, in contrast with usual clarinets. Nevertheless, we recover one usual feature of instruments, namely that gradually larger tone holes occur when the distance to the reed increases. A fully chromatic prototype instrument has been built to check these calculations, and tested experimentally with an artificial blowing machine, providing good agreement with the numerical predictions

Simulation of Single Reed Instruments Oscillations Based on Modal Decomposition of Bore and Reed Dynamics

This paper investigates the sound production in a system made of a bore coupled with a reed valve. Extending previous work (Debut, 2004), the input impedance of the bore is projected on the modes of the air column. The acoustic pressure is therefore calculated as the sum of modal components. The airrrflow blown into the bore is modulated by reed motion, assuming the reed to be a single degree of freedom oscillator. Calculation of self-sustained oscillations controlled by time-varying mouth pressure and player's embouchure parameter is performed using ODE solvers. Results emphasize the par ticipation of the whole set of components in the mode locking process. Another impor tant feature is the mutual innnfluence of reed and bore resonance during growing blowing pressure transients, oscillation threshold being altered by the reed natural frequency and the reed damping. Steady-state oscillations are also investigated and compared with results given by harmonic balance method and by digital sound synthesis

Some roles of the vocal tract in clarinet breath attacks: natural sounds analysis and model-based synthesis

International audienceA simplified physical model mainly devoted to the reproduction of some transients of clarinet-like instruments is presented. From time-frequency analyses of natural clarinet sounds, it is shown that the vocal tract can play a significant role in some attacks as well as in the permanent regime. The model proposed consists in supplying a pressure source at the entrance of a cylindrical bore attached to the mouthpiece, allowing to reach various vocal tract configurations. For real-time synthesis purposes, a digital scheme solving the physical problem is proposed. It is shown that this synthesis model is able to reproduce some of the complex features observed during the attacks of the natural sounds analyzed, as well as known effects of the vocal tract in permanent regime

An instrumented saxophone mouthpiece and its use to understand how an experienced musician play

International audienceAn instrumented saxophone mouthpiece has been developed to measure, during the player's performance, the evolution of important variables: the mouth pressure, the mouthpiece pressure and the force applied on the reed by the lower lip. Moreover, according to the pressure signals in the mouth and in the mouthpiece, the instantaneous ratio of the vocal tract input impedance and of the saxophone input impedance is estimated at frequencies multiple of the playing frequency (using the concept of Gabor mask). On the selected sound examples, analyses reveal many aspects of the strategies of the player. First of all, the role of the vocal tract in the characteristics of the sound production is sometimes prominent. Secondly, the sound production on the desired note (and register) as well as pitch correction seem to be the result of complementary adjustments of the mouth pressure and of the lip pressure on the reed. This is not in agreement with musicians feeling, since they often claim to let their force on the reed unchanged during the note and from note to note

Synthèse sonore de la clarinette avec modèle de résonateur à trous latéraux optimisé sur des impédances d'entrée d'une clarinette réelle

CDROMSound synthesis can be developed using physics-based modelling of the musical instruments. These methods need the description of the various parts of sound production mechanism, in particular a model of the acoustic resonator that have to be simple enough due to the real-time constraint. However, in the case of the clarinet, the bore is quite not a cylindrical tube. An implementation of a resonator including a open-tone holes lattice is presented in this paper

Cutoff frequencies of a clarinet. What is acoustical regularity?

International audienceA characteristic of woodwind instruments is the cutoff frequency of their tone-hole lattice. Benade proposed a practical definition using the measurement of the input impedance, for which at least two frequency bands appear. The first one is a stop band, while the second is a pass band. The value of this cutoff frequency, which is a global quantity, depends on the whole geometry of the instrument, but is rather independent of the fingering. This seems to justify the consideration of a woodwind with several open holes as a periodic lattice. However the holes on a clarinet are very irregular. The paper investigates first the experimental method of determination of the cutoff frequency, then the question of the acoustical regularity: an acoustically regular lattice of tone holes is defined as a lattice built with T-shaped cells of equal eigenfrequencies. Then the paper discusses the possibility of division of a real lattice into cells of equal eigenfrequencies. It is shown that it is not straightforward but possible, explaining the apparent paradox of the Benade theory. From this division, a narrow range of possible constant cutoff frequencies is found, and it is in very good accordance with the experimental results from impedance measurements. When considering the open holes from the input of the instrument to its output, the distances between holes are enlarged together with their radii: this explains the relative constancy of the eigenfrequencies

Predicting playing frequencies for clarinets: a comparison between numerical simulations and simplified analytical formulas

International audienceWhen designing a wind instrument such as a clarinet it is interesting to be able to predict the playing frequencies. These depend on the resonance frequencies, deduced from the input impedance, but not only. Indeed, several control parameters such as the blowing pressure and reed opening have a significant influence on the playing frequency. Their role has to be taken into account in order to determine the playing frequencies. This paper presents a method to deduce these frequencies analytically from the different control parameters, using the input impedance curve. Four effects are known to alter the playing frequency and are examined separately: the flow rate due to the reed motion, the reed dynamics, the inharmonicity of the resonator, and the temperature gradient within the clarinet. The results for the first register of a particular clarinet are given and compared to simulated playing frequencies found using a numerical model

Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet

International audienceThis paper investigates the modal analysis of wind instruments as seen from the input of their air column. Beside the treatment of analytical models, a particular emphasis is given to the analysis of measured input impedances. This requires special care because the measurements cover only a limited frequency band and are affected by some unknown errors. This paper describes how the Prony analysis and the Least Squares Complex Exponential (LSCE) classical techniques can be used in this context and how the main pitfalls can be avoided in their application. A physically acceptable method of reconstruction of the low frequency band is proposed. A technique using fictitious points in the high frequency range is described in order to ensure the passivity of the resonator in the whole frequency band. The principles of a real-time synthesis of clarinet sounds based on the modal representation of the resonator is given as an application, with a method to efficiently handle the modal representation during the transition between fingerings

Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies

International audienceWe investigate the behaviour of the continuous wavelet and Gabor coefficients in the asymptotic limit, using stationary phase approximations. In particular, we show how, under some additional assumptions, these coefficients allow the extraction of some characteristics of the analysed signal, like for example frequency and amplitude modulation laws. We also briefly discuss applications to spectral lines estimations and matched filtering