Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure : influence of noise

This paper presents an analysis of the effects of noise and precision on a simplified model of the clarinet driven by a variable control parameter. When the control parameter is varied the clarinet model undergoes a dynamic bifurcation. A consequence of this is the phenomenon of bifurcation delay: the bifurcation point is shifted from the static oscillation threshold to an higher value called dynamic oscillation threshold. In a previous work [8], the dynamic oscillation threshold is obtained analytically. In the present article, the sensitivity of the dynamic threshold on precision is analyzed as a stochastic variable introduced in the model. A new theoretical expression is given for the dynamic thresholds in presence of the stochastic variable, providing a fair prediction of the thresholds found in finite-precision simulations. These dynamic thresholds are found to depend on the increase rate and are independent on the initial value of the parameter, both in simulations and in theory.Comment: 14 page

Objective and subjective characterization of saxophone reeds

The subjective quality of single cane reeds used for saxophone or clarinet may be very different from a reed to another although reeds present the same shape and the same strength. In this work, we propose to compare three approaches for the characterization of reeds properties. The first approach consists in measuring the reed mechanical response ("in vitro" measurement) by means of a specific bench which gives equivalent dynamic parameters (mass, damping, stiffness) of the first vibration mode. The second approach deals with the measurement of playing parameters "in vivo", using specific sensors mounted on the instrument mouthpiece. These measurements provide specific parameters in playing condition, such as the threshold pressure or the spectral centroid of the sounds. Finally, subjective tests are performed with a musician in order to assess the reeds according to subjective criteria, characteristic of the perceived quality. Different reeds chosen for their subjective differences (rather difficult and dark, medium, rather easy and bright) are characterized by the three methods. First results show that correlations can be established between "in vivo" measurements and subjective assessments

Prediction of the dynamic oscillation threshold of a clarinet model: comparison between analytical predictions and simulation results

International audienceSimple models of clarinet instruments based on iterated maps have been used in the past to successfully estimate the threshold of oscillation of this instrument as a function of a constant blowing pressure. However, when the blowing pressure gradually increases through time, the oscillations appear at a much higher value than what is predicted in the static case. This is known as bifurcation delay, a phenomenon studied in [1] for a clarinet model. In numerical simulations the bifurcation delay showed a strong sensitivity to numerical precision

Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure

14 pagesInternational audienceReed instruments are modeled as self-sustained oscillators driven by the pressure inside the mouth of the musician. A set of nonlinear equations connects the control parameters (mouth pressure, lip force) to the system output, hereby considered as the mouthpiece pressure. Clarinets can then be studied as dynamical systems, their steady behavior being dictated uniquely by the values of the control parameters. Considering the resonator as a lossless straight cylinder is a dramatic yet common simplification that allows for simulations using nonlinear iterative maps. In this paper, we investigate analytically the effect of a time-varying blowing pressure on the behavior of this simplified clarinet model. When the control parameter varies, results from the so-called dynamic bifurcation theory are required to properly analyze the system. This study highlights the phenomenon of bifurcation delay and defines a new quantity, the dynamic oscillation threshold. A theoretical estimation of the dynamic oscillation threshold is proposed and compared with numerical simulations

Response of an artificially blown clarinet to different blowing pressure profiles

14 pagesInternational audienceUsing 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

WHAT WE UNDERSTAND TODAY ON FORMANTS IN SAXOPHONE SOUNDS?

International audienceThe question of the formants in saxophone sounds involves several paradoxes. The analogy with "cylindrical saxophones", i.e. cylindrical tubes excited at a given proportion of the length, is classical and can be extended to the bowed string. This analogy leads to an approximation of the spectrum of the pressure inside the mouthpiece valid only at low frequencies. Nevertheless it gives good results even at higher frequency, this paradox being now understood. The spectrum of the external pressure contains formants which are different from that of the internal spectrum. The question of what is the cause of the formants remains open

Oscillation threshold of a clarinet model: a numerical continuation approach

This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. Previous works have shown interesting tendencies, using analytical expressions with simplified models. In the present study, a more elaborated physical model is considered. The influence of several parameters, depending on the reed properties, the design of the instrument or the control operated by the player, are studied. Previous results on the influence of the reed resonance frequency are confirmed. New results concerning the simultaneous influence of two model parameters on oscillation threshold, regime selection and playing frequency are presented and discussed. The authors use a numerical continuation approach. Numerical continuation consists in following a given solution of a set of equations when a parameter varies. Considering the instrument as a dynamical system, the oscillation threshold problem is formulated as a path following of Hopf bifurcations, generalizing the usual approach of the characteristic equation, as used in previous works. The proposed numerical approach proves to be useful for the study of musical instruments. It is complementary to analytical analysis and direct time-domain or frequency-domain simulations since it allows to derive information that is hardly reachable through simulation, without the approximations needed for analytical approach

EXPERIMENTAL CHARACTERISATIONS OF SINGLE CANE REEDS

International audienceSingle cane reeds used for playing clarinets or saxophones are described by makers by their strength and shapes (cutting). For reeds assumed to be identical according to the maker (same strength and shape), strong differences in the perceived quality are expressed by musicians. In this context, the experimental characterization of reeds (from the perceptive and objective sides) is a key issue for reed makers in order to better predict reed musical abilities. This paper presents and discuss different measurement methods. These methods can be divided into two families, measurement of the reed alone through static or dynamic measurements in order to derive stiffness and modal parameters, measurement of the "embouchure" (reed+mouthpiece+lip) alone through static or quasi-static measurements in order to estimate the non linear characteristics, the non linear reed stiffness or other mechanical parameters. Finally it appears that the most efficient characterisation of the "embouchure" is probably a static measurement

Insertion d'informations numériques dans un signal : Application à la classification de données expérimentales en anémométrie laser Doppler

Ce travail propose d'évaluer une procédure de marquage de signaux expérimentaux en anémométrie laser à effet Doppler. La méthode adoptée est basée sur une technique d'étalement de spectre et des mesures de corrélation. L'impact du marquage sur la qualité des estimations des paramètres de la vitesse particulaire acoustique est mesuré de manière objective à l'aide d'une méthode basée sur la dérivée de la phase du signal