Estimation of saxophone reed parameters during playing.

An approach for the estimation of single reed parameters during playing, using an instrumented mouthpiece and an iterative method, is presented. Different physical models describing the reed tip movement are tested in the estimation method. The uncertainties of the sensors installed on the mouthpiece and the limits of the estimation method are studied. A tenor saxophone reed is mounted on this mouthpiece connected to a cylinder, played by a musician, and characterized at different dynamic levels. Results show that the method can be used to estimate the reed parameters with a small error for low and medium sound levels (piano and mezzoforte dynamic levels). The analysis reveals that the complexity of the physical model describing the reed behavior must increase with dynamic levels. For medium level dynamics, the most relevant physical model assumes that the reed is an oscillator with non-linear stiffness and damping, the effect of mass (inertia) being very small.

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

When designing a wind instrument such as a clarinet, it can be useful to be able to predict the playing frequencies. This paper presents an analytical method to deduce these playing frequencies using the input impedance curve. Specifically there are two control parameters that have a significant influence on the playing frequency, the blowing pressure and reed opening. 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 resulting playing frequencies for the first register of a particular professional level clarinet are found using the analytical formulas presented in this paper. The analytical predictions are then compared to numerically simulated results to validate the prediction accuracy. The main conclusion is that in general the playing frequency decreases above the oscillation threshold because of inharmonicity, then increases above the beating reed regime threshold because of the decrease of the flow rate effect.

Measurements of the impedance matrix of a thermoacoustic core: applications to the design of thermoacoustic engines.

The successful design of a thermoacoustic engine depends on the appropriate description of the processes involved inside the thermoacoustic core (TAC). This is a difficult task when considering the complexity of both the heat transfer phenomena and the geometry of the porous material wherein the thermoacoustic amplification process occurs. An attempt to getting round this difficulty consists in measuring the TAC transfer matrix under various heating conditions, the measured transfer matrices being exploited afterward into analytical models describing the complete apparatus. In this paper, a method based on impedance measurements is put forward, which allows the accurate measurement of the TAC transfer matrix, contrarily to the classical two-load method. Four different materials are tested, each one playing as the porous element allotted inside the TAC, which is submitted to different temperature gradients to promote thermoacoustic amplification. The experimental results are applied to the modeling of basic standing-wave and traveling-wave engines, allowing the prediction of the engine operating frequency and thermoacoustic amplification gain, as well as the optimum choice of the components surrounding the TAC.

Effects of bending portions of the air column on the acoustical resonances of a wind instrument.

The need to keep long wind musical instruments compact imposes the bending of portions of the air column. Although manufacturers and players mention its effects as being significant, the curvature is generally not included in physical models and only a few studies, in only simplified cases, attempted to evaluate its influence. The aim of the study is to quantify the influence of the curvature both theoretically and experimentally. A multimodal formulation of the wave propagation in bent ducts is used to calculate the resonances frequencies and input impedance of a duct segment with a bent portion. From these quantities an effective length is defined. Its dependence on frequency is such that, compared to an equivalent straight tube, the shift in resonance frequencies in a tube with bent sections is not always positive, as generally stated. The curvature does not always increase the resonances frequencies, but may decrease them, resulting in a complex inharmonicity. An experimental measurement of the effect of the curvature is also shown, with good agreement with theoretical predictions.

On the accuracy of bore reconstruction from input impedance measurements: application to bassoon crook measurements.

The determination of a pipe bore from the measured reflection function is a technique that has reached a certain maturity. However, the measurement of the reflection function in the time domain (pulse reflectometry) requires equipment that is rather difficult to operate. On the other hand, the techniques for measuring the input impedance have reached an unquestionable maturity with respect to measurement setup and to calibration. It is thus likely that impedance measurements might be able to give the same information. By doing simulations, it is first shown that the reflection function deduced from the input impedance gives access to the bore with a precision comparable with that obtained with pulse reflectometry. It is then shown that the accuracy obtained with measurements is of the same order as that obtained from simulations. The technique is then used for the dimensional inspection of bassoon crooks.

Static model of a violin bow: influence of camber and hair tension on mechanical behavior.

Experienced bow makers empirically know the influence of wood, tapering, and camber on the playing and tonal qualities of a bow. However, the way each parameter affects the bow mechanical behavior is not clearly established. An in-plane finite element model is developed to highlight the link between the adjustable design parameters and the mechanical behavior of a bow. This model takes into account geometric nonlinearity as well as compliance of the hair. Its validity is discussed from measurements on a bow. Results from simulations are compared to experimental results from previous studies. The consequences of adjusting hair tension and camber are then investigated.

Theoretical prediction of the onset of thermoacoustic instability from the experimental transfer matrix of a thermoacoustic core.

The aim of this paper is to propose a method to predict the onset conditions of the thermoacoustic instability for various thermoacoustic engines. As an accurate modeling of the heat exchangers and the stack submitted to a temperature gradient is a difficult task, an experimental approach for the characterization of the amplifying properties of the thermoacoustic core is proposed. An experimental apparatus is presented which allows to measure the transfer matrix of a thermoacoustic core under various heating conditions by means of a four-microphone method. An analytical model for the prediction of the onset conditions from this measured transfer matrix is developed. The experimental data are introduced in the model and theoretical predictions of the onset conditions are compared with those actually observed in standing-wave and traveling-wave engines. The results show good agreement between predictions from the model and experiments.

Trumpet with near-perfect harmonicity: design and acoustic results.

This paper presents a mathematical design methodology for determining the shape of a trumpet air column that has near-perfect harmonicity, whose components are discontinuity-free, and whose input impedance peak heights are balanced over the playing range. The simulation model employed assumes linear wave propagation and uses cylindrical element discretization with a plane wave approximation. Acoustic measurements are made using a test set-up with an estimated relative measurement error of ±3 cents. Comparisons of measured results are given for the presented design (Macaluso trumpet) and the same trumpet air column with the bell replaced by a commercially used generic trumpet bell of unknown shape (Generic trumpet). For acoustic resonance modes 2-13 (233-1515 Hz), the measured root-mean-square (rms) harmonicity deviation is 5 cents for the Macaluso trumpet, whereas it is 18 cents for the Generic trumpet. However, considering the estimated measurement uncertainty, each of those deviations is somewhat over-stated. For that same range of resonances, the rms deviation between measured and calculated resonance frequencies for the Macaluso trumpet is 3 cents, thus validating the presented simulation model and equations.

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.

Oscillation and extinction thresholds of the clarinet: comparison of analytical results and experiments.

In the context of a simplified model of the clarinet in which the losses are assumed to be frequency independent the analytic expressions of the various thresholds have been calculated in a previous paper [Dalmont et al., J. Acoust. Soc. Am. 118, 32.94-3305 (2005)]. The present work is a quantitative comparison between "theoretical" values of the thresholds and their experimental values measured by using an artificial mouth. It is shown that the "Raman" model, providing that nonlinear losses are taken into account, is reliable and able to predict the values of thresholds.

Tracking high amplitude auto-oscillations with digital Fresnel holograms.

Method for tracking vibrations with high amplitude of several hundreds of micrometers is presented. It is demonstrated that it is possible to reconstruct a synthetic high amplitude deformation of auto-oscillations encoded with digital Fresnel holograms. The setup is applied to the auto-oscillation of a clarinet reed in a synthetic mouth. Tracking of the vibration is performed by using the pressure signal delivered by the mouth. Experimental results show the four steps of the reed movement and especially emphasize the shocks of the reed on the mouthpiece.

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 (Raman's 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.

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.