Statistical Estimation of Mechanical Parameters of Clarinet Reeds Using Experimental and Numerical Approaches

A set of 55 clarinet reeds is observed by holography, collecting 2 series of measurements made under 2 different moisture contents, from which the resonance frequencies of the 15 first modes are deduced. A statistical analysis of the results reveals good correlations, but also significant differences between both series. Within a given series, flexural modes are not strongly correlated. A Principal Component Analysis (PCA) shows that the measurements of each series can be described with 3 factors capturing more than $90\%$ of the variance: the first is linked with transverse modes, the second with flexural modes of high order and the third with the first flexural mode. A forth factor is necessary to take into account the individual sensitivity to moisture content. Numerical 3D simulations are conducted by Finite Element Method, based on a given reed shape and an orthotropic model. A sensitivity analysis revels that, besides the density, the theoretical frequencies depend mainly on 2 parameters: $E_L$ and $G_{LT}$. An approximate analytical formula is proposed to calculate the resonance frequencies as a function of these 2 parameters. The discrepancy between the observed frequencies and those calculated with the analytical formula suggests that the elastic moduli of the measured reeds are frequency dependent. A viscoelastic model is then developed, whose parameters are computed as a linear combination from 4 orthogonal components, using a standard least squares fitting procedure and leading to an objective characterization of the material properties of the cane \textit{Arundo donax}

Is nonlinear propagation responsible for the brassiness of elephant trumpet calls?

African elephants (Loxodonta africana) produce a broad diversity of sounds ranging from infrasonic rumbles to much higher frequency trumpets. Trumpet calls are very loud voiced signals given by highly aroused elephants, and appear to be produced by a forceful expulsion of air through the trunk. Some trumpet calls have a very distinctive quality that is unique in the animal kingdom, but resemble the "brassy" sounds that can be produced with brass musical instruments such as trumpets or trombones. Brassy musical sounds are characterised by a flat spectral slope caused by the nonlinear propagation of the source wave as it travels through the long bore of the instrument. The extent of this phenomenon, which normally occurs at high intensity levels (e.g. fortissimo), depends on the fundamental frequency (F0) of the source as well as on the length of the resonating tube. Interestingly, the length of the vocal tract of the elephant (as measured from the vocal folds to the end of the trunk) approximates the critical length for shockwave formation, given the fundamental frequency and intensity of trumpet calls. We suggest that this phenomenon could explain the unique, distinctive brassy quality of elephant trumpet calls

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

The irish Uillean pipe: a story of lore, hell and hard D

International audienceThe irish Uillean pipe is a bellows-blown bagpipe that resembles other baroque musettes (french musettes de cour) such as the english Northumbrian pipe and french Musette. According to A. Baines, it appeared in Ireland in the late seventeenth century, in a version somewhat simpler than the instrument known in the present days. It is surely among the most evoluated bagpipes nowadays with a rather complex playing. The lowest note of the chanter has the noticeable characteristic, searched after by musicians, of having two different timbres. One of these, known among musicians as the hard D, is strikingly louder and clearer than the other, the soft D. The contrast between them is traditionally a much appreciated quality of an instrument. In this paper, we concentrate on this particular note and propose an explanation for the appearance of these two distinct timbres

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

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

Analysis of Nonlinear Characteristics of the Clarinet Exciter Obtained via a New Measurement Method

International audienceA new method for measuring the nonlinear characteristic of the clarinet exciter, which binds the air flow entering into the clarinet with the pressure drop (∆p) across the reed, is described. It uses a clarinet mouthpiece equipped with a reed and an artificial lip whose position ψ is controlled by a micrometer screw. The mouthpiece is connected to a bottle in which a moderate vacuum is generated at the beginning of the experiment. After a short time lapse, the opening of the reed occurs. The ther-modynamics of the volume in isochoric conditions enables the calculation of the volume velocity entering the mouthpiece from the pressure measurement. 13 reeds with 10 different embouchures are measured. The measurements enabled the estimation of the equivalent aeraulic section S(∆p, ψ). We propose a model of S as a convex function of ∆p and ψ, defined as the sum of two 1D stiffening springs plus a porosity constant. The mean standard error of the model is 0.2%

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

Lattices of sound tubes with harmonically related eigenfrequencies

International audienceThe only continuous acoustic horns (in plane wave approximation) known for having harmonic eigenfrequencies are conical and cylindrical. Because of this, these shapes have been widely used for woodwind musical instruments. Other, non continuous, shapes are shown here to have the same property: they consist of a succession of truncate cones (or cylinders) of equal length, which are defined by three initial values for the radii (e.g. the input and output radii of the first cone and the input radius of the second one). The recurrence relations are obtained in the frequency domain, the principle being to impose the existence of travelling waves at the nodes of the lattice: the successive reflections at discontinuities are cancelled at the nodes (but only there). Several kinds of boundary conditions are studied. For the "closed-open" conditions, the unique solution is based upon cylinders and the input impedance curves and its Fourier Transform are shown to have interesting properties. Measurements have been made and the agreement between experiment and theory is satisfactory

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