R´esum´e
Ce Chapitre r´ealise une synth`ese entre les ´el´ements d´evelopp´es lors des chapitres pr´ec´edents, en confrontant 3 types de donn´ees r´ecolt´ees `a partir d’un panel de 40 anches de clarinette: i) Mesures physiques objectives: pour chaque anche (et diff´erentes embouchure), les donn´ees collect´ees comportent des exp´eriences statiques (mesures a´erauliques, d´eflection m´ecanique et photographies du canal) et une exp´erience dynamique (diagramme de bifurcation, ´etabli sur un crescendo / decrescendo). ii) Evaluations musicales subjectives: un clarinettiste a jou´e ces mˆemes anches `a l’aveugle (avant que les mesures ne soient analys´ees) et les a not´ees sur la base de 4 descripteurs diff´erents. iii) Synth`ese sonore: les mod`eles physiques d´evelopp´es dans la partie III) sont mis en application pour simuler les diagrammes de bifurcation.
L’analyse canonique des corr´elations atteste la pr´esence d’un lien tr`es fort entre toutes les mesures physiques objectives r´ealis´ees `a l’int´erieur du panel d’anches ´etudi´e. L’existence de plus d’une dizaine de facteurs ind´ependants est prouv´ee de mani`ere statistiquement significative. La confrontation entre les mesures objectives et les donn´ees issues de la synth`ese sonore montre l’existence de liens indubitables pour au moins 13 facteurs. Les 4 plus importants facteurs objec-tifs d´etect´es sont corr´el´es de mani`ere statistiquement significative avec les ´evaluations subjectives r´ealis´ees par le clarinettiste. Cela ouvre la voie `a une s´election automatis´ee des anches, r´ealis´ee directement `a l’usine.
8.1 Introduction
This study aims at summarizing the work done in recent years and described in the Parts II and III, by investigating a reed panel through various approaches (acoustics, music, sound synthesis, statistics). Its main purpose is to verify the solidity of the link between the physical measurements acquired from this panel of reeds and the subjective musical evaluation of these same reeds, blindly, by a clarinettist. The second aim of the study is to check summarily the relevance of the physical models developed, by confronting them with the experimental data acquired by playing this panel of reed by an artificial mouth.
This study is conducted in three successive phases: In the first phase, 3 categories of data are collected, namely:
— simulations by physical model
The second phase consists of confronting these data on a statistical basis, by canonical cor-relation analysis and to verify the statistical significance of the corcor-relations found. In the third phase the acoustic and musical results are interpreted in the light of the statistically significant correlations found between canonical factors. Incidentally, it will also be necessary to check if the objective measurements made on dry reeds (in ambient conditions, without prior humidification) are well representative of the behavior of the wet reed, in playing situation.
The present study establishes also a link with the initial sparkle that conducted me to acous-tics in 2001: the invention of the Claripatch system1. To develop the range of commercially available models, I performed a perceptive study by Principal Component Analysis (PCA) in 2002, using a panel of about thirty reeds. On the basis of the determined factors, I selected 8 reeds located at the extremes of the first 4 factors and I empirically tried to improve their functioning, according to the thickness profile conferred to the patch.
Since then, many authors have performed perceptual studies on simple reeds and have tried to find a connection with objective measurements. Pinard [140, 47], Stetson [163], Mukhopadhyay [124], Casadonte [15], Kolesik [104], Obataya [134], Gazengel [61, 62], Petiot [139] and Mu˜noz [128, 127, 126, 129] can be cited. A good summary of these works can be found in the first chapter of Mu˜noz’s thesis [125]. The studies - whose statistical significance has been evaluated - have come to the conclusion that the reeds can be classified on the basis of 2 descriptors (playability and timbre). This is for instance the case of the study described in the cited thesis, Chapter 3, as well as that of Gazengel [62]. Mu˜noz has evaluated 20 reeds of 4 different brands, using a panel of 7 musicians. Large differences were found between musicians: some discern reliably the differences between reeds, others do not. There is no general consensus about the analyzed descriptors: a musician has evaluated the same descriptor in a way that is reproducible but very different from the other musicians, whom evaluations are more coherent among themselves. The descriptors ”ease of playing” and ”timbre” are correlated to 0.95. No canonical correlations analysis has been made, so it is not possible to know if more than one statistically significant canonical factor could be highlighted by this panel of musicians. The only significant factor is correlated with the stiffness of the reed at low pressure (linear component of the stiffness of the reed at rest). In order to allow a fair comparison, Mu˜noz’s data should be analyzed with the methods proposed in this Chapter.
The investigations comparing a synthesis model and experimental measurements are not very numerous and are generally based on the study of a single reed, which prohibits any validation on a statistical basis, among which [17] and [125] can be cited. In this sense, the proposed approach is innovative.
The study of Guillemain [9] comparing perceptively the sounds generated by a synthesis model should be mentioned, as well as a study of scraping techniques for correcting the function of the reed [167].
The experimental setup is described in Sec.8.2and the collected data are detailed in Sec.8.3. The methods of analysis are presented in Sec.8.4, with which the data is analysed, in Sec. 8.5, then an interpretation of the detected factors is attempted in Sec8.6, followed by the conclusions in Sec.8.7.
8.2 Experimental setup
The measuring bench is described in§4.3. The physical symbols related to the measurements are listed in Table8.1.
1. This system allows the clarinetist to regulate the behavior of his reeds by modifying the shape of the mouthpiece lay, by the mean of a wedge (patch). This wedge has a variable thickness, precisely defined, which modifies the bending of the reed against the lay [166].
40 ”Vandoren classic” clarinet reeds were purchased in a music shop, of strength 2, 2.5, 3, 3.5 (10 of each). The reeds were randomly numbered from R00 to R39. In principle, all reeds should have the same geometry, since they were all manufactured in the same way. Theoretically, only the stiffness and the homogeneity of the wood differs, but in reality, the machining is not as regular as supposed, as showed a preliminary (unpublished) study on a panel of 15 reeds. Significant differences in geometry were found, which correlate with aeraulic measurements. The geometry of the reeds of the studied panel has not (yet) been measured.
During the measurements, the reeds undergo all the same ”aging” protocol and have an equivalent hydric history (see §8.3.6). However, it is questionable whether this treatment is comparable to a normal playing situation.
8.2.2 Photographs of the channel
The photographs of the channel (slot between reed and mouthpiece through which the air enters into the instrument) were made by a Nikon D5200 SLR camera attached to a tripod and equipped with a macro lens2Micro Nikkor AF, 105 mm 1/2.8 D. The focal plane of the device is approx. 32 cm away from the tip of the mouthpiece, frontally to the channel. This relatively large distance comparatively to the about 1 mm height of the channel, allows to neglect the effects of parallax.
The size of the pixel at the tip of the reed is determined by a millimeter scale (4.15 microns). The origin of the coordinate system is defined by the intersection between the plane of the mouthpiece lay and the median plane of symmetry of the reed, at the tip (see Fig. 3 in Chapter
3). The reference line - corresponding on the photos to the plane of the mouthpiece lay - is determined photographically, by clamping on the lay a flat, reed-like metal plate. The pictures are deliberately overexposed, so as to optimize the exposure of the reed. The illumination is provided by the flash of the camera.
8.2.3 Artificial mouth
The measuring bench was transformed into an artificial mouth in ”suction” (i.e. working with a negative pressure in the instrument) by connecting a 261 mm long PVC tube (15.5 mm inner diameter) to the instrumented mouthpiece. The end of the tube was inserted (in airtight manner) into a circular hole made in the smallest face of a parallelepipedic container (volume: about 100 liters). The hole was off centered by a few centimeters from the center of the face, to avoid unwanted acoustical effects due to symmetry.
The dimensions of the container (410× 510 × 600 mm) have been optimized so as to spread the first acoustic resonances as evenly as possible. Pieces of carpet were glued on all interior walls, so as to dampen these resonances. An Endevco sensor was introduced through a small orifice to measure the pressure in the container. A cock valve allows to establish a moderate vacuum in the container, using a vacuum cleaner.
8.3 Collected data
8.3.1 Channel height
Several thousands photographs were made to determine the height of the channel h(ψ, y), as a function of the embouchure ψ and the transverse coordinate y3. Only two series of photos (denoted PhotoNew and PhotoBreakIn) were included in the analysis.
For PhotoNew, 16 embouchures were measured for the position of the lip support ψ ranging from 3.400 to 0.400 mm, in 0.200 mm increments, plus 2 photos without lip contact, before 2. This professional lens was kindly lent by the naturalist and wildlife photographer Jean-Lou Zimmermann, whom I thank warmly.
3. Since y is the transverse coordinate, the deflection of the reed (traditionally denoted y, like in Chapter5) is now denoted z, in this Chapter.