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v1 (29-03-2012)

v2 (17-09-2012)

v3 (31-03-2013)

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

Daniel Noreland 1, Jean Kergomard 2, Franck Laloë 3, Christophe Vergez 2, Philippe Guillemain 2

(28/03/2012)

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.

1 :	Department of Computing Science
	Umea University
2 :	Laboratoire de Mécanique et d'Acoustique (LMA)
	CNRS : UPR7051
3 :	Laboratoire Kastler Brossel (LKB (Lhomond))
	CNRS : UMR8552 – Université Pierre et Marie Curie [UPMC] - Paris VI – Ecole normale supérieure de Paris - ENS Paris

Domaine

:

Physique/Physique/Physique Générale Sciences de l'ingénieur/Acoustique Physique/Mécanique/Acoustique

Mots Clés : Clarinet – woodwind – harmonicity – tone hole – optimization

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Contributeur : Jean Kergomard <>

Soumis le : Mercredi 28 Mars 2012, 18:31:48

Dernière modification le : Jeudi 29 Mars 2012, 10:55:01