title: Predicting playing frequencies for clarinets: A comparison between numerical simulations and simplified analytical formulas.
abstract: 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.
authors.affiliation: Graduate Program in Acoustics, The Pennsylvania State University, 201 Applied Science Building, University Park, Pennsylvania 16802, USA.
authors.forename: Whitney L
authors.initials: WL
authors.lastname: Coyle
authors.affiliation: Laboratoire de Mécanique et d'Acoustique (LMA, Research Unit of CNRS 7051), 4 impasse Nikola Tesla, CS 40006, 13454 Marseille cedex 13, France.
authors.forename: Philippe
authors.initials: P
authors.lastname: Guillemain
authors.affiliation: Laboratoire de Mécanique et d'Acoustique (LMA, Research Unit of CNRS 7051), 4 impasse Nikola Tesla, CS 40006, 13454 Marseille cedex 13, France.
authors.forename: Jean
authors.initials: J
authors.lastname: Kergomard
authors.affiliation: LUNAM Université, Université du Maine, Unité Mixte de Recherche CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France.
authors.forename: Jean-Pierre
authors.initials: JP
authors.lastname: Dalmont