Rapid creation of tuning maps for a clarinet using analytic formulasReport as inadecuate




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1 PennState University Pennsylvania 2 Sons LMA - Laboratoire de Mécanique et d-Acoustique Marseille 3 LMA - Laboratoire de Mécanique et d-Acoustique Marseille

Abstract : One measure that a clarinetist uses to judge an instrument is its ability to play in-tune, over the entire range of the instrument without a large amount of added effort on the players part. Thus, in order to design the most - playable - clarinet we must know the actual playing frequencies, which depend on several control parameters including the blowing pressure, reed opening and the input impedance. We can now rapidly deduce these frequencies analytically from the different control parameters and input impedance curve. Four effects are known to influence the playing frequency and are examined separately within the analytic formulas: the flow rate due to the reed motion, the reed dynamics, the inharmonicity of the resonator and the temperature gradient within the clarinet. Numerical simulations have been used to test the validity of the analytic formulas in the first playing register of the clarinet. These numerical simulations have the added ability to distinguish in which register the clarinet is playing depending on the chosen value of reed opening and blowing pressure. This paper will present the - maps - which can be created from the analytic formulas and numerical simulations which show, over the full range of blowing pressures and reed openings possible, the expected resulting playing frequencies for a particular clarinet. These resulting maps could be used by an instrumentalist or manufacturer to better understand the expected tuning homogeneity over the range of an instrument and perhaps aid in the future design of an even more - playable - clarinet.





Author: Whitney Coyle - Jean Kergomard - Philippe Guillemain -

Source: https://hal.archives-ouvertes.fr/



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