[hal-01095846] Predicting playing frequencies for clarinets: a comparison between numerical simulations and simplified analytical formulas

When 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.



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