The non-linear excitation of wind instruments generates higher harmonics of the playing frequency. These higher harmonics are coupled to resonances in the pipe. This is called mode locking. When the pipe modes are not harmonic, the playing frequency shifts away from the fundamental in order to maximize the output. It may go up or down, depending on the position of the modes and the amplitude. The effect is especially manifest for fork fingerings. Three fork fingerings on a clarinet were investigated. They were artificially blown between the threshold and extinction pressure. A time domain simulation was carried out based on a lumped model of the excitation coupled to an input impedance calculated from the instrument dimensions. At low amplitudes the fundamental frequency dominates and the playing frequency is governed by the position of the first peak in the input impedance spectra. At higher blowing pressures the playing frequency shifts. For both blowing and simulation this follows the same pattern. The frequencies predicted by the calculations are higher than the values found by blowing, which may be due to inadequacies in the model description, to uncertainties of the various parameters, as reed stiffness, moving reed area, and the properties of the slit flow.
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