Effects of bending portions of the air column on the acoustical resonances of a wind instrument.

The need to keep long wind musical instruments compact imposes the bending of portions of the air column. Although manufacturers and players mention its effects as being significant, the curvature is generally not included in physical models and only a few studies, in only simplified cases, attempted to evaluate its influence. The aim of the study is to quantify the influence of the curvature both theoretically and experimentally. A multimodal formulation of the wave propagation in bent ducts is used to calculate the resonances frequencies and input impedance of a duct segment with a bent portion. From these quantities an effective length is defined. Its dependence on frequency is such that, compared to an equivalent straight tube, the shift in resonance frequencies in a tube with bent sections is not always positive, as generally stated. The curvature does not always increase the resonances frequencies, but may decrease them, resulting in a complex inharmonicity. An experimental measurement of the effect of the curvature is also shown, with good agreement with theoretical predictions.

Mode locking effects on the playing frequency for fork fingerings on the clarinet.

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.