Abstract:
That wind musical instruments in conjunction with their players are highly nonlinear can be inferred from measurements of their output spectra. These show that, for a given performed pitch, bandwidth generally increases with increasing rms amplitude. The cause of this harmonic generation is generally attributed to a nonlinear pressure/flow excitation mechanism which interacts with the instrument's resonant input impedance characteristic. Since there are no analytical solutions which predict mouthpiece spectra, one must rely on simulations and empirical measurements. Meanwhile, the pipe portion of the wind instrument has long been assumed to be a linear resonant system acting as a high pass filter with resonant minima corresponding to the input impedance maxima. This at least is true at low amplitudes. However, for the trombone large discrepancies in the filter response have been found between measurements made with sine wave input and those made under actual performance conditions, particularly above resonant cutoff. The general effect is that spectral bandwidth (and attendant tonal brightness) increases even more with increasing amplitude than if the system were linear. There is now evidence that this may be due to shock wave formation in the pipe of the instrument.