Computational study of brass instrument configurations

Abstract

Input impedance curves are computed for several bores related to brass wind instrument shapes, such as a cylinder, cone, French horn bell, “catenoidal bell,” some “bell + cylinder” combinations, and a complete French horn. The impulse response curve for each is obtained by performing a Fourier transform of the complex input impedance. These will be shown and discussed with respect to physical interpretations and interesting insights. A sinusoidal input volume velocity is then introduced, and the steady‐state (sinusoidal) pressure response at the inlet is determined by convolving the velocity input with the impulse response. This is done for various frequencies, and the resulting pressure amplitudes are shown to be consistent with those of the impedance curve. An input volume velocity composed of several harmonically related sinusoidal components, approximating the output from a player's lips, is then introduced. The resulting pressure response is computed at the inlet of a French horn, whose resonant frequencies are quite harmonic. The same computations are then made for a relatively inharmonic system, and the results are compared to those for the French horn.