Conical reed instruments: A hierarchy of parameters

Abstract

Some aspects of sound production by wind musical instruments are rather well understood. A minimum model for reed cylindrical instruments was proposed in 1983 by Mc Intyre et al. When the reed dynamics and resonator losses are ignored, the mouthpiece pressure is a square signal. Three primary parameters are necessary: (i) the mouth pressure; (ii) the “valve” parameter (based on the reed opening and its stiffness); (iii) the length of the cylinder. The model gives a simplified shape of the waveform; the playing frequency and the amplitude are rather well predicted. For further spectrum details, it is necessary to add losses, therefore a secondary parameter, the radius. Furthermore other parameters influence the spectrum: reed dynamics, toneholes, vocal tract.... What happens for conical reed instruments? Considering the waveform of the mouthpiece pressure, a fourth primary parameter is the length of the missing part of the truncated cone. Similarly to cylindrical instruments, a secondary parameter is relat...