Reed Cavity and Neck Proportions in Conical Woodwinds

Abstract

Stable pitch and good attack in the low register (also good octaves) require accurate harmonicity of the lower two air column resonances under playing conditions. This implies a particular impedance pattern, as viewed from the main bore into the oboe reed staple, bassoon bocal, or saxophone neck. At low frequencies the impedance must be nearly that of a cavity of volume V0 equal to the missing part of the cone. The impedance then falls to its first zero and turns mass-like at resonance frequency ω0 such that x0 = half-wavelength (x0 = missing length to apex). These basic points determine the total equivalent volume Ve, of reed plus staple, etc., including effects from the yielding reed wall (Weber, 1830), and also determine the frequency ωe, of the reed cavity-plus-(staple, bocal, or neck) played alone with normal embouchure. If the tone-hole lattice cutoff frequency is low (as on the tarogato), then ωe>ω0. Departures from exact conicity also require changes in Ve and ωe. Attention to strength of second harmonic in the tone (plus octave consistency) guides adjustment of impedance function for all ω via changes in proportions: e.g., Vienna oboes require a shorter staple, broader reed, and lower ωe than Conservatory oboes. Reeds, staples, and bocals are correctly predicted for baroque, classical, and modern oboes and bassoons. Useful saxophone neck and mouthpiece modifications have been devised and are in use.