Abstract
We have analyzed a simple theoretical model of an oboe, having a truncated conical air column of variable length and a reed assembly consisting of a tapered neck leading to a closed, cylindrical cavity. Proportions are chosen for this assembly so that its input admittance at the bottom of the neck is very closely the same function of frequency as the admittance of the missing conical segment at the apex of the air column for frequencies below the tone‐hole cutoff. The most important requirements are that the reed assembly by itself possess the same volume and lowest‐mode frequency as the missing apex. The intervals between the first‐mode frequency and the below‐cutoff frequencies of the second, third, and fourth modes of the model instrument can be made harmonic to within five cents as the length of the air column is varied to sweep the first mode through an octave range. We have investigated the effects of small variations in the proportions of the reed assembly on the natural frequencies of the model instrument. The results provide practical guidance for adjustment of the reed structure of a real oboe to special features of its own not‐quite‐conical acoustical behavior.
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