Abstract:

An idealized conical bore that is complete to its apex has been used as the basic model for several wind instruments with tone holes, such as oboe, bassoon, saxophone, and cornetto. The useful playing frequencies for these relatively short instruments include those near the first peak in |Z|. A uniform pipe that is closed at both ends has been proposed as the basic bore shape for the brasses, including even their strongly conical representatives, such as tube and cavalry bugle [R. D. Ayers, J. Acoust. Soc. Am. 98, 81--87 (1995)]. The relationship should be considered one of mimicry, since there are major discrepancies at low frequencies, and these extend to the first (anti)resonance or higher. The nature of that relationship and the way in which it is achieved are perhaps most easily understood by examining a conical frustum, with or without a lumped-element mouthpiece, from this new perspective. Fairly simple behaviors in the time domain provide the explanation for the mimicry in the frequency domain.