Conical bores suppress the reflection at the narrow end, yielding all harmonic modes

Evidence

Suppose by some means we can start a compression from the narrow end; the pipe will behave just as our pipe open at both ends until the rarefaction has returned to the start. Now, because the pipe has shrunk to a very small bore, the speed of the wave slows down and no real reflection occurs… . The result is that we need only consider one journey out and one back regardless of whether the pipe is open or closed at the narrow end… . The conical pipe will behave something like a pipe open at both ends as far as its modes are concerned. The conical resonator therefore supports all modes, and the overblown mode of instruments with conical resonators, such as the oboe, cor Anglais, bassoon and saxophone family, is therefore to the second mode, or up an octave. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1215

Categorization

• XREF: This completes the physical story behind why conical instruments (oboe, bassoon, sax) overblow an octave while the cylindrical clarinet overblows a twelfth — the acoustic mechanism grounding instrument design.