Conical-bore instruments need only 12 chromatic holes because they overblow an octave

Evidence

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. Sufficient holes are therefore required for at least 12 chromatic notes to be fingered to enable the player to arrive at the second mode from the first. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1216

Categorization

• XREF: Counts of required tone holes distil two overblowing mechanisms into a design constraint — useful pairing with the clarinet’s 19-hole requirement. — connects to: Only bores keeping fixed mode ratios as holes open are musically useful — David Howard, Jamie Angus, coustics and Psychoacoustics, 1240