exchemist

Surely the point about octaves is that if you double the frequency you get something that resonates with the fundamental. And if you double it again, the same occurs. So doubling has a real significance, both from the point of view of physics and from the point of view of the hearer. In fact, when you play a certain pitch on any instrument, you also excite a whole series of so-called "overtones" at the same time, which are frequency multiples of 2, 4, 8 etc above the fundamental. You also get a sort of resonance at the fifth of the scale. It sounds, well, harmonious. Whereas if you play 2 pitches that are only a tone, or semitone, apart, you get no resonance but a harsh sounding beat frequency as the two pitches go in and out of phase with one another. So I do not think it is just a matter of convention. Doubling the frequency has a physical significance that the ear recognises.