Note 447 — Chapter II · (continued 2)

The true scientific reason why octaves resemble each other so much more closely than two notes at any other interval is that the upper of two notes at an octave's distance is the first "upper-partial" tone of the lower, and all its harmonies are also harmonies of the lower note; the compound tone, for there is no entirely simple tone, of the higher note contains no new sound, which is not in the compound tone of the lower. This is not the case with two notes at any other interval.