The octave

The octave is the one distance any ear recognises without being taught: the two notes sound like “the same one, higher”, and they almost melt into one. There is an exact physical reason: the upper note vibrates at precisely twice the rate, so its waves nest inside the other's. That is why the scale repeats every eight notes and not every ten or twelve, and why a man and a woman singing “the same thing” are usually an octave apart without noticing. When it falls a semitone short or long, the fusion breaks and you hear it at once.