The octave

Play a C, then the next C to its right. They sound like the same note, just higher. That distance is an octave, and there is a beautiful physical reason: the higher C vibrates at exactly double the frequency of the lower one.

Middle C is about 262 Hz; the C an octave up is 523 Hz; another octave, 1047 Hz. Every octave doubles the number again. Our ears hear this 2:1 ratio as the strongest possible family resemblance between two pitches.