Origins: Tuning Up

White, black, white, black, white, white; black, white, black, white, black, white, white. This is the irregular series that the piano notes present across an octave from C to C. The series repeats itself from end to end of the keyboard. But why have two different colors? Or why not have them alternating regularly? Why is the whole palette of notes arranged in octaves? And why are half a dozen different notes, some high, some low, all called C, as if they were the same?

To find the answers we must go back to ancient Greece and Babylon. The starting-point is the fact that the octave makes the most convenient frame in which to organize musical space, because two notes an octave apart blend together particularly well and, in a way, almost do sound the same. A scale starting from one of them, however many notes you put in or leave out, feels complete when it reaches the other. There is a physical reason for this. Each note travels on a sound wave with a particular frequency—the higher the frequency, the higher the note—and when two notes are an octave apart their frequencies stand in the simple ratio of 2:1. This means that there is a regular coincidence of wave-peaks, as each peak of the slower wave matches every second peak of the faster one. The more constantly this agreement occurs, the better the sounds seem to blend.