As I understand Western music, there’s a diatonic scale, whose notes correspond to seven consecutive white keys of a piano. The eighth white key (from the left) is an octave above the first. The terminology makes some sense, since an octopus has eight arms, and an octagon has eight sides.
Between two white piano-keys that are an octave apart, there are five black keys. When their notes are added to the diatonic scale, the chromatic scale results.
Perhaps I was given some such understanding in school. It was never quite satisfactory. In part to remedy this problem, I have drafted a paper, “Numbers and Notes in Plato and Euclid,” for which this blog post is now a repository. (The pdf file just linked to has 103 pages, but they are small, size B6; the date is September 22, 2026.)
The draft paper may explain itself, sufficiently well. Its most interesting element may be a black-and-white version of the following diagram, which I am also going to say more about in this post.
