@TobyBartels - interesting. There's always this tension in music between whether you end where you started or just before, e.g. 1 through 7 (the "heptatonic scale") versus 1 through 8 (the "octave"). Maybe Boethius was a 1 through 7 guy.

(In theory there's also the option of 0 through 7, but I guess Western music notation solidified before zero was fully accepted.)

From the late 1100s to about 1600 people called describe pitches that lie outside 7-tone system "musica ficta" ("false" or "fictitious") notes. But gradually these notes - the black keys on the piano if you're playing in C major - became more accepted.

To keep things simple for mathematicians, I'll usually denote these with the "flat" symbol, ♭. For example, G♭ is the black note one down from the white note G.

(Musicians really need both flats and sharps, and they'd also call G♭ something else: F♯. I'll actually need both G♭ and F♯ at some points in this talk!)

(6/n)

@johncarlosbaez G# always sounds so tasty to me!

@edgarchavez @johncarlosbaez

We use those names in English as well, except with Ti instead of Si. (If you know your English-language musicals, then you may have heard them used in The Sound of Music.) But the difference between these and the letters is that the letter notes are at (or at least near) specific frequencies, while solfege (as we call it) is relative. That is, A is always about 440 Hz (modulo a power of 2), but La could be anywhere (with the others arranged at the same relative frequencies).

@edgarchavez @johncarlosbaez in Hindustani classical, the notes are {sa, re, ga, ma, pa, dha, ni} and the alphabet is called "sargam", for the first 4 names