> Doesn't this just get you the octaves, which are by no means unique to the 12-tone scale? Correct, I was just referring to the convention that you use the sa

> Doesn't this just get you the octaves, which are by no means unique to the 12-tone scale? Correct, I was just referring to the convention that you use the same letter for f and 2f. > Can you expand on this? "Group" in what sense? C12? The cyclic group with 12 elements https://en.m.wikipedia.org/wiki/Cyclic_group https://en.m.wikipedia.org/wiki/Cyclic_group Isomorphic to the integers mod 12 (Z/Z12) - this is just a set with 12 things that wraps around. Things like the "circle of fifths" falls naturally out of the behavior of this group (7 is a generator of C12, and adding 7 in this group corresponds to multiplying by 2^(7/12) \approx 3/2).