This question about notation is simple as dirt, but would be useful for me regardless, because of some work that I'm doing in music theory.
Basically, while there's a notation for subdividing the degree into arcminutes and arcseconds, so that "180 degrees, 30 minutes, 30 seconds" becomes 180º30'30", I can't find any notation for any unit which is then further subdivided into 360 degrees.
I thought there might be one for angles, so that rather than writing 1980º, I could write something like "5 cycles 180º" using some symbol for "cycles," but I couldn't find anything.
Is there any notation for something like this, or for any other unit of measure habitually subdivided into 360 parts, even if they aren't called "degrees?"
I would be interested both in any modern units of measure with some such notation, or in obsolete ones used only in antiquity.
Also, for those curious about how this question could possibly be relevant to anything, it has to do with that the established convention in music theory is to subdivide individual steps in the Western 12-note musical scale into 100 "cents."
I'm writing something now about the presentational advantages of instead subdividing the step by some highly composite number, especially when the scale being subdivided is an arbitrary non-Western scale. This can be useful for various specific music-theoretical reasons that aren't relevant here, but which are related to the same reason that highly composite numbers caught on when subdividing units of measure in general.
A subdivision into 360 parts, specifically, stands out for a few different mathematical reasons, also not relevant here. But, while writing a proposal to this effect, I realized that I knew of no established notation in which something is divided into 360 parts. So before I just make one up, so that two and a half steps becomes 2;180º or something, I want to see if any such common or historical notation is known to mathematicians.
A soft question, no doubt, but any insights would be much appreciated!