### Re: A proposal to simplify the notation of EDOs with bad fifths

Posted:

**Sat Jul 21, 2018 5:51 pm**I agree. But I don't understand why this is relevant to whether or not a division should have a native fifth notation. There are many other things people may want to do with an EDO besides refret a guitar, and some of them might benefit from a native-fifth notation, if it is simple enough.George Secor wrote:72 is as good a cutoff as any. As I said before, I don't think anyone is going to refret a guitar to any division this complex.

Subset notations are often more complex than native fifth notations because they have the same complexity as the superset notation. The exceptions are 11, 6, 8, 13 and 18. I think the SS notations are simpler than the NF notations for these. The NF notations are LF and AF notations in these cases, and the SS notations are of 22, 12, 24, 26 and 36.

OK. I'm happy to leave 44's SS notation being of 176.There are two reasons for making [44] a subset of 176-EDO:

1) 176 is a much better division than 132; and

2) The notation for 88-EDO is as a subset of 176, so the tones common to 44 and 88 would be notated alike.

I checked those possible 61-edo notations I flagged, and I find that the 54-edo AF notation is not valid for 61, because the 5-comma is 2 degrees, not 3. But the 68-edo notation is valid for 61. And yes, 61 is 1:3:5:11:13 consistent.

61: JB (same as 68)

66 is 1:3:17 consistent. It is not 1:3:p consistent for any other prime p up to 19 (no higher primes were checked). So no useful JI-based notation is possible for it. But the following apotome-fraction notation is acceptable. Although is not valid as 2 degrees, it's close.

66: AF (same as 59)