I've been exploring the idea that we could have apotome-fraction notations that produce consistent notation stacks for other sets of EDOs which are multiples of each other (when they have the same best fifth), like 22, 44, 66, and 19, 38, 57, in the same way that we have long had a consistent notation stack for 12, 24, 36, ... , and now (thanks to this topic) we have them for 5, 10, 15, 20, 25, 30 and 7, 14, 21, 28, 35. Such apotome-fraction notations can operate over a small range of fifth sizes, 2 to 4 cents wide. For example an apotome fraction-notation for meantones would include multiples of 31 as well as multiples of 19, and would also include 50-edo whose fifth size is intermediate between those two.

I have found that only 10 such ranges are required, to cover all EDOs from 5 to 72-edo. I've given fifth errors in cents as tentative boundaries.

Boundary
(fifth
error) Colour Description, EDOs
------ ------ ------------------------------------------------------------------------------------
**Black**
+98.1c
**Gold** Bad fifths apotome fraction notation, 5n, 32, 37, 42, 59 (6,8,13,18 pref ⊂ 12,24,26,36)
+9.8c
**Green** Super pythagorean notation, 22n, 27n, 49, 61, 71
+6.0c
**Blue** 17n, 39, 46, 56, 63
+2.0c
**Magenta** 29n, 70
+0.8c
**Grey** Pythagorean notation (JI), 41, 53, 65
-1.2c
**Orange** 12-relative notation (Trojan notation), 12n
-2.8c
**Pink** (Possible future colour) 91, 103
-3.2c
**Yellow** 43, 55, 67
-4.4c
**Cyan** Meantone notation, 19n, 31n, 50, 69
-7.5c
**Purple** Sub meantone notation, 26n, 45, 64
-10.5879c (4+15ϕ)\(7+26ϕ) [See viewtopic.php?p=1976#p1976]
**Rose** Bad fifths limma fraction notation, 7n, 9, 16, 23, 33, 40, 47 (11 pref subset of 22)
-47.5c
**White**