Monotonicity levels of small EDOs

An EDO N is monotone with respect to a set of rational numbers S if there exists a mapping for N that preserves each elements's size order. If S is the q-odd-limit diamond, we say N is q-odd-limit monotone. Below is a table of every EDO up to 72.

EDO	Monotonicity Level	Associated Vals
1	3	1
2	5	2
3	5	3
4	7	4
5	9	5
6	7	6
7	5	7 or 7c
8	7	8d
9	7	9
10	9	10 or 10c [5]
11	7	11b
12	11	12
13	7	13b
14	13	14c
15	13	15
16	7	16
17	15	17c
18	7	18 or 18bd [9]
19	17	19
20	9	20c
21	7	21
22	15	22f
23	7	23bc
24	13	24
25	9	25 or 25c
26	13	26
27	15	27e
28	13	28ccde [14c]
29	15	29
30	13	30f [15]
31	17	31
32	13	32cf
33	13	33cd
34	19	34d
35	9	35b, 35bc, etc.
36	15	36
37	15	37
38	19	38df
39	15	39df
40	13	40c
41	21	41
42	13	42ef
43	17	43
44	19	44
45	13	45ef
46	17	46
47	13	47ccde or 47bcff
48	21	48c
49	15	49f
50	19	50
51	15	51
52	13	52c [26]
53	23	53e
54	15	54c or 54cee [27e]
55	17	55f
56	21	56
57	17	57ddf or 57ddefgg [19]
58	23	58hi
59	15	59f
60	23	60e
61	15	61d
62	25	62
63	19	63
64	15	64be
65	25	65d
66	15	66 or 66cdef
67	17	67
68	27	68e
69	17	69de, 69d, or 69dg
70	21	70cd
71	15	71d
72	29	72

See also

• Diamond monotone