Monotonicity limits 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 limit |
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 |