Consistency limits of small EDOs: Difference between revisions

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An [[EDO|edo]] N is [[consistent]] with respect to a set of rational numbers s if the [[patent val]] mapping of every element of s is the nearest N-edo approximation. It is ''uniquely consistent'' if every element of s is mapped to a unique value. If the set s is the q [[odd limit]], we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of every edo up to 99. "Consistent" gives the consistency level, and "Distinct" the distinct consistency level.
An [[edo]] N is [[consistent]] with respect to a set of rational numbers s if the [[patent val]] mapping of every element of s is the nearest N-edo approximation. It is ''uniquely consistent'' if every element of s is mapped to a unique value. If the set s is the q [[odd limit]], we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of every edo up to 99. "Consistent" gives the consistency level, and "Distinct" the distinct consistency level.


{| class="wikitable"
{| class="wikitable"
|-
|-
| | EDO
! EDO
| | Consistent
! Consistent
| | Distinct
! Distinct
|-
|-
| | 1
| 1
| | 3
| 3
| | 1
| 1
|-
|-
| | 2
| 2
| | 3
| 3
| | 1
| 1
|-
|-
| | 3
| 3
| | 5
| 5
| | 3
| 3
|-
|-
| | 4
| 4
| | 7
| 7
| | 1
| 1
|-
|-
| | 5
| 5
| | 9
| 9
| | 3
| 3
|-
|-
| | 6
| 6
| | 7
| 7
| | 3
| 3
|-
|-
| | 7
| 7
| | 5
| 5
| | 3
| 3
|-
|-
| | 8
| 8
| | 5
| 5
| | 3
| 3
|-
|-
| | 9
| 9
| | 7
| 7
| | 5
| 5
|-
|-
| | 10
| 10
| | 7
| 7
| | 3
| 3
|-
|-
| | 11
| 11
| | 3
| 3
| | 3
| 3
|-
|-
| | 12
| 12
| | 9
| 9
| | 5
| 5
|-
|-
| | 13
| 13
| | 3
| 3
| | 3
| 3
|-
|-
| | 14
| 14
| | 3
| 3
| | 3
| 3
|-
|-
| | 15
| 15
| | 7
| 7
| | 5
| 5
|-
|-
| | 16
| 16
| | 7
| 7
| | 5
| 5
|-
|-
| | 17
| 17
| | 3
| 3
| | 3
| 3
|-
|-
| | 18
| 18
| | 7
| 7
| | 5
| 5
|-
|-
| | 19
| 19
| | 9
| 9
| | 5
| 5
|-
|-
| | 20
| 20
| | 3
| 3
| | 3
| 3
|-
|-
| | 21
| 21
| | 3
| 3
| | 3
| 3
|-
|-
| | 22
| 22
| | 11
| 11
| | 5
| 5
|-
|-
| | 23
| 23
| | 5
| 5
| | 5
| 5
|-
|-
| | 24
| 24
| | 5
| 5
| | 5
| 5
|-
|-
| | 25
| 25
| | 5
| 5
| | 5
| 5
|-
|-
| | 26
| 26
| | 13
| 13
| | 5
| 5
|-
|-
| | 27
| 27
| | 9
| 9
| | 7
| 7
|-
|-
| | 28
| 28
| | 5
| 5
| | 5
| 5
|-
|-
| | 29
| 29
| | 15
| 15
| | 5
| 5
|-
|-
| | 30
| 30
| | 5
| 5
| | 5
| 5
|-
|-
| | 31
| 31
| | 11
| 11
| | 7
| 7
|-
|-
| | 32
| 32
| | 3
| 3
| | 3
| 3
|-
|-
| | 33
| 33
| | 3
| 3
| | 3
| 3
|-
|-
| | 34
| 34
| | 5
| 5
| | 5
| 5
|-
|-
| | 35
| 35
| | 7
| 7
| | 7
| 7
|-
|-
| | 36
| 36
| | 7
| 7
| | 7
| 7
|-
|-
| | 37
| 37
| | 7
| 7
| | 7
| 7
|-
|-
| | 38
| 38
| | 5
| 5
| | 5
| 5
|-
|-
| | 39
| 39
| | 5
| 5
| | 5
| 5
|-
|-
| | 40
| 40
| | 3
| 3
| | 3
| 3
|-
|-
| | 41
| 41
| | 15
| 15
| | 9
| 9
|-
|-
| | 42
| 42
| | 7
| 7
| | 7
| 7
|-
|-
| | 43
| 43
| | 7
| 7
| | 7
| 7
|-
|-
| | 44
| 44
| | 5
| 5
| | 5
| 5
|-
|-
| | 45
| 45
| | 7
| 7
| | 7
| 7
|-
|-
| | 46
| 46
| | 13
| 13
| | 9
| 9
|-
|-
| | 47
| 47
| | 5
| 5
| | 5
| 5
|-
|-
| | 48
| 48
| | 5
| 5
| | 5
| 5
|-
|-
| | 49
| 49
| | 7
| 7
| | 7
| 7
|-
|-
| | 50
| 50
| | 9
| 9
| | 7
| 7
|-
|-
| | 51
| 51
| | 3
| 3
| | 3
| 3
|-
|-
| | 52
| 52
| | 3
| 3
| | 3
| 3
|-
|-
| | 53
| 53
| | 9
| 9
| | 9
| 9
|-
|-
| | 54
| 54
| | 3
| 3
| | 3
| 3
|-
|-
| | 55
| 55
| | 5
| 5
| | 5
| 5
|-
|-
| | 56
| 56
| | 7
| 7
| | 7
| 7
|-
|-
| | 57
| 57
| | 7
| 7
| | 7
| 7
|-
|-
| | 58
| 58
| | 17
| 17
| | 11
| 11
|-
|-
| | 59
| 59
| | 7
| 7
| | 7
| 7
|-
|-
| | 60
| 60
| | 9
| 9
| | 9
| 9
|-
|-
| | 61
| 61
| | 5
| 5
| | 5
| 5
|-
|-
| | 62
| 62
| | 7
| 7
| | 7
| 7
|-
|-
| | 63
| 63
| | 7
| 7
| | 7
| 7
|-
|-
| | 64
| 64
| | 3
| 3
| | 3
| 3
|-
|-
| | 65
| 65
| | 5
| 5
| | 5
| 5
|-
|-
| | 66
| 66
| | 3
| 3
| | 3
| 3
|-
|-
| | 67
| 67
| | 3
| 3
| | 3
| 3
|-
|-
| | 68
| 68
| | 9
| 9
| | 9
| 9
|-
|-
| | 69
| 69
| | 5
| 5
| | 5
| 5
|-
|-
| | 70
| 70
| | 9
| 9
| | 9
| 9
|-
|-
| | 71
| 71
| | 5
| 5
| | 5
| 5
|-
|-
| | 72
| 72
| | 17
| 17
| | 11
| 11
|-
|-
| | 73
| 73
| | 7
| 7
| | 7
| 7
|-
|-
| | 74
| 74
| | 5
| 5
| | 5
| 5
|-
|-
| | 75
| 75
| | 5
| 5
| | 5
| 5
|-
|-
| | 76
| 76
| | 7
| 7
| | 7
| 7
|-
|-
| | 77
| 77
| | 9
| 9
| | 9
| 9
|-
|-
| | 78
| 78
| | 7
| 7
| | 7
| 7
|-
|-
| | 79
| 79
| | 5
| 5
| | 5
| 5
|-
|-
| | 80
| 80
| | 19
| 19
| | 11
| 11
|-
|-
| | 81
| 81
| | 7
| 7
| | 7
| 7
|-
|-
| | 82
| 82
| | 9
| 9
| | 9
| 9
|-
|-
| | 83
| 83
| | 7
| 7
| | 7
| 7
|-
|-
| | 84
| 84
| | 9
| 9
| | 9
| 9
|-
|-
| | 85
| 85
| | 3
| 3
| | 3
| 3
|-
|-
| | 86
| 86
| | 3
| 3
| | 3
| 3
|-
|-
| | 87
| 87
| | 15
| 15
| | 13
| 13
|-
|-
| | 88
| 88
| | 7
| 7
| | 7
| 7
|-
|-
| | 89
| 89
| | 11
| 11
| | 11
| 11
|-
|-
| | 90
| 90
| | 7
| 7
| | 7
| 7
|-
|-
| | 91
| 91
| | 9
| 9
| | 9
| 9
|-
|-
| | 92
| 92
| | 5
| 5
| | 5
| 5
|-
|-
| | 93
| 93
| | 7
| 7
| | 7
| 7
|-
|-
| | 94
| 94
| | 23
| 23
| | 13
| 13
|-
|-
| | 95
| 95
| | 7
| 7
| | 7
| 7
|-
|-
| | 96
| 96
| | 5
| 5
| | 5
| 5
|-
|-
| | 97
| 97
| | 5
| 5
| | 5
| 5
|-
|-
| | 98
| 98
| | 3
| 3
| | 3
| 3
|-
|-
| | 99
| 99
| | 9
| 9
| | 9
| 9
|}
|}


[[Category:Theory]]
[[Category:Theory]]

Revision as of 20:18, 22 November 2020

An edo N is consistent with respect to a set of rational numbers s if the patent val mapping of every element of s is the nearest N-edo approximation. It is uniquely consistent if every element of s is mapped to a unique value. If the set s is the q odd limit, we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of every edo up to 99. "Consistent" gives the consistency level, and "Distinct" the distinct consistency level.

EDO Consistent Distinct
1 3 1
2 3 1
3 5 3
4 7 1
5 9 3
6 7 3
7 5 3
8 5 3
9 7 5
10 7 3
11 3 3
12 9 5
13 3 3
14 3 3
15 7 5
16 7 5
17 3 3
18 7 5
19 9 5
20 3 3
21 3 3
22 11 5
23 5 5
24 5 5
25 5 5
26 13 5
27 9 7
28 5 5
29 15 5
30 5 5
31 11 7
32 3 3
33 3 3
34 5 5
35 7 7
36 7 7
37 7 7
38 5 5
39 5 5
40 3 3
41 15 9
42 7 7
43 7 7
44 5 5
45 7 7
46 13 9
47 5 5
48 5 5
49 7 7
50 9 7
51 3 3
52 3 3
53 9 9
54 3 3
55 5 5
56 7 7
57 7 7
58 17 11
59 7 7
60 9 9
61 5 5
62 7 7
63 7 7
64 3 3
65 5 5
66 3 3
67 3 3
68 9 9
69 5 5
70 9 9
71 5 5
72 17 11
73 7 7
74 5 5
75 5 5
76 7 7
77 9 9
78 7 7
79 5 5
80 19 11
81 7 7
82 9 9
83 7 7
84 9 9
85 3 3
86 3 3
87 15 13
88 7 7
89 11 11
90 7 7
91 9 9
92 5 5
93 7 7
94 23 13
95 7 7
96 5 5
97 5 5
98 3 3
99 9 9
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