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An [[EDO|edo]] N is [[consistent]] with respect to a set of rational numbers s if the [[Patent_val|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|odd limit]], we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of the least consistent, and least uniquely consistent, edo for every odd number up to 135.
An [[EDO]] N is [[consistent]] with respect to a set of rational numbers s if the [[Patent_val|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|odd limit]], we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of the least consistent, and least uniquely consistent, edo for every odd number up to 135.


{| class="wikitable"
{| class="wikitable"
|-
|-
! | Odd limit
! Odd limit
! | Smallest consistent
! Smallest consistent
! | Smallest uniquely consistent
! Smallest uniquely consistent
|-
|-
| | 1
| 1
| | 1
| 1
| | 1
| 1
|-
|-
| | 3
| 3
| | 1
| 1
| | 3
| 3
|-
|-
| | 5
| 5
| | 3
| 3
| | 9
| 9
|-
|-
| | 7
| 7
| | 4
| 4
| | 27
| 27
|-
|-
| | 9
| 9
| | 5
| 5
| | 41
| 41
|-
|-
| | 11
| 11
| | 22
| 22
| | 58
| 58
|-
|-
| | 13
| 13
| | 26
| 26
| | 87
| 87
|-
|-
| | 15
| 15
| | 29
| 29
| | 111
| 111
|-
|-
| | 17
| 17
| | 58
| 58
| | 149
| 149
|-
|-
| | 19
| 19
| | 80
| 80
| | 217
| 217
|-
|-
| | 21
| 21
| | 94
| 94
| | 282
| 282
|-
|-
| | 23
| 23
| | 94
| 94
| | 282
| 282
|-
|-
| | 25
| 25
| | 282
| 282
| | 388
| 388
|-
|-
| | 27
| 27
| | 282
| 282
| | 388
| 388
|-
|-
| | 29
| 29
| | 282
| 282
| | 1323
| 1323
|-
|-
| | 31
| 31
| | 311
| 311
| | 1600
| 1600
|-
|-
| | 33
| 33
| | 311
| 311
| | 1600
| 1600
|-
|-
| | 35
| 35
| | 311
| 311
| | 1600
| 1600
|-
|-
| | 37
| 37
| | 311
| 311
| | 1600
| 1600
|-
|-
| | 39
| 39
| | 311
| 311
| | 2554
| 2554
|-
|-
| | 41
| 41
| | 311
| 311
| | 2554
| 2554
|-
|-
| | 43
| 43
| | 17461
| 17461
| | 17461
| 17461
|-
|-
| | 45
| 45
| | 17461
| 17461
| | 17461
| 17461
|-
|-
| | 47
| 47
| | 20567
| 20567
| | 20567
| 20567
|-
|-
| | 49
| 49
| | 20567
| 20567
| | 20567
| 20567
|-
|-
| | 51
| 51
| | 20567
| 20567
| | 20567
| 20567
|-
|-
| | 53
| 53
| | 20567
| 20567
| | 20567
| 20567
|-
|-
| | 55
| 55
| | 20567
| 20567
| | 20567
| 20567
|-
|-
| | 57
| 57
| | 20567
| 20567
| | 20567
| 20567
|-
|-
| | 59
| 59
| | 253389
| 253389
| | 253389
| 253389
|-
|-
| | 61
| 61
| | 625534
| 625534
| | 625534
| 625534
|-
|-
| | 63
| 63
| | 625534
| 625534
| | 625534
| 625534
|-
|-
| | 65
| 65
| | 625534
| 625534
| | 625534
| 625534
|-
|-
| | 67
| 67
| | 625534
| 625534
| | 625534
| 625534
|-
|-
| | 69
| 69
| | 759630
| 759630
| | 759630
| 759630
|-
|-
| | 71
| 71
| | 759630
| 759630
| | 759630
| 759630
|-
|-
| | 73
| 73
| | 759630
| 759630
| | 759630
| 759630
|-
|-
| | 75
| 75
| | 2157429
| 2157429
| | 2157429
| 2157429
|-
|-
| | 77
| 77
| | 2157429
| 2157429
| | 2157429
| 2157429
|-
|-
| | 79
| 79
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 81
| 81
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 83
| 83
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 85
| 85
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 87
| 87
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 89
| 89
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 91
| 91
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 93
| 93
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 95
| 95
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 97
| 97
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 99
| 99
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 101
| 101
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 103
| 103
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 105
| 105
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 107
| 107
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 109
| 109
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 111
| 111
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 113
| 113
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 115
| 115
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 117
| 117
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 119
| 119
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 121
| 121
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 123
| 123
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 125
| 125
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 127
| 127
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 129
| 129
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 131
| 131
| | 2901533
| 2901533
| | 2901533
| 2901533
|-
|-
| | 133
| 133
| | 70910024
| 70910024
| | 70910024
| 70910024
|-
|-
| | 135
| 135
| | 70910024
| 70910024
| | 70910024
| 70910024
|-
|-
| | 137
| 137
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|-
|-
| | 139
| 139
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|-
|-
| | 141
| 141
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|-
|-
| | 143
| 143
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|-
|-
| | 145
| 145
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|-
|-
| | 147
| 147
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|-
|-
| | 149
| 149
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|-
|-
| | 151
| 151
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|-
|-
| | 153
| 153
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|-
|-
| | 155
| 155
| | 5407372813
| 5407372813
| | 5407372813
| 5407372813
|}
|}


=OEIS integer sequences links=
== OEIS integer sequences links ==
 
* {{OEIS|A116474|Equal divisions of the octave with progressively increasing consistency levels}}
* {{OEIS|A116474|Equal divisions of the octave with progressively increasing consistency levels}}
* {{OEIS|A116475|Equal divisions of the octave with progressively increasing consistency limits and distinct approximations for all the ratios in the tonality diamond of that limit}}
* {{OEIS|A116475|Equal divisions of the octave with progressively increasing consistency limits and distinct approximations for all the ratios in the tonality diamond of that limit}}
Retrieved from "https://en.xen.wiki/w/Minimal_consistent_EDOs"