View source for Minimal consistent EDOs

An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent'' if its [[relative interval error|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135.

{| class="wikitable right-all"
|-
! Odd<br>limit
! Smallest<br>consistent edo*
! Smallest distinctly<br>consistent edo
! Smallest ''purely<br>consistent''** edo
|-
| 1
| 1
| 1
| 1
|-
| 3
| 1
| 3
| 2
|-
| 5
| 3
| 9
| 3
|-
| 7
| 4
| 27
| 10
|-
| 9
| 5
| 41
| 41
|-
| 11
| 22
| 58
| 41
|-
| 13
| 26
| 87
| 46
|-
| 15
| 29
| 111
| 87
|-
| 17
| 58
| 149
| 311
|-
| 19
| 80
| 217
| 311
|-
| 21
| 94
| 282
| 311
|-
| 23
| 94
| 282
| 311
|-
| 25
| 282
| 388
| 311
|-
| 27
| 282
| 388
| 311
|-
| 29
| 282
| 1323
| 311
|-
| 31
| 311
| 1600
| 311
|-
| 33
| 311
| 1600
| 311
|-
| 35
| 311
| 1600
| 311
|-
| 37
| 311
| 1600
| 311
|-
| 39
| 311
| 2554
| 311
|-
| 41
| 311
| 2554
| 311
|-
| 43
| 17461
| 17461
| 20567
|-
| 45
| 17461
| 17461
| 20567
|-
| 47
| 20567
| 20567
| 20567
|-
| 49
| 20567
| 20567
| 459944
|-
| 51
| 20567
| 20567
| 459944
|-
| 53
| 20567
| 20567
| 1705229
|-
| 55
| 20567
| 20567
| 1705229
|-
| 57
| 20567
| 20567
| 1705229
|-
| 59
| 253389
| 253389
| 3159811
|-
| 61
| 625534
| 625534
| 3159811
|-
| 63
| 625534
| 625534
| 3159811
|-
| 65
| 625534
| 625534
| 3159811
|-
| 67
| 625534
| 625534
| 7317929
|-
| 69
| 759630
| 759630
| 8595351
|-
| 71
| 759630
| 759630
| 8595351
|-
| 73
| 759630
| 759630
| 27783092
|-
| 75
| 2157429
| 2157429
| 34531581
|-
| 77
| 2157429
| 2157429
| 34531581
|-
| 79
| 2901533
| 2901533
| 50203972
|-
| 81
| 2901533
| 2901533
| 50203972
|-
| 83
| 2901533
| 2901533
| 50203972
|-
| 85
| 2901533
| 2901533
| 50203972
|-
| 87
| 2901533
| 2901533
| 50203972
|-
| 89
| 2901533
| 2901533
| 50203972
|-
| 91
| 2901533
| 2901533
| 50203972
|-
| 93
| 2901533
| 2901533
| 50203972
|-
| 95
| 2901533
| 2901533
| 50203972
|-
| 97
| 2901533
| 2901533
| 
|-
| 99
| 2901533
| 2901533
| 
|-
| 101
| 2901533
| 2901533
| 
|-
| 103
| 2901533
| 2901533
| 
|-
| 105
| 2901533
| 2901533
| 
|-
| 107
| 2901533
| 2901533
| 
|-
| 109
| 2901533
| 2901533
| 
|-
| 111
| 2901533
| 2901533
| 
|-
| 113
| 2901533
| 2901533
| 
|-
| 115
| 2901533
| 2901533
| 
|-
| 117
| 2901533
| 2901533
| 
|-
| 119
| 2901533
| 2901533
| 
|-
| 121
| 2901533
| 2901533
| 
|-
| 123
| 2901533
| 2901533
| 
|-
| 125
| 2901533
| 2901533
| 
|-
| 127
| 2901533
| 2901533
| 
|-
| 129
| 2901533
| 2901533
| 
|-
| 131
| 2901533
| 2901533
| 
|-
| 133
| 70910024
| 70910024
| 
|-
| 135
| 70910024
| 70910024
| 
|}
<nowiki>*</nowiki> apart from 0edo

<nowiki>**</nowiki> ''purely consistent'' is an {{idiosyncratic}}

The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is [[5407372813edo|5407372813]], reported to be consistent to the 155-odd-limit.

== OEIS integer sequences links ==
* {{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|A117577|Equal divisions of the octave with nondecreasing consistency levels.}}
* {{OEIS|A117578|Equal divisions of the octave with nondecreasing consistency limits and distinct approximations for all the ratios in the tonality diamond of that limit}}

[[Category:Mapping]]
[[Category:Consistency]]
[[Category:Odd limit]]