Minimal consistent EDOs: Difference between revisions

Tristanbay (talk | contribs)
Added a note mentioning that the table excludes 0edo from consistent EDOs (it has no consistency limit because it's consistent in all odd-limits)
ArrowHead294 (talk | contribs)
mNo edit summary
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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. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135.
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"
{| class="wikitable right-all"
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! Smallest<br>Consistent Edo*
! Smallest<br>Consistent Edo*
! Smallest<br>Distinctly Consistent Edo
! Smallest<br>Distinctly Consistent Edo
! Smallest<br>Purely consistent Edo
|-
|-
| 1
| 1
| 1
| 1
| 1
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| 1
| 1
| 3
| 3
| 2
|-
|-
| 5
| 5
| 3
| 3
| 9
| 9
| 5
|-
|-
| 7
| 7
| 4
| 4
| 27
| 27
| 10
|-
|-
| 9
| 9
| 5
| 5
| 41
| 41
| 41
|-
|-
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| 22
| 22
| 58
| 58
| 41
|-
|-
| 13
| 13
| 26
| 26
| 87
| 87
| 46
|-
|-
| 15
| 15
| 29
| 29
| 111
| 111
| 87
|-
|-
| 17
| 17
| 58
| 58
| 149
| 149
| 311
|-
|-
| 19
| 19
| 80
| 80
| 217
| 217
| 311
|-
|-
| 21
| 21
| 94
| 94
| 282
| 282
| 311
|-
|-
| 23
| 23
| 94
| 94
| 282
| 282
| 311
|-
|-
| 25
| 25
| 282
| 282
| 388
| 388
| 311
|-
|-
| 27
| 27
| 282
| 282
| 388
| 388
| 311
|-
|-
| 29
| 29
| 282
| 282
| 1323
| 1323
| 311
|-
|-
| 31
| 31
| 311
| 311
| 1600
| 1600
| 311
|-
|-
| 33
| 33
| 311
| 311
| 1600
| 1600
| 311
|-
|-
| 35
| 35
| 311
| 311
| 1600
| 1600
| 311
|-
|-
| 37
| 37
| 311
| 311
| 1600
| 1600
| 311
|-
|-
| 39
| 39
| 311
| 311
| 2554
| 2554
| 311
|-
|-
| 41
| 41
| 311
| 311
| 2554
| 2554
| 311
|-
|-
| 43
| 43
| 17461
| 17461
| 17461
| 17461
| 20567
|-
|-
| 45
| 45
| 17461
| 17461
| 17461
| 17461
| 20567
|-
|-
| 47
| 47
| 20567
| 20567
| 20567
| 20567
| 20567
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| 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
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|-
|-
| 83
| 83
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 85
| 85
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 87
| 87
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 89
| 89
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 91
| 91
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 93
| 93
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 95
| 95
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 97
| 97
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 99
| 99
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 101
| 101
| 2901533
| 2901533
| 2901533
| 2901533
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|-
| 103
| 103
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 105
| 105
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 107
| 107
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 109
| 109
| 2901533
| 2901533
| 2901533
| 2901533
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| 111
| 111
| 2901533
| 2901533
| 2901533
| 2901533
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| 113
| 113
| 2901533
| 2901533
| 2901533
| 2901533
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| 115
| 115
| 2901533
| 2901533
| 2901533
| 2901533
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| 117
| 117
| 2901533
| 2901533
| 2901533
| 2901533
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| 119
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| 2901533
| 2901533
| 2901533
| 2901533
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| 121
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| 2901533
| 2901533
| 2901533
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| 123
| 123
| 2901533
| 2901533
| 2901533
| 2901533
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| 125
| 125
| 2901533
| 2901533
| 2901533
| 2901533
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|-
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| 127
| 127
| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 129
| 129
| 2901533
| 2901533
| 2901533
| 2901533
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|-
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| 131
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| 2901533
| 2901533
| 2901533
| 2901533
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|-
|-
| 133
| 133
| 70910024
| 70910024
| 70910024
| 70910024
|
|-
|-
| 135
| 135
| 70910024
| 70910024
| 70910024
| 70910024
|
|}
|}