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Minimal consistent EDOs: Difference between revisions

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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, 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.
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" style="text-align: center;"
{| class="wikitable right-all"
|-
! Odd<br>limit
! Odd<br>limit
! Smallest<br>consistent edo*
! Smallest<br>consistent edo*
Line 8: Line 9:
|-
|-
| 1
| 1
| rowspan="2" | 1
| 1
| 1
| 1
| 1
| 1
|-
|-
| 3
| 3
| 1
| 3
| 3
| 2
| 2
Line 29: Line 31:
| 5
| 5
| 41
| 41
| rowspan="2" | 41
| 41
|-
|-
| 11
| 11
| 22
| 22
| 58
| 58
| 41
|-
|-
| 13
| 13
Line 48: Line 51:
| 58
| 58
| 149
| 149
| rowspan="13" | 311
| 311
|-
|-
| 19
| 19
| 80
| 80
| 217
| 217
| 311
|-
|-
| 21
| 21
| rowspan="2" | 94
| 94
| rowspan="2" | 282
| 282
| 311
|-
|-
| 23
| 23
| 94
| 282
| 311
|-
|-
| 25
| 25
| rowspan="3" | 282
| 282
| rowspan="2" | 388
| 388
| 311
|-
|-
| 27
| 27
| 282
| 388
| 311
|-
|-
| 29
| 29
| 282
| 1323
| 1323
| 311
|-
|-
| 31
| 31
| rowspan="6" | 311
| 311
| rowspan="4" | 1600
| 1600
| 311
|-
|-
| 33
| 33
| 311
| 1600
| 311
|-
|-
| 35
| 35
| 311
| 1600
| 311
|-
|-
| 37
| 37
| 311
| 1600
| 311
|-
|-
| 39
| 39
| rowspan="2" | 2554
| 311
| 2554
| 311
|-
|-
| 41
| 41
| 311
| 2554
| 311
|-
|-
| 43
| 43
| rowspan="2" | 17461
| 17461
| rowspan="2" | 17461
| 17461
| rowspan="3" | 20567
| 20567
|-
|-
| 45
| 45
| 17461
| 17461
| 20567
|-
|-
| 47
| 47
| rowspan="6" | 20567
| 20567
| rowspan="6" | 20567
| 20567
| 20567
|-
|-
| 49
| 49
| rowspan="2" | 459944
| 20567
| 20567
| 459944
|-
|-
| 51
| 51
| 20567
| 20567
| 459944
|-
|-
| 53
| 53
| rowspan="3" | 1705229
| 20567
| 20567
| 1705229
|-
|-
| 55
| 55
| 20567
| 20567
| 1705229
|-
|-
| 57
| 57
| 20567
| 20567
| 1705229
|-
|-
| 59
| 59
| 253389
| 253389
| 253389
| 253389
| rowspan="4" | 3159811
| 3159811
|-
|-
| 61
| 61
| rowspan="4" | 625534
| 625534
| rowspan="4" | 625534
| 625534
| 3159811
|-
|-
| 63
| 63
| 625534
| 625534
| 3159811
|-
|-
| 65
| 65
| 625534
| 625534
| 3159811
|-
|-
| 67
| 67
| 625534
| 625534
| 7317929
| 7317929
|-
|-
| 69
| 69
| rowspan="3" | 759630
| 759630
| rowspan="3" | 759630
| 759630
| rowspan="2" | 8595351
| 8595351
|-
|-
| 71
| 71
| 759630
| 759630
| 8595351
|-
|-
| 73
| 73
| 759630
| 759630
| 27783092
| 27783092
|-
|-
| 75
| 75
| rowspan="2" | 2157429
| 2157429
| rowspan="2" | 2157429
| 2157429
| rowspan="2" | 34531581
| 34531581
|-
|-
| 77
| 77
| 2157429
| 2157429
| 34531581
|-
|-
| 79
| 79
| rowspan="27" | 2901533
| 2901533
| rowspan="27" | 2901533
| 2901533
| rowspan="9" | 50203972
| 50203972
|-
|-
| 81
| 81
| 2901533
| 2901533
| 50203972
|-
|-
| 83
| 83
| 2901533
| 2901533
| 50203972
|-
|-
| 85
| 85
| 2901533
| 2901533
| 50203972
|-
|-
| 87
| 87
| 2901533
| 2901533
| 50203972
|-
|-
| 89
| 89
| 2901533
| 2901533
| 50203972
|-
|-
| 91
| 91
| 2901533
| 2901533
| 50203972
|-
|-
| 93
| 93
| 2901533
| 2901533
| 50203972
|-
|-
| 95
| 95
| 2901533
| 2901533
| 50203972
|-
|-
| 97
| 97
| rowspan="2" | 1297643131
| 2901533
| 2901533
| 1297643131
|-
|-
| 99
| 99
| 2901533
| 2901533
| 1297643131
|-
|-
| 101
| 101
| rowspan="3" | 3888109922
| 2901533
| 2901533
| 3888109922
|-
|-
| 103
| 103
| 2901533
| 2901533
| 3888109922
|-
|-
| 105
| 105
| 2901533
| 2901533
| 3888109922
|-
|-
| 107
| 107
| 2901533
| 2901533
| 13805152233
| 13805152233
|-
|-
| 109
| 109
| rowspan="5" | 27218556026
| 2901533
| 2901533
| 27218556026
|-
|-
| 111
| 111
| 2901533
| 2901533
| 27218556026
|-
|-
| 113
| 113
| 2901533
| 2901533
| 27218556026
|-
|-
| 115
| 115
| 2901533
| 2901533
| 27218556026
|-
|-
| 117
| 117
| 2901533
| 2901533
| 27218556026
|-
|-
| 119
| 119
| rowspan="6" | 42586208631
| 2901533
| 2901533
| 42586208631
|-
|-
| 121
| 121
| 2901533
| 2901533
| 42586208631
|-
|-
| 123
| 123
| 2901533
| 2901533
| 42586208631
|-
|-
| 125
| 125
| 2901533
| 2901533
| 42586208631
|-
|-
| 127
| 127
| 2901533
| 2901533
| 42586208631
|-
|-
| 129
| 129
| 2901533
| 2901533
| 42586208631
|-
|-
| 131
| 131
| rowspan="3" | 93678217813
| 2901533
| 2901533
| 93678217813
|-
|-
| 133
| 133
| rowspan="2" | 70910024
| 70910024
| rowspan="2" | 70910024
| 70910024
| 93678217813
|-
|-
| 135
| 135
| 70910024
| 70910024
| 93678217813***
|}
|}
<nowiki>*</nowiki> apart from 0edo
<nowiki>*</nowiki> apart from 0edo
Retrieved from "https://en.xen.wiki/w/Minimal_consistent_EDOs"