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" | ||
Line 6: | Line 6: | ||
! 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 | ||
Line 14: | Line 16: | ||
| 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 | ||
|- | |- | ||
Line 30: | Line 36: | ||
| 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 | ||
| | |||
|- | |- | ||
| 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 | ||
| | |||
|} | |} | ||