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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Idiosyncratic terms}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | 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''{{idiosyncratic}} 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. Odd limits of {{nowrap|2<sup>''n''</sup> − 1}} are '''highlighted'''. |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2017-01-05 11:21:15 UTC</tt>.<br>
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| : The original revision id was <tt>603143824</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| |
| <h4>Original Wikitext content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">
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| || Odd limit || Smallest consistent || Smallest uniquely consistent ||
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| || 1 || 1 || 1 ||
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| || 3 || 1 || 3 ||
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| || 5 || 3 || 9 ||
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| || 7 || 4 || 27 ||
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| || 9 || 5 || 41 ||
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| || 11 || 22 || 58 ||
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| || 13 || 26 || 87 ||
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| 15: 29, 111
| | <onlyinclude>{| class="wikitable center-all" |
| 17: 58, 149
| | |+ style="font-size: 105%;" | Smallest consistent EDOs per odd limit |
| 19: 80, 217
| | |- |
| 21: 94, 282
| | ! Odd<br>limit !! Smallest<br>consistent edo* !! Smallest distinctly<br>consistent edo !! Smallest purely<br>consistent edo* !! Smallest edo<br>consistent to<br>[[Consistency #Generalization|distance 2]]* !! Smallest edo<br>distinctly consistent<br>to distance 2 |
| 23: 94, 282
| | |- style="font-weight: bold; background-color: #dddddd;" |
| 25: 282, 388
| | | 1 || 1 || 1 || 1 || 1 || 1 |
| 27: 282, 388
| | |- style="font-weight: bold; background-color: #dddddd;" |
| 29: 282, 1323
| | | 3 || 1 || 3 || 2 || 2 || 3 |
| 31: 311, 1600
| | |- |
| 33: 311, 1600
| | | 5 || 3 || 9 || 3 || 3 || 12 |
| 35: 311, 1600
| | |- style="font-weight: bold; background-color: #dddddd;" |
| 37: 311, 1600
| | | 7 || 4 || 27 || 10 || 31 || 31 |
| 39: 311, 2554
| | |- |
| 41: 311, 2554
| | | 9 || 5 || 41 || 41 || 41 || 41 |
| 43: 17461, 17461
| | |- |
| 45: 17461, 17461
| | | 11 || 22 || 58 || 41 || 72 || 72 |
| 47: 20567, 20567
| | |- |
| 49: 20567, 20567
| | | 13 || 26 || 87 || 46 || 270 || 270 |
| 51: 20567, 20567
| | |- style="font-weight: bold; background-color: #dddddd;" |
| 53: 20567, 20567
| | | 15 || 29 || 111 || 87 || 494 || 494 |
| 55: 20567, 20567
| | |- |
| 57: 20567, 20567
| | | 17 || 58 || 149 || 311 || 3395 || 3395 |
| 59: 253389, 253389
| | |- |
| 61: 625534, 625534
| | | 19 || 80 || 217 || 311 || 8539 || 8539 |
| 63: 625534, 625534
| | |- |
| 65: 625534, 625534
| | | 21 || 94 || 282 || 311 || 8539 || 8539 |
| 67: 625534, 625534
| | |- |
| 69: 759630, 759630
| | | 23 || 94 || 282 || 311 || 16808 || 16808 |
| 71: 759630, 759630
| | |- |
| 73: 759630, 759630
| | | 25 || 282 || 388 || 311 || 16808 || 16808 |
| 75: 2157429, 2157429
| | |- |
| | | 27 || 282 || 388 || 311 || 16808 || 16808 |
| | |- |
| | | 29 || 282 || 1323 || 311 || 16808 || 16808 |
| | |- style="font-weight: bold; background-color: #dddddd;" |
| | | 31 || 311 || 1600 || 311 || 16808 || 16808 |
| | |- |
| | | 33 || 311 || 1600 || 311 || 16808 || 16808 |
| | |- |
| | | 35 || 311 || 1600 || 311 || 16808 || 16808 |
| | |- |
| | | 37 || 311 || 1600 || 311 || 324296 || 324296 |
| | |- |
| | | 39 || 311 || 2554 || 311 || 2398629 || 2398629 |
| | |- |
| | | 41 || 311 || 2554 || 311 || 19164767 || 19164767 |
| | |- |
| | | 43 || 17461 || 17461 || 20567 || 19735901 || 19735901 |
| | |- |
| | | 45 || 17461 || 17461 || 20567 || 19735901 || 19735901 |
| | |- |
| | | 47 || 20567 || 20567 || 20567 || 152797015 || 152797015 |
| | |- |
| | | 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 || || |
| | |- style="font-weight: bold; background-color: #dddddd;" |
| | | 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 || || |
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| | | 87 || 2901533 || 2901533 || 50203972 || || |
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| | | 89 || 2901533 || 2901533 || 50203972 || || |
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| | | 91 || 2901533 || 2901533 || 50203972 || || |
| | |- |
| | | 93 || 2901533 || 2901533 || 50203972 || || |
| | |- |
| | | 95 || 2901533 || 2901533 || 50203972 || || |
| | |- |
| | | 97 || 2901533 || 2901533 || 1297643131 || || |
| | |- |
| | | 99 || 2901533 || 2901533 || 1297643131 || || |
| | |- |
| | | 101 || 2901533 || 2901533 || 3888109922 || || |
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| | | 103 || 2901533 || 2901533 || 3888109922 || || |
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| | | 105 || 2901533 || 2901533 || 3888109922 || || |
| | |- |
| | | 107 || 2901533 || 2901533 || 13805152233 || || |
| | |- |
| | | 109 || 2901533 || 2901533 || 27218556026 || || |
| | |- |
| | | 111 || 2901533 || 2901533 || 27218556026 || || |
| | |- |
| | | 113 || 2901533 || 2901533 || 27218556026 || || |
| | |- |
| | | 115 || 2901533 || 2901533 || 27218556026 || || |
| | |- |
| | | 117 || 2901533 || 2901533 || 27218556026 || || |
| | |- |
| | | 119 || 2901533 || 2901533 || 42586208631 || || |
| | |- |
| | | 121 || 2901533 || 2901533 || 42586208631 || || |
| | |- |
| | | 123 || 2901533 || 2901533 || 42586208631 || || |
| | |- |
| | | 125 || 2901533 || 2901533 || 42586208631 || || |
| | |- style="font-weight: bold; background-color: #dddddd;" |
| | | 127 || 2901533 || 2901533 || 42586208631 || || |
| | |- |
| | | 129 || 2901533 || 2901533 || 42586208631 || || |
| | |- |
| | | 131 || 2901533 || 2901533 || 93678217813** || || |
| | |- |
| | | 133 || 70910024 || 70910024 || 93678217813 || || |
| | |- |
| | | 135 || 70910024 || 70910024 || 93678217813 || || |
| | |} |
| | <nowiki />* Apart from 0edo |
|
| |
|
| </pre></div> | | <nowiki />** Purely consistent to the 137-odd-limit</onlyinclude> |
| <h4>Original HTML content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Minimal consistent EDOs</title></head><body><br />
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| | 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. |
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|
| <table class="wiki_table">
| | == OEIS integer sequences links == |
| <tr>
| | * {{OEIS|A116474|Equal divisions of the octave with progressively increasing consistency levels}} |
| <td>Odd limit<br />
| | * {{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}} |
| </td>
| | * {{OEIS|A117577|Equal divisions of the octave with nondecreasing consistency levels.}} |
| <td>Smallest consistent<br />
| | * {{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}} |
| </td>
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| <td>Smallest uniquely consistent<br />
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| </td>
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| </tr>
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| <td>1<br />
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| </td>
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| <td>1<br />
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| </td>
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| <td>1<br />
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| </td>
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| <td>3<br />
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| </td>
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| <td>1<br />
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| </td>
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| <td>3<br />
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| </td>
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| <td>5<br />
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| </td>
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| <td>3<br />
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| </td>
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| <td>9<br />
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| </td>
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| <td>7<br />
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| </td>
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| <td>4<br />
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| <td>27<br />
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| <td>9<br />
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| <td>5<br />
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| <td>41<br />
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| <td>11<br />
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| <td>22<br />
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| <td>58<br />
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| <td>13<br />
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| <td>26<br />
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| <td>87<br />
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| <td>15<br />
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| <td>17<br />
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| <br />
| | == See also == |
| 15: 29, 111<br />
| | * [[Consistency limits of small EDOs]] |
| 17: 58, 149<br />
| | * {{u|ArrowHead294|Purely consistent EDOs by odd limit}} |
| 19: 80, 217<br />
| | |
| 21: 94, 282<br />
| | [[Category:Mapping]] |
| 23: 94, 282<br />
| | [[Category:Consistency]] |
| 25: 282, 388<br />
| | [[Category:Odd limit]] |
| 27: 282, 388<br />
| |
| 29: 282, 1323<br />
| |
| 31: 311, 1600<br />
| |
| 33: 311, 1600<br />
| |
| 35: 311, 1600<br />
| |
| 37: 311, 1600<br />
| |
| 39: 311, 2554<br />
| |
| 41: 311, 2554<br />
| |
| 43: 17461, 17461<br />
| |
| 45: 17461, 17461<br />
| |
| 47: 20567, 20567<br />
| |
| 49: 20567, 20567<br />
| |
| 51: 20567, 20567<br />
| |
| 53: 20567, 20567<br />
| |
| 55: 20567, 20567<br />
| |
| 57: 20567, 20567<br />
| |
| 59: 253389, 253389<br />
| |
| 61: 625534, 625534<br />
| |
| 63: 625534, 625534<br />
| |
| 65: 625534, 625534<br />
| |
| 67: 625534, 625534<br />
| |
| 69: 759630, 759630<br />
| |
| 71: 759630, 759630<br />
| |
| 73: 759630, 759630<br />
| |
| 75: 2157429, 2157429</body></html></pre></div>
| |