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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-08-01 11:30:27 UTC</tt>.<br>
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| : The original revision id was <tt>588470276</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>
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| <h4>Original Wikitext content:</h4>
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| <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">**//101-EDO//** divides the [[octave]] into 101 equal parts of 11.881 [[cent]]s each. It can be used to tune the [[Schismatic family|grackle temperament]]. It is the 26th [[prime numbers|prime]] edo. The 101cd val provides an excellent tuning for [[Magic family#Witchcraft|witchcraft temperament]], falling between the 13 and 15 limit least squares tuning.
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| [[5-limit]] commas: 32805/32768, <5 13 -11| | | == Theory == |
| | 101edo is in[[consistent]] in the [[5-odd-limit]], with [[harmonic]]s [[5/1|5]] and [[7/1|7]] falling about halfway between its steps. As such, {{val| 101 160 '''235''' '''284''' }} ([[patent val]]) and {{val| 101 160 '''234''' '''283''' }} (101cd) are about as viable. Using the patent val, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and 51018336/48828125 in the 5-limit; [[126/125]] and [[2430/2401]] in the [[7-limit]]. It can be used to tune the [[grackle]] temperament. The 101cd val provides an excellent tuning for [[witchcraft]] temperament, falling between the 13- and 15-odd-limit least squares tuning. |
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| [[7-limit]] commas: 126/125, 32805/32768, 2430/2401
| | === Odd harmonics === |
| | {{Harmonics in equal|101}} |
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| ==__Some important MOS scales:__== | | === Subsets and supersets === |
| | 101edo is the 26th [[prime edo]], following [[97edo]] and before [[103edo]]. [[202edo]], which doubles it, provides a good correction to the 5th, 7th, and 11th harmonics. |
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| **25 13 25 25 13:** //3L2s MOS// (Pentatonic)
| | == Intervals == |
| || 25/101 || 297.03 ||
| | {{Interval table}} |
| || 38/101 || 451.485 ||
| |
| || 63/101 || 748.515 ||
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| || 88/101 || 1045.545 ||
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| **17 17 8 17 17 17 8:** //5L2s MOS// (Diatonic Pythagorean)
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| || **17/101** || **201.98** ||
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| || 34/101 || 403.96 ||
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| || **42/101** || **499.01** ||
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| || **59/101** || **700.99** ||
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| || **76/101** || **902.97** ||
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| || 93/101 || 1104.95 ||
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| **13 13 13 13 13 13 13 10:** //7L1s MOS// (Grumpy Octatonic)
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| || 13/101 || 154.455 ||
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| || 26/101 || 308.911 ||
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| || 39/101 || 463.366 ||
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| || 52/101 || 617.822 ||
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| || 65/101 || 772.277 ||
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| || 78/101 || 926.733 ||
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| || 91/101 || 1081.188 ||
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| **13 13 13 5 13 13 13 13 5:** //7L2s MOS// (Superdiatonic 1/13-tone 13;5 relation)
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| || **13/101** || **154.455** ||
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| || **26/101** || **308.911** ||
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| || 39/101 || 463.366 ||
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| || **44/101** || **522.772** ||
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| || **57/101** || **677.228** ||
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| || **70/101** || **831.683** ||
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| || **83/101** || **986.139** ||
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| || 96/101 || 1045.545 ||
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| **10 10 7 10 10 10 7 10 10 10 7:** //8L3s MOS// (Improper Sensi-11)
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| || **10/101** || **118.812** ||
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| || 20/101 || 237.624 ||
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| || **27/101** || **320.792** ||
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| || **37/101** || **439.604** ||
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| || **47/101** || **558.416** ||
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| || 57/101 || 677.228 ||
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| || **64/101** || **760.396** ||
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| || **74/101** || **879.218** ||
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| || **84/101** || **998.03** ||
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| || 94/101 || 1116.842 ||
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| **7 7 7 8 7 7 7 7 8 7 7 7 7 8:** //3L11s MOS// (Anti-Ketradektriatoh form)
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| =Links= | | == Scales == |
| [[http://tech.groups.yahoo.com/group/tuning-math/message/11157|The Ellis duodene in 101-equal]]</pre></div>
| | === Mos scales === |
| <h4>Original HTML content:</h4>
| | * 3L 2s: 25 13 25 25 13 ((25 38 63 88 101)\101){{clarify}} <!-- why is this significant? --> |
| <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>101edo</title></head><body><strong><em>101-EDO</em></strong> divides the <a class="wiki_link" href="/octave">octave</a> into 101 equal parts of 11.881 <a class="wiki_link" href="/cent">cent</a>s each. It can be used to tune the <a class="wiki_link" href="/Schismatic%20family">grackle temperament</a>. It is the 26th <a class="wiki_link" href="/prime%20numbers">prime</a> edo. The 101cd val provides an excellent tuning for <a class="wiki_link" href="/Magic%20family#Witchcraft">witchcraft temperament</a>, falling between the 13 and 15 limit least squares tuning.<br />
| | * Grackle[7] 5L 2s: 17 17 8 17 17 17 8 ((17 34 42 59 76 93)\101) |
| <br />
| | * Pine 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101) |
| <a class="wiki_link" href="/5-limit">5-limit</a> commas: 32805/32768, &lt;5 13 -11|<br />
| | * Superdiatonic 1/13-tone 13;5 relation: 13 13 13 5 13 13 13 13 5 ((13 26 39 44 57 70 83 96 101)\101) |
| <br />
| | * Sensi[11] 8L 3s: 10 10 7 10 10 10 7 10 10 10 7 ((10 20 27 37 47 57 64 74 84 94)\101){{clarify}} <!-- which val? --> |
| <a class="wiki_link" href="/7-limit">7-limit</a> commas: 126/125, 32805/32768, 2430/2401<br />
| | * Anti-Ketradektriatoh 3L 11s: 7 7 7 8 7 7 7 7 8 7 7 7 7 8 ((7 14 22 29 36 43 50 58 65 72 79 86 93 101)\101) |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Some important MOS scales:"></a><!-- ws:end:WikiTextHeadingRule:0 --><u>Some important MOS scales:</u></h2>
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| <br />
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| <strong>25 13 25 25 13:</strong> <em>3L2s MOS</em> (Pentatonic)<br />
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| | == Instruments == |
| | * [[Lumatone mapping for 101edo]] |
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|
| <table class="wiki_table">
| | == Music == |
| <tr>
| | ; [[Francium]] |
| <td>25/101<br />
| | * "Eggclent" from ''Eggs'' (2025) – [https://open.spotify.com/track/4S0BTeb9yDdMUuT1QJy26H Spotify] | [https://francium223.bandcamp.com/track/eggclent Bandcamp] | [https://www.youtube.com/watch?v=FAe4O71Mvj0 YouTube] |
| </td>
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| <td>297.03<br />
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| </td>
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| </tr>
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| <tr>
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| <td>38/101<br />
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| </td>
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| <td>451.485<br />
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| </td>
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| </tr>
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| <tr>
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| <td>63/101<br />
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| </td>
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| <td>748.515<br />
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| </td>
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| </tr>
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| <tr>
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| <td>88/101<br />
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| </td>
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| <td>1045.545<br />
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| </td>
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| </tr>
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| </table>
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|
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| <strong>17 17 8 17 17 17 8:</strong> <em>5L2s MOS</em> (Diatonic Pythagorean)<br />
| | == External links == |
| | * [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}} |
|
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|
| | | [[Category:Armodue]] |
| <table class="wiki_table">
| | [[Category:Grackle]] |
| <tr>
| |
| <td><strong>17/101</strong><br />
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| </td>
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| <td><strong>201.98</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td>34/101<br />
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| </td>
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| <td>403.96<br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>42/101</strong><br />
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| </td>
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| <td><strong>499.01</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>59/101</strong><br />
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| </td>
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| <td><strong>700.99</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>76/101</strong><br />
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| </td>
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| <td><strong>902.97</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td>93/101<br />
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| </td>
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| <td>1104.95<br />
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| </td>
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| </tr>
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| </table>
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| | |
| <strong>13 13 13 13 13 13 13 10:</strong> <em>7L1s MOS</em> (Grumpy Octatonic)<br />
| |
| | |
| | |
| <table class="wiki_table">
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| <tr>
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| <td>13/101<br />
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| </td>
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| <td>154.455<br />
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| </td>
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| </tr>
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| <tr>
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| <td>26/101<br />
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| </td>
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| <td>308.911<br />
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| </td>
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| </tr>
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| <tr>
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| <td>39/101<br />
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| </td>
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| <td>463.366<br />
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| </td>
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| </tr>
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| <tr>
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| <td>52/101<br />
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| </td>
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| <td>617.822<br />
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| </td>
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| </tr>
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| <tr>
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| <td>65/101<br />
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| </td>
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| <td>772.277<br />
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| </td>
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| </tr>
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| <tr>
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| <td>78/101<br />
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| </td>
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| <td>926.733<br />
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| </td>
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| </tr>
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| <tr>
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| <td>91/101<br />
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| </td>
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| <td>1081.188<br />
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| </td>
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| </tr>
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| </table>
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| | |
| <strong>13 13 13 5 13 13 13 13 5:</strong> <em>7L2s MOS</em> (Superdiatonic 1/13-tone 13;5 relation)<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
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| <td><strong>13/101</strong><br />
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| </td>
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| <td><strong>154.455</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>26/101</strong><br />
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| </td>
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| <td><strong>308.911</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td>39/101<br />
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| </td>
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| <td>463.366<br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>44/101</strong><br />
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| </td>
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| <td><strong>522.772</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>57/101</strong><br />
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| </td>
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| <td><strong>677.228</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>70/101</strong><br />
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| </td>
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| <td><strong>831.683</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>83/101</strong><br />
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| </td>
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| <td><strong>986.139</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td>96/101<br />
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| </td>
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| <td>1045.545<br />
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| </td>
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| </tr>
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| </table>
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| | |
| <strong>10 10 7 10 10 10 7 10 10 10 7:</strong> <em>8L3s MOS</em> (Improper Sensi-11)<br />
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| | |
| | |
| <table class="wiki_table">
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| <tr>
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| <td><strong>10/101</strong><br />
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| </td>
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| <td><strong>118.812</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td>20/101<br />
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| </td>
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| <td>237.624<br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>27/101</strong><br />
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| </td>
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| <td><strong>320.792</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>37/101</strong><br />
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| </td>
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| <td><strong>439.604</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>47/101</strong><br />
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| </td>
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| <td><strong>558.416</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td>57/101<br />
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| </td>
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| <td>677.228<br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>64/101</strong><br />
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| </td>
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| <td><strong>760.396</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>74/101</strong><br />
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| </td>
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| <td><strong>879.218</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td><strong>84/101</strong><br />
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| </td>
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| <td><strong>998.03</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td>94/101<br />
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| </td>
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| <td>1116.842<br />
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| </td>
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| </tr>
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| </table>
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| <strong>7 7 7 8 7 7 7 7 8 7 7 7 7 8:</strong> <em>3L11s MOS</em> (Anti-Ketradektriatoh form)<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:2 -->Links</h1>
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| <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/11157" rel="nofollow">The Ellis duodene in 101-equal</a></body></html></pre></div>
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