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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-04-23 01:26:52 UTC</tt>.<br>
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| : The original revision id was <tt>222374016</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">=<span style="background-color: #000000; color: #c97aff; font-size: 109%;">101 tone equal temperament</span>=
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| //101edo// divides the [[octave]] into 101 equal parts of 11.881 [[cent]]s each. It can be used to tune the [[Schismatic family|grackle temperament]]. | | == 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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| [[5-limit]] commas: 32805/32768, <5 13 -11|
| | === Odd harmonics === |
| | {{Harmonics in equal|101}} |
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| [[7-limit]] commas: 126/125, 32805/32768, 2430/2401 | | === 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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| ==__Some important MOS scales:__== | | == Intervals == |
| | {{Interval table}} |
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| **17 17 8 17 17 17 8:** //5L2s MOS// (Diatonic Pythagorean [Heptadiatonic Mold]) | | == Scales == |
| **13 13 13 13 13 13 13 10:** //7L1s MOS// (Grumpy Octatonic [Octamonatonic Mold]) | | === Mos scales === |
| **13 13 13 5 13 13 13 13 5:** //7L2s MOS// (Armodue-Hornbostel 1/13-tone [Nonadiatonic Mold]) | | * 3L 2s: 25 13 25 25 13 ((25 38 63 88 101)\101){{clarify}} <!-- why is this significant? --> |
| **10 10 7 10 10 10 7 10 10 10 7:** //8L3s MOS// (Improper Sensi-11 [Undecimal Triatonic Mold]) | | * Grackle[7] 5L 2s: 17 17 8 17 17 17 8 ((17 34 42 59 76 93)\101) |
| **7 7 7 8 7 7 7 7 8 7 7 7 7 8:** //3L11s MOS// (Anti-Tetradecimal Triatonic mode)</pre></div> | | * Pine 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101) |
| <h4>Original HTML content:</h4>
| | * 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) |
| <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><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x101 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="background-color: #000000; color: #c97aff; font-size: 109%;">101 tone equal temperament</span></h1>
| | * 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? --> |
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| | * 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) |
| <em>101edo</em> 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>.<br />
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| | == Instruments == |
| <a class="wiki_link" href="/5-limit">5-limit</a> commas: 32805/32768, &lt;5 13 -11|<br />
| | * [[Lumatone mapping for 101edo]] |
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| <a class="wiki_link" href="/7-limit">7-limit</a> commas: 126/125, 32805/32768, 2430/2401<br />
| | == Music == |
| <br />
| | ; [[Francium]] |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x101 tone equal temperament-Some important MOS scales:"></a><!-- ws:end:WikiTextHeadingRule:2 --><u>Some important MOS scales:</u></h2>
| | * "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] |
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| <strong>17 17 8 17 17 17 8:</strong> <em>5L2s MOS</em> (Diatonic Pythagorean [Heptadiatonic Mold])<br />
| | == External links == |
| <strong>13 13 13 13 13 13 13 10:</strong> <em>7L1s MOS</em> (Grumpy Octatonic [Octamonatonic Mold])<br />
| | * [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}} |
| <strong>13 13 13 5 13 13 13 13 5:</strong> <em>7L2s MOS</em> (Armodue-Hornbostel 1/13-tone [Nonadiatonic Mold])<br />
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| <strong>10 10 7 10 10 10 7 10 10 10 7:</strong> <em>8L3s MOS</em> (Improper Sensi-11 [Undecimal Triatonic Mold])<br />
| | [[Category:Armodue]] |
| <strong>7 7 7 8 7 7 7 7 8 7 7 7 7 8:</strong> <em>3L11s MOS</em> (Anti-Tetradecimal Triatonic mode)</body></html></pre></div>
| | [[Category:Grackle]] |