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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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-01-03 23:25:32 UTC</tt>.<br>
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| : The original revision id was <tt>289421963</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="color: #006985; font-family: "Times New Roman",Times,serif; font-size: 113%;">131 tone equal temperament</span>=
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| **131-EDO**, or **131-tET**, divides the octave into 131 equal steps of approx. 9.160305 Cents, each one. 131edo is the next [[EDO]], after [[81edo]], on the "Golden Tone System" ([[Das Goldene Tonsystem]]) of Thorvald Kornerup, using the 131b val. The patent val has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out 81/80 it tempers out the immunity comma, 1638400/1594323. In the 7-limit it tempers out 3125/3087 and 245/243, so that it supports [[Sensamagic clan#Bohpier|bophier temperament]].
| | == Theory == |
| | 131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]]. |
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| 131edo is the 32nd [[prime numbers|prime]] EDO. | | 131edo is also notable for having a good approximation to [[natave|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and logarithmic divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[4/3]] (2\7[[EDN|edn]] = 54\131), [[5/4]] (2\9edn = 42\131), [[15/13]] (1\7edn = 27\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction. |
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| __**Some MOS Scales 'enjoyable' in 131-EDO:**__
| | === Odd harmonics === |
| | {{Harmonics in equal|131|columns=15}} |
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| || 33 16 33 33 16 || [[Sub-diatonic Tuning]] (comparable with [[8edo]] and [[99edo]]) ||
| | === Subsets and supersets === |
| || 23 23 8 23 23 23 8 || [[Pytagorean tuning]] (comparable with [[17edo]]) ||
| | 131edo is the 32nd [[prime]] edo, following [[127edo]] and before [[137edo]]. |
| || 21 21 13 21 21 21 13 || [[Meantone tuning]] (comparable with [[50edo]]) ||
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| || 19 12 19 19 12 19 19 12 || [[Father Tuning]] ([Octal Triatonic mold] comparable with [[55edo]]) ||
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| || 18 18 18 18 18 18 18 5 || [[Porcupine Tuning]] (comparable with [[29edo]] and [[80edo]]) ||
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| || 17 17 17 6 17 17 17 17 6 || [[Armodue-Hornbostel Tuning]] (comparable with [[23edo]]) ||
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| || 13 13 9 13 13 13 9 13 13 13 9 || Improper [[Sensi-11 Tuning]] [Undecimal Triatonic mold] ||
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| || 11 11 11 11 11 5 11 11 11 11 11 11 5 || De Vries 13-tone Tuning ||
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| || 10 10 10 7 10 10 10 10 7 10 10 10 10 7 || [[11L 3s|[WITNOTS Tuning]]] [Tetradecimal Triatonic mold] ||
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| || 21 17 21 17 17 21 17 || [[mohaha7]] ||
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| || 4 17 17 17 4 17 17 4 17 17 || [[mohaha10]] ||
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| ==!!!'!!!!'== </pre></div> | | == Scales == |
| <h4>Original HTML content:</h4>
| | === Mos scales === |
| <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>131edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x131 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #006985; font-family: "Times New Roman",Times,serif; font-size: 113%;">131 tone equal temperament</span></h1>
| | {| class="wikitable" |
| <br />
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| <strong>131-EDO</strong>, or <strong>131-tET</strong>, divides the octave into 131 equal steps of approx. 9.160305 Cents, each one. 131edo is the next <a class="wiki_link" href="/EDO">EDO</a>, after <a class="wiki_link" href="/81edo">81edo</a>, on the &quot;Golden Tone System&quot; (<a class="wiki_link" href="/Das%20Goldene%20Tonsystem">Das Goldene Tonsystem</a>) of Thorvald Kornerup, using the 131b val. The patent val has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out 81/80 it tempers out the immunity comma, 1638400/1594323. In the 7-limit it tempers out 3125/3087 and 245/243, so that it supports <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bophier temperament</a>.<br />
| | | 33 16 33 33 16 |
| <br />
| | | [[3L_2s|Pentatonic]] (comparable with [[8edo]] and [[99edo]]) |
| 131edo is the 32nd <a class="wiki_link" href="/prime%20numbers">prime</a> EDO.<br />
| | |- |
| <br />
| | | 23 23 8 23 23 23 8 |
| <u><strong>Some MOS Scales 'enjoyable' in 131-EDO:</strong></u><br />
| | | [[5L_2s|Pythagorean tuning]] (comparable with [[17edo]]) |
| <br />
| | |- |
| | | 21 21 13 21 21 21 13 |
| | | [[5L_2s|Meantone tuning]] (comparable with [[50edo]]) |
| | |- |
| | | 19 12 19 19 12 19 19 12 |
| | | [[5L_3s|Oneirotonic tuning]] (comparable with [[55edo]]) |
| | |- |
| | | 18 18 18 18 18 18 18 5 |
| | | [[7L_1s|Porcupine tuning]] (comparable with [[29edo]] and [[80edo]]) |
| | |- |
| | | 17 17 17 6 17 17 17 17 6 |
| | | [[7L_2s|Superdiatonic tuning]] (comparable with [[23edo]]) |
| | |- |
| | | 16 16 16 16 16 16 16 16 3 |
| | | [[8L 1s|Bohpier tuning]] (comparable with [[41edo]]) |
| | |- |
| | | 13 13 9 13 13 13 9 13 13 13 9 |
| | | [[8L 3s|Sensi-11 Tuning]] |
| | |- |
| | | 11 11 11 11 11 5 11 11 11 11 11 11 5 |
| | | De Vries 13-tone Tuning |
| | |- |
| | | 10 10 10 7 10 10 10 10 7 10 10 10 10 7 |
| | | [[11L_3s|Ketradektriatoh Tuning]] |
| | |- |
| | | 21 17 21 17 17 21 17 |
| | | [[mohaha7]] |
| | |- |
| | | 4 17 17 17 4 17 17 4 17 17 |
| | | [[mohaha10]] |
| | |} |
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| | | [[Category:Bohpier]] |
| <table class="wiki_table">
| | [[Category:Immunity]] |
| <tr>
| | [[Category:Meantone]] |
| <td>33 16 33 33 16<br />
| | [[Category:Golden meantone]] |
| </td>
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| <td><a class="wiki_link" href="/Sub-diatonic%20Tuning">Sub-diatonic Tuning</a> (comparable with <a class="wiki_link" href="/8edo">8edo</a> and <a class="wiki_link" href="/99edo">99edo</a>)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>23 23 8 23 23 23 8<br />
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| </td>
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| <td><a class="wiki_link" href="/Pytagorean%20tuning">Pytagorean tuning</a> (comparable with <a class="wiki_link" href="/17edo">17edo</a>)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>21 21 13 21 21 21 13<br />
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| </td>
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| <td><a class="wiki_link" href="/Meantone%20tuning">Meantone tuning</a> (comparable with <a class="wiki_link" href="/50edo">50edo</a>)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>19 12 19 19 12 19 19 12<br />
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| </td>
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| <td><a class="wiki_link" href="/Father%20Tuning">Father Tuning</a> ([Octal Triatonic mold] comparable with <a class="wiki_link" href="/55edo">55edo</a>)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>18 18 18 18 18 18 18 5<br />
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| </td>
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| <td><a class="wiki_link" href="/Porcupine%20Tuning">Porcupine Tuning</a> (comparable with <a class="wiki_link" href="/29edo">29edo</a> and <a class="wiki_link" href="/80edo">80edo</a>)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>17 17 17 6 17 17 17 17 6<br />
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| </td>
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| <td><a class="wiki_link" href="/Armodue-Hornbostel%20Tuning">Armodue-Hornbostel Tuning</a> (comparable with <a class="wiki_link" href="/23edo">23edo</a>)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>13 13 9 13 13 13 9 13 13 13 9<br />
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| </td>
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| <td>Improper <a class="wiki_link" href="/Sensi-11%20Tuning">Sensi-11 Tuning</a> [Undecimal Triatonic mold]<br />
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| </td>
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| </tr>
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| <tr>
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| <td>11 11 11 11 11 5 11 11 11 11 11 11 5<br />
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| </td>
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| <td>De Vries 13-tone Tuning<br />
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| </td>
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| </tr>
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| <tr>
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| <td>10 10 10 7 10 10 10 10 7 10 10 10 10 7<br />
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| </td>
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| <td><a class="wiki_link" href="/11L%203s">[WITNOTS Tuning</a>] [Tetradecimal Triatonic mold]<br />
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| </td>
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| </tr>
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| <tr>
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| <td>21 17 21 17 17 21 17<br />
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| </td>
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| <td><a class="wiki_link" href="/mohaha7">mohaha7</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>4 17 17 17 4 17 17 4 17 17<br />
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| </td>
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| <td><a class="wiki_link" href="/mohaha10">mohaha10</a><br />
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| </td>
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| </tr>
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| </table>
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x131 tone equal temperament-!!!'!!!!'"></a><!-- ws:end:WikiTextHeadingRule:2 -->!!!'!!!!'</h2>
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| </body></html></pre></div>
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