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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | #redirect [[Miscellaneous 7-limit temperaments #Canopic a.k.a. mirkwai]] |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-22 13:35:31 UTC</tt>.<br>
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| : The original revision id was <tt>247712219</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">[[toc|flat]]
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| The mirkwai family of [[planar temperament]]s tempers out the mirkwai comma, 16875/16807.
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| =Vital statistics=
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| [[Comma]]: mirkwai 16875/16807
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| 7-limit minimax
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| [|1 0 0 0>, |0 4/7 -4/7 5/7>,
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| |0 -3/7 3/7 5/7>, |0 0 0 1>]
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| [[Eigenmonzo|Eigenmonzos]]: 2, 8/7, 6/5
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| 9-limit minimax
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| [|1 0 0 0>, |0 8/11 -4/11 5/11>,
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| |0 -6/11 3/11 10/11>, |0 0 0 1>]
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| [[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 8/7
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| Map: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]
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| [[Generator|Generators]]: 2, 3, 7/5
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| [[edo|Edos]]: [[72edo|72]], [[152edo|152]], [[193edo|193]], [[224edo|224]], [[296edo|296]], [[327edo|327]], [[775edo|775]]
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| Badness: 0.000342
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| [[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5
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| =Indra=
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| [[Comma|Commas]]: 540/539, 1375/1372
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| [[Minimax tuning]]
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| [|1 0 0 0 0>, |10 10 -3 0 -5>, |0 0 1 0 0>,
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| |6 6 -1 0 -3>, |20 18 -6 0 -9>]
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| [[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 5/4
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| Lattice basis: 15/14 length 0.6184 55/36 length 0.7585
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| Angle(15/14, 55/36) = 68.1048 cents
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| Map to lattice: [<0 2 1 2 3|, <0 -1 2 1 -3|]
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| Map: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|]
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| [[Generator|Generators]]: 2, 3, 7/5
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| [[edo|Edos]]: 31, 41, [[72edo|72]], [[152edo|152]], [[224edo|224]], [[296edo|296]], [[703edo|703]]
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| Badness: 0.000266
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| [[Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5
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| Scales: [[indra31]]
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| ==Shibi==
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| Commas: 540/539, 729/728, 1375/1372
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| Map: [<1 0 0 0 2 -4 -3|, <0 1 3 3 0 11 3|, <0 0 -5 -4 3 4|]
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| EDOs: 41, 72, 111, 183, 224, 703
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| Badness: 0.000721
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| ==Yajna==
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| [[Comma|Commas]]: 540/539, 625/624, 1375/1372
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| 13-limit minimax
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| [|1 0 0 0 0 0>, |4/5 6/5 -4/5 0 0 1/5>,
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| |8/5 2/5 -3/5 0 0 2/5>,
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| |44/25 26/25 -24/25 0 0 11/25>,
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| |62/25 48/25 -27/25 0 0 3/25>,
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| |8/5 2/5 -8/5 0 0 7/5>]
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| [[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/10
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| 15-limit minimax
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| [|1 0 0 0 0 0>, |0 1 0 0 0 0>,
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| |5/4 1/2 0 -5/16 0 5/16>,
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| |1 1 0 -1/4 0 1/4>,
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| |5/4 3/2 0 3/16 0 -3/16>,
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| |1 1 0 -5/4 0 5/4>]
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| [[Eigenmonzo|Eigenmonzos]]: 2, 14/13, 4/3
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| Map: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|]
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| [[Generator|Generators]]: 2, 3, 7/5
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| [[edo|Edos]]: [[31edo|31]], [[72edo|72]], [[103edo|103]], [[193edo|193]], 224, 296, 520, 703
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| Badness: 0.000700
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| ==Vibhu==
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| [[Comma|Commas]]: 540/539, 1375/1372, 351/350
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| ==Vish==
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| [[Comma|Commas]]: 540/539, 1375/1372, 325/324
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| </pre></div>
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| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Mirkwai family</title></head><body><!-- ws:start:WikiTextTocRule:12:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Vital statistics">Vital statistics</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Indra">Indra</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: -->
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| <!-- ws:end:WikiTextTocRule:19 --><br />
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| <br />
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| The mirkwai family of <a class="wiki_link" href="/planar%20temperament">planar temperament</a>s tempers out the mirkwai comma, 16875/16807.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h1>
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| <a class="wiki_link" href="/Comma">Comma</a>: mirkwai 16875/16807<br />
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| <br />
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| 7-limit minimax<br />
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| [|1 0 0 0&gt;, |0 4/7 -4/7 5/7&gt;, <br />
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| |0 -3/7 3/7 5/7&gt;, |0 0 0 1&gt;]<br />
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| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 8/7, 6/5<br />
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| <br />
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| 9-limit minimax<br />
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| [|1 0 0 0&gt;, |0 8/11 -4/11 5/11&gt;, <br />
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| |0 -6/11 3/11 10/11&gt;, |0 0 0 1&gt;]<br />
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| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9, 8/7<br />
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| <br />
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| Map: [&lt;1 0 0 0|, &lt;0 1 3 3|, &lt;0 0 -5 -4|]<br />
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| <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 7/5<br />
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| <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/152edo">152</a>, <a class="wiki_link" href="/193edo">193</a>, <a class="wiki_link" href="/224edo">224</a>, <a class="wiki_link" href="/296edo">296</a>, <a class="wiki_link" href="/327edo">327</a>, <a class="wiki_link" href="/775edo">775</a><br />
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| Badness: 0.000342<br />
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| <br />
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| <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 5 84375/16807 7 16875/2401 to 2.3.7/5<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Indra"></a><!-- ws:end:WikiTextHeadingRule:2 -->Indra</h1>
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| <a class="wiki_link" href="/Comma">Commas</a>: 540/539, 1375/1372<br />
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| <br />
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| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br />
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| [|1 0 0 0 0&gt;, |10 10 -3 0 -5&gt;, |0 0 1 0 0&gt;, <br />
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| |6 6 -1 0 -3&gt;, |20 18 -6 0 -9&gt;]<br />
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| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9, 5/4<br />
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| <br />
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| Lattice basis: 15/14 length 0.6184 55/36 length 0.7585<br />
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| Angle(15/14, 55/36) = 68.1048 cents<br />
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| Map to lattice: [&lt;0 2 1 2 3|, &lt;0 -1 2 1 -3|]<br />
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| <br />
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| Map: [&lt;1 0 0 0 2|, &lt;0 1 3 3 0|, &lt;0 0 -5 -4 3|]<br />
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| <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 7/5<br />
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| <a class="wiki_link" href="/edo">Edos</a>: 31, 41, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/152edo">152</a>, <a class="wiki_link" href="/224edo">224</a>, <a class="wiki_link" href="/296edo">296</a>, <a class="wiki_link" href="/703edo">703</a><br />
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| Badness: 0.000266<br />
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| <br />
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| <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5<br />
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| <br />
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| Scales: <a class="wiki_link" href="/indra31">indra31</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Indra-Shibi"></a><!-- ws:end:WikiTextHeadingRule:4 -->Shibi</h2>
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| Commas: 540/539, 729/728, 1375/1372<br />
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| <br />
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| Map: [&lt;1 0 0 0 2 -4 -3|, &lt;0 1 3 3 0 11 3|, &lt;0 0 -5 -4 3 4|]<br />
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| EDOs: 41, 72, 111, 183, 224, 703<br />
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| Badness: 0.000721<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Indra-Yajna"></a><!-- ws:end:WikiTextHeadingRule:6 -->Yajna</h2>
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| <a class="wiki_link" href="/Comma">Commas</a>: 540/539, 625/624, 1375/1372<br />
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| <br />
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| 13-limit minimax<br />
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| [|1 0 0 0 0 0&gt;, |4/5 6/5 -4/5 0 0 1/5&gt;, <br />
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| |8/5 2/5 -3/5 0 0 2/5&gt;, <br />
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| |44/25 26/25 -24/25 0 0 11/25&gt;, <br />
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| |62/25 48/25 -27/25 0 0 3/25&gt;, <br />
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| |8/5 2/5 -8/5 0 0 7/5&gt;]<br />
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| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9, 13/10<br />
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| <br />
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| 15-limit minimax<br />
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| [|1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;, <br />
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| |5/4 1/2 0 -5/16 0 5/16&gt;,<br />
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| |1 1 0 -1/4 0 1/4&gt;, <br />
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| |5/4 3/2 0 3/16 0 -3/16&gt;, <br />
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| |1 1 0 -5/4 0 5/4&gt;]<br />
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| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 14/13, 4/3<br />
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| <br />
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| Map: [&lt;1 0 0 0 2 -4|, &lt;0 1 3 3 0 11|, &lt;0 0 -5 -4 3 -20|]<br />
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| <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 7/5<br />
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| <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/103edo">103</a>, <a class="wiki_link" href="/193edo">193</a>, 224, 296, 520, 703<br />
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| Badness: 0.000700<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Indra-Vibhu"></a><!-- ws:end:WikiTextHeadingRule:8 -->Vibhu</h2>
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| <a class="wiki_link" href="/Comma">Commas</a>: 540/539, 1375/1372, 351/350<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Indra-Vish"></a><!-- ws:end:WikiTextHeadingRule:10 -->Vish</h2>
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| <a class="wiki_link" href="/Comma">Commas</a>: 540/539, 1375/1372, 325/324</body></html></pre></div>
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