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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The mirkwai family of [[Planar_Temperament|planar temperament]]s tempers out the mirkwai comma, 16875/16807.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-23 17:54:47 UTC</tt>.<br>
: The original revision id was <tt>267688398</tt>.<br>
: The revision comment was: <tt></tt><br>
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">[[toc]]
 
 
The mirkwai family of [[planar temperament]]s tempers out the mirkwai comma, 16875/16807.


=Vital statistics=
=Vital statistics=
[[Comma]]: mirkwai 16875/16807
[[Comma|Comma]]: mirkwai 16875/16807


7-limit minimax
7-limit minimax
[|1 0 0 0&gt;, |0 4/7 -4/7 5/7&gt;,  
[|1 0 0 0&gt;, |0 4/7 -4/7 5/7&gt;,  
|0 -3/7 3/7 5/7&gt;, |0 0 0 1&gt;]
|0 -3/7 3/7 5/7&gt;, |0 0 0 1&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 8/7, 6/5
[[Eigenmonzo|Eigenmonzos]]: 2, 8/7, 6/5


9-limit minimax
9-limit minimax
[|1 0 0 0&gt;, |0 8/11 -4/11 5/11&gt;,  
[|1 0 0 0&gt;, |0 8/11 -4/11 5/11&gt;,  
|0 -6/11 3/11 10/11&gt;, |0 0 0 1&gt;]
|0 -6/11 3/11 10/11&gt;, |0 0 0 1&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 8/7
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 8/7


Map: [&lt;1 0 0 0|, &lt;0 1 3 3|, &lt;0 0 -5 -4|]
Map: [&lt;1 0 0 0|, &lt;0 1 3 3|, &lt;0 0 -5 -4|]
[[Generator|Generators]]: 2, 3, 7/5
 
[[edo|Edos]]: [[72edo|72]], [[152edo|152]], [[193edo|193]], [[224edo|224]], [[296edo|296]], [[327edo|327]], [[775edo|775]]
[[generator|Generators]]: 2, 3, 7/5
 
[[EDO|Edos]]: [[72edo|72]], [[152edo|152]], [[193edo|193]], [[224edo|224]], [[296edo|296]], [[327edo|327]], [[775edo|775]]
 
Badness: 0.000342
Badness: 0.000342


[[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5
[[Projection_pair|Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5


=Indra=
=Indra=
[[Comma|Commas]]: 540/539, 1375/1372
[[Comma|Commas]]: 540/539, 1375/1372


[[Minimax tuning]]
[[Minimax_tuning|Minimax tuning]]
 
[|1 0 0 0 0&gt;, |10 10 -3 0 -5&gt;, |0 0 1 0 0&gt;,  
[|1 0 0 0 0&gt;, |10 10 -3 0 -5&gt;, |0 0 1 0 0&gt;,  
|6 6 -1 0 -3&gt;, |20 18 -6 0 -9&gt;]
|6 6 -1 0 -3&gt;, |20 18 -6 0 -9&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 5/4
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 5/4


Lattice basis: 15/14 length 0.6184 55/36 length 0.7585
Lattice basis: 15/14 length 0.6184 55/36 length 0.7585
Angle(15/14, 55/36) = 68.1048 cents
Angle(15/14, 55/36) = 68.1048 cents
Map to lattice: [&lt;0 2 1 2 3|, &lt;0 -1 2 1 -3|]
Map to lattice: [&lt;0 2 1 2 3|, &lt;0 -1 2 1 -3|]


Map: [&lt;1 0 0 0 2|, &lt;0 1 3 3 0|, &lt;0 0 -5 -4 3|]
Map: [&lt;1 0 0 0 2|, &lt;0 1 3 3 0|, &lt;0 0 -5 -4 3|]
[[Generator|Generators]]: 2, 3, 7/5
 
[[edo|Edos]]: 31, 41, [[72edo|72]], [[152edo|152]], [[224edo|224]], [[296edo|296]], [[703edo|703]]
[[generator|Generators]]: 2, 3, 7/5
 
[[EDO|Edos]]: 31, 41, [[72edo|72]], [[152edo|152]], [[224edo|224]], [[296edo|296]], [[703edo|703]]
 
Badness: 0.000266
Badness: 0.000266


[[Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5
[[Projection_pair|Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5


Scales: [[indra31]]
Scales: [[indra31|indra31]]


==Shibi==
==Shibi==
Line 56: Line 61:


Map: [&lt;1 0 0 0 2 -4 -3|, &lt;0 1 3 3 0 11 3|, &lt;0 0 -5 -4 3 4|]
Map: [&lt;1 0 0 0 2 -4 -3|, &lt;0 1 3 3 0 11 3|, &lt;0 0 -5 -4 3 4|]
EDOs: 41, 72, 111, 183, 224, 703
EDOs: 41, 72, 111, 183, 224, 703
Badness: 0.000721
Badness: 0.000721


Line 63: Line 70:


13-limit minimax
13-limit minimax
[|1 0 0 0 0 0&gt;, |4/5 6/5 -4/5 0 0 1/5&gt;,  
[|1 0 0 0 0 0&gt;, |4/5 6/5 -4/5 0 0 1/5&gt;,  
|8/5 2/5 -3/5 0 0 2/5&gt;,  
|8/5 2/5 -3/5 0 0 2/5&gt;,  
Line 68: Line 76:
|62/25 48/25 -27/25 0 0 3/25&gt;,  
|62/25 48/25 -27/25 0 0 3/25&gt;,  
|8/5 2/5 -8/5 0 0 7/5&gt;]
|8/5 2/5 -8/5 0 0 7/5&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/10
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/10


15-limit minimax
15-limit minimax
[|1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;,  
[|1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;,  
|5/4 1/2 0 -5/16 0 5/16&gt;,
|5/4 1/2 0 -5/16 0 5/16&gt;,
Line 76: Line 86:
|5/4 3/2 0 3/16 0 -3/16&gt;,  
|5/4 3/2 0 3/16 0 -3/16&gt;,  
|1 1 0 -5/4 0 5/4&gt;]
|1 1 0 -5/4 0 5/4&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 14/13, 4/3
[[Eigenmonzo|Eigenmonzos]]: 2, 14/13, 4/3


Map: [&lt;1 0 0 0 2 -4|, &lt;0 1 3 3 0 11|, &lt;0 0 -5 -4 3 -20|]
Map: [&lt;1 0 0 0 2 -4|, &lt;0 1 3 3 0 11|, &lt;0 0 -5 -4 3 -20|]
[[Generator|Generators]]: 2, 3, 7/5
 
[[edo|Edos]]: [[31edo|31]], [[72edo|72]], [[103edo|103]], [[193edo|193]], 224, 296, 520, 703
[[generator|Generators]]: 2, 3, 7/5
 
[[EDO|Edos]]: [[31edo|31]], [[72edo|72]], [[103edo|103]], [[193edo|193]], 224, 296, 520, 703
 
Badness: 0.000700
Badness: 0.000700


Line 87: Line 101:


Map: [&lt;1 0 0 0 2 1|, &lt;0 1 3 3 0 6|, &lt;0 0 -5 -4 3 -14|]
Map: [&lt;1 0 0 0 2 1|, &lt;0 1 3 3 0 6|, &lt;0 0 -5 -4 3 -14|]
EDOs: 31, 72, 103, 111, 152, 183
EDOs: 31, 72, 103, 111, 152, 183
Badness: 0.000826
Badness: 0.000826


Line 94: Line 110:


Map: [&lt;1 0 0 0 2 2], &lt;0 1 3 3 0 -2], &lt;0 0 -5 -4 3 10|]
Map: [&lt;1 0 0 0 2 2], &lt;0 1 3 3 0 -2], &lt;0 0 -5 -4 3 10|]
EDOs: 41, 72, 121, 193
EDOs: 41, 72, 121, 193
Badness: 0.000930</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000930
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Mirkwai family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Vital statistics"&gt;Vital statistics&lt;/a&gt;&lt;/div&gt;
[[Category:family]]
&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Indra"&gt;Indra&lt;/a&gt;&lt;/div&gt;
[[Category:mirkwai]]
&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Indra-Shibi"&gt;Shibi&lt;/a&gt;&lt;/div&gt;
[[Category:theory]]
&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Indra-Yajna"&gt;Yajna&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Indra-Vibhu"&gt;Vibhu&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Indra-Vish"&gt;Vish&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
&lt;br /&gt;
The mirkwai family of &lt;a class="wiki_link" href="/planar%20temperament"&gt;planar temperament&lt;/a&gt;s tempers out the mirkwai comma, 16875/16807.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Vital statistics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Vital statistics&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: mirkwai 16875/16807&lt;br /&gt;
&lt;br /&gt;
7-limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 4/7 -4/7 5/7&amp;gt;, &lt;br /&gt;
|0 -3/7 3/7 5/7&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 8/7, 6/5&lt;br /&gt;
&lt;br /&gt;
9-limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 8/11 -4/11 5/11&amp;gt;, &lt;br /&gt;
|0 -6/11 3/11 10/11&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 10/9, 8/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0|, &amp;lt;0 1 3 3|, &amp;lt;0 0 -5 -4|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 7/5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/152edo"&gt;152&lt;/a&gt;, &lt;a class="wiki_link" href="/193edo"&gt;193&lt;/a&gt;, &lt;a class="wiki_link" href="/224edo"&gt;224&lt;/a&gt;, &lt;a class="wiki_link" href="/296edo"&gt;296&lt;/a&gt;, &lt;a class="wiki_link" href="/327edo"&gt;327&lt;/a&gt;, &lt;a class="wiki_link" href="/775edo"&gt;775&lt;/a&gt;&lt;br /&gt;
Badness: 0.000342&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 5 84375/16807 7 16875/2401 to 2.3.7/5&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Indra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Indra&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 540/539, 1375/1372&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |10 10 -3 0 -5&amp;gt;, |0 0 1 0 0&amp;gt;, &lt;br /&gt;
|6 6 -1 0 -3&amp;gt;, |20 18 -6 0 -9&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/9, 5/4&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 15/14 length 0.6184 55/36 length 0.7585&lt;br /&gt;
Angle(15/14, 55/36) = 68.1048 cents&lt;br /&gt;
Map to lattice: [&amp;lt;0 2 1 2 3|, &amp;lt;0 -1 2 1 -3|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 2|, &amp;lt;0 1 3 3 0|, &amp;lt;0 0 -5 -4 3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 7/5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 31, 41, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/152edo"&gt;152&lt;/a&gt;, &lt;a class="wiki_link" href="/224edo"&gt;224&lt;/a&gt;, &lt;a class="wiki_link" href="/296edo"&gt;296&lt;/a&gt;, &lt;a class="wiki_link" href="/703edo"&gt;703&lt;/a&gt;&lt;br /&gt;
Badness: 0.000266&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/indra31"&gt;indra31&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Indra-Shibi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Shibi&lt;/h2&gt;
Commas: 540/539, 729/728, 1375/1372&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 2 -4 -3|, &amp;lt;0 1 3 3 0 11 3|, &amp;lt;0 0 -5 -4 3 4|]&lt;br /&gt;
EDOs: 41, 72, 111, 183, 224, 703&lt;br /&gt;
Badness: 0.000721&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Indra-Yajna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Yajna&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 540/539, 625/624, 1375/1372&lt;br /&gt;
&lt;br /&gt;
13-limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |4/5 6/5 -4/5 0 0 1/5&amp;gt;, &lt;br /&gt;
|8/5 2/5 -3/5 0 0 2/5&amp;gt;, &lt;br /&gt;
|44/25 26/25 -24/25 0 0 11/25&amp;gt;, &lt;br /&gt;
|62/25 48/25 -27/25 0 0 3/25&amp;gt;, &lt;br /&gt;
|8/5 2/5 -8/5 0 0 7/5&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 10/9, 13/10&lt;br /&gt;
&lt;br /&gt;
15-limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |0 1 0 0 0 0&amp;gt;, &lt;br /&gt;
|5/4 1/2 0 -5/16 0 5/16&amp;gt;,&lt;br /&gt;
|1 1 0 -1/4 0 1/4&amp;gt;, &lt;br /&gt;
|5/4 3/2 0 3/16 0 -3/16&amp;gt;, &lt;br /&gt;
|1 1 0 -5/4 0 5/4&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 14/13, 4/3&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 2 -4|, &amp;lt;0 1 3 3 0 11|, &amp;lt;0 0 -5 -4 3 -20|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 7/5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/103edo"&gt;103&lt;/a&gt;, &lt;a class="wiki_link" href="/193edo"&gt;193&lt;/a&gt;, 224, 296, 520, 703&lt;br /&gt;
Badness: 0.000700&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Indra-Vibhu"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Vibhu&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 540/539, 1375/1372, 351/350&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 2 1|, &amp;lt;0 1 3 3 0 6|, &amp;lt;0 0 -5 -4 3 -14|]&lt;br /&gt;
EDOs: 31, 72, 103, 111, 152, 183&lt;br /&gt;
Badness: 0.000826&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Indra-Vish"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Vish&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 325/324, 364/363, 540/539&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 2 2], &amp;lt;0 1 3 3 0 -2], &amp;lt;0 0 -5 -4 3 10|]&lt;br /&gt;
EDOs: 41, 72, 121, 193&lt;br /&gt;
Badness: 0.000930&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The mirkwai family of planar temperaments tempers out the mirkwai comma, 16875/16807.

Vital statistics

Comma: mirkwai 16875/16807

7-limit minimax

[|1 0 0 0>, |0 4/7 -4/7 5/7>, |0 -3/7 3/7 5/7>, |0 0 0 1>]

Eigenmonzos: 2, 8/7, 6/5

9-limit minimax

[|1 0 0 0>, |0 8/11 -4/11 5/11>, |0 -6/11 3/11 10/11>, |0 0 0 1>]

Eigenmonzos: 2, 10/9, 8/7

Map: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]

Generators: 2, 3, 7/5

Edos: 72, 152, 193, 224, 296, 327, 775

Badness: 0.000342

Projection pairs: 5 84375/16807 7 16875/2401 to 2.3.7/5

Indra

Commas: 540/539, 1375/1372

Minimax tuning

[|1 0 0 0 0>, |10 10 -3 0 -5>, |0 0 1 0 0>, |6 6 -1 0 -3>, |20 18 -6 0 -9>]

Eigenmonzos: 2, 11/9, 5/4

Lattice basis: 15/14 length 0.6184 55/36 length 0.7585

Angle(15/14, 55/36) = 68.1048 cents

Map to lattice: [<0 2 1 2 3|, <0 -1 2 1 -3|]

Map: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|]

Generators: 2, 3, 7/5

Edos: 31, 41, 72, 152, 224, 296, 703

Badness: 0.000266

Projection pairs: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5

Scales: indra31

Shibi

Commas: 540/539, 729/728, 1375/1372

Map: [<1 0 0 0 2 -4 -3|, <0 1 3 3 0 11 3|, <0 0 -5 -4 3 4|]

EDOs: 41, 72, 111, 183, 224, 703

Badness: 0.000721

Yajna

Commas: 540/539, 625/624, 1375/1372

13-limit minimax

[|1 0 0 0 0 0>, |4/5 6/5 -4/5 0 0 1/5>, |8/5 2/5 -3/5 0 0 2/5>, |44/25 26/25 -24/25 0 0 11/25>, |62/25 48/25 -27/25 0 0 3/25>, |8/5 2/5 -8/5 0 0 7/5>]

Eigenmonzos: 2, 10/9, 13/10

15-limit minimax

[|1 0 0 0 0 0>, |0 1 0 0 0 0>, |5/4 1/2 0 -5/16 0 5/16>, |1 1 0 -1/4 0 1/4>, |5/4 3/2 0 3/16 0 -3/16>, |1 1 0 -5/4 0 5/4>]

Eigenmonzos: 2, 14/13, 4/3

Map: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|]

Generators: 2, 3, 7/5

Edos: 31, 72, 103, 193, 224, 296, 520, 703

Badness: 0.000700

Vibhu

Commas: 540/539, 1375/1372, 351/350

Map: [<1 0 0 0 2 1|, <0 1 3 3 0 6|, <0 0 -5 -4 3 -14|]

EDOs: 31, 72, 103, 111, 152, 183

Badness: 0.000826

Vish

Commas: 325/324, 364/363, 540/539

Map: [<1 0 0 0 2 2], <0 1 3 3 0 -2], <0 0 -5 -4 3 10|]

EDOs: 41, 72, 121, 193

Badness: 0.000930

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