Canopic family: Difference between revisions

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**Imported revision 166482393 - Original comment: **
This family isn't needed, as there's only one extension
Tag: New redirect
 
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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>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-29 14:59:58 UTC</tt>.<br>
: The original revision id was <tt>166482393</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">===Vital statistics===
[[Comma]]: mirkwai 16875/16807
 
7-limit minimax
[|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;]
[[Eigenmonzo|Eigenmonzos]]: 2, 8/7, 6/5
 
9-limit minimax
[|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;]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 8/7
 
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]]
 
==11-limit children==
 
===Indra===
[[Comma|Commas]]: 540/539, 1375/1372
 
[[Minimax tuning]]
[|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;]
[[Eigenmonzo|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: [&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|]
[[Generator|Generators]]: 2, 3, 7/5
[[edo|Edos]]: [[72edo|72]], [[152edo|152]], [[224edo|224]], [[296edo|296]]
 
13-limit
 
====Yajna====
Commas: 540/539, 1375/1372, 625/624
 
13-limit minimax
[|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;,
|44/25 26/25 -24/25 0 0 11/25&gt;,
|62/25 48/25 -27/25 0 0 3/25&gt;,
|8/5 2/5 -8/5 0 0 7/5&gt;]
Eigenmonzos: 2, 10/9, 13/10
 
15-limit minimax
[|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;,
|1 1 0 -1/4 0 1/4&gt;,
|5/4 3/2 0 3/16 0 -3/16&gt;,
|1 1 0 -5/4 0 5/4&gt;]
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|]
Generators: 2, 3, 7/5
Edos: 31, 72, 103, 193, 224, 296, 520
 
====Shibi====
Commas: 540/539, 1375/1372, 729/728
 
====Vibhu====
Commas: 540/539, 1375/1372, 351/350
 
====Vish====
Commas: 540/539, 1375/1372, 325/324
</pre></div>
<h4>Original HTML 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;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:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Vital statistics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Vital statistics&lt;/h3&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;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-11-limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit children&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-11-limit children-Indra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Indra&lt;/h3&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;: &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;br /&gt;
&lt;br /&gt;
13-limit&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc3"&gt;&lt;a name="x-11-limit children-Indra-Yajna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Yajna&lt;/h4&gt;
Commas: 540/539, 1375/1372, 625/624&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;
Eigenmonzos: 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;
Eigenmonzos: 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;
Generators: 2, 3, 7/5&lt;br /&gt;
Edos: 31, 72, 103, 193, 224, 296, 520&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc4"&gt;&lt;a name="x-11-limit children-Indra-Shibi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Shibi&lt;/h4&gt;
Commas: 540/539, 1375/1372, 729/728&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc5"&gt;&lt;a name="x-11-limit children-Indra-Vibhu"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Vibhu&lt;/h4&gt;
Commas: 540/539, 1375/1372, 351/350&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc6"&gt;&lt;a name="x-11-limit children-Indra-Vish"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Vish&lt;/h4&gt;
Commas: 540/539, 1375/1372, 325/324&lt;/body&gt;&lt;/html&gt;</pre></div>

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