Hemimage family: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 247451161 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
===Vital statistics===
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
[[Comma|Comma]]: hemimage 10976/10935
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-21 17:06:48 UTC</tt>.<br>
: The original revision id was <tt>247451161</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]]: hemimage 10976/10935


7-limit minimax
7-limit minimax
[|1 0 0 0&gt;, |5/8 1/8 -1/8 3/8&gt;,  
[|1 0 0 0&gt;, |5/8 1/8 -1/8 3/8&gt;,  
|5/8 -7/8 7/8 3/8&gt;, |0 0 0 1&gt;]
|5/8 -7/8 7/8 3/8&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;, |5/9 2/9 -1/9 1/3&gt;,  
[|1 0 0 0&gt;, |5/9 2/9 -1/9 1/3&gt;,  
|10/9 -14/9 7/9 2/3&gt;, |0 0 0 1&gt;]
|10/9 -14/9 7/9 2/3&gt;, |0 0 0 1&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 8/7
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 8/7


Map: [&lt;1 0 2 -1|, &lt;0 1 2 3|, &lt;0 0 -3 -1|]
Map: [&lt;1 0 2 -1|, &lt;0 1 2 3|, &lt;0 0 -3 -1|]
[[Generator|Generators]]: 2, 3, 27/14
 
[[edo|Edos]]: 14, 19, 41, 58, 77, 80, [[99edo|99]], [[118edo|118]], [[140edo|140]], [[217edo|217]], [[316edo|316]], [[338edo|338]], [[357edo|357]], [[415edo|415]], [[456edo|456]], [[654edo|654]], [[695edo|695]]
[[generator|Generators]]: 2, 3, 27/14
 
[[EDO|Edos]]: 14, 19, 41, 58, 77, 80, [[99edo|99]], [[118edo|118]], [[140edo|140]], [[217edo|217]], [[316edo|316]], [[338edo|338]], [[357edo|357]], [[415edo|415]], [[456edo|456]], [[654edo|654]], [[695edo|695]]
 
Badness: 0.000199
Badness: 0.000199


[[Projection pair]]: 5 10976/2187 to 2.3.7
[[Projection_pair|Projection pair]]: 5 10976/2187 to 2.3.7


==Uni==
==Uni==
[[Comma|Commas]]: 540/539, 896/891
[[Comma|Commas]]: 540/539, 896/891


[[Minimax tuning]]
[[Minimax_tuning|Minimax tuning]]
 
[|1 0 0 0 0&gt;, |16/11 6/11 1/11 0 -3/11&gt;,  
[|1 0 0 0 0&gt;, |16/11 6/11 1/11 0 -3/11&gt;,  
|0 0 1 0 0&gt;, |19/11 14/11 6/11 0 -7/11&gt;,  
|0 0 1 0 0&gt;, |19/11 14/11 6/11 0 -7/11&gt;,  
|32/11 -10/11 2/11 0 5/11&gt;]
|32/11 -10/11 2/11 0 5/11&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 5/4
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 5/4


Map: [&lt;1 0 2 -1 6|, &lt;0 1 2 3 -1|, &lt;0 0 -3 -1 -1|]
Map: [&lt;1 0 2 -1 6|, &lt;0 1 2 3 -1|, &lt;0 0 -3 -1 -1|]
[[Generator|Generators]]: 2, 3, 27/14
 
[[edo|Edos]]: [[19edo|19]], [[22edo|22]], [[41edo|41]], [[58edo|58]], [[80edo|80]], [[121edo|121]]
[[generator|Generators]]: 2, 3, 27/14
 
[[EDO|Edos]]: [[19edo|19]], [[22edo|22]], [[41edo|41]], [[58edo|58]], [[80edo|80]], [[121edo|121]]
 
Badness: 0.000702
Badness: 0.000702


Line 44: Line 49:


Map: [&lt;1 0 2 -1 6 11|, &lt;0 1 2 3 -1 -4|, &lt;0 0 -3 -1 -1 -1|]
Map: [&lt;1 0 2 -1 6 11|, &lt;0 1 2 3 -1 -4|, &lt;0 0 -3 -1 -1 -1|]
EDOs: 22, 41, 58, 80, 121
EDOs: 22, 41, 58, 80, 121
Badness: 0.00106
Badness: 0.00106


Line 51: Line 58:


Map: [&lt;1 0 2 -1 6 -2|, &lt;0 1 2 3 -1 3|, &lt;0 0 -3 -1 -1 1|]
Map: [&lt;1 0 2 -1 6 -2|, &lt;0 1 2 3 -1 3|, &lt;0 0 -3 -1 -1 1|]
EDOs: 19, 36, 41, 58
EDOs: 19, 36, 41, 58
Badness: 0.00107
Badness: 0.00107


Line 57: Line 66:
[[Comma|Commas]]: 10976/10935, 441/440
[[Comma|Commas]]: 10976/10935, 441/440


[[Minimax tuning]]
[[Minimax_tuning|Minimax tuning]]
 
[|1 0 0 0 0&gt;, |19/12 -2/3 1/12 0 1/4&gt;,  
[|1 0 0 0 0&gt;, |19/12 -2/3 1/12 0 1/4&gt;,  
|19/6 -10/3 7/6 0 1/2&gt;,  
|19/6 -10/3 7/6 0 1/2&gt;,  
|37/12 -8/3 7/12 0 3/4&gt;,  
|37/12 -8/3 7/12 0 3/4&gt;,  
|19/6 -10/3 1/6 0 3/2&gt;]
|19/6 -10/3 1/6 0 3/2&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 11/9
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 11/9


Map: [&lt;1 0 2 -1 -7|, &lt;0 1 2 3 6|, &lt;0 0 -3 -1 1|]
Map: [&lt;1 0 2 -1 -7|, &lt;0 1 2 3 6|, &lt;0 0 -3 -1 1|]
[[Generator|Generators]]: 2, 3, 27/14
 
[[edo|Edos]]: [[41edo|41]], [[58edo|58]], [[118edo|118]], [[159edo|159]], [[217edo|217]], [[335edo|335]]
[[generator|Generators]]: 2, 3, 27/14
Badness: 0.000936</pre></div>
 
<h4>Original HTML content:</h4>
[[EDO|Edos]]: [[41edo|41]], [[58edo|58]], [[118edo|118]], [[159edo|159]], [[217edo|217]], [[335edo|335]]
<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;Hemimage 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;: hemimage 10976/10935&lt;br /&gt;
Badness: 0.000936
&lt;br /&gt;
[[Category:family]]
7-limit minimax&lt;br /&gt;
[[Category:hemimage]]
[|1 0 0 0&amp;gt;, |5/8 1/8 -1/8 3/8&amp;gt;, &lt;br /&gt;
[[Category:theory]]
|5/8 -7/8 7/8 3/8&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;, |5/9 2/9 -1/9 1/3&amp;gt;, &lt;br /&gt;
|10/9 -14/9 7/9 2/3&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 2 -1|, &amp;lt;0 1 2 3|, &amp;lt;0 0 -3 -1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 27/14&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 14, 19, 41, 58, 77, 80, &lt;a class="wiki_link" href="/99edo"&gt;99&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/217edo"&gt;217&lt;/a&gt;, &lt;a class="wiki_link" href="/316edo"&gt;316&lt;/a&gt;, &lt;a class="wiki_link" href="/338edo"&gt;338&lt;/a&gt;, &lt;a class="wiki_link" href="/357edo"&gt;357&lt;/a&gt;, &lt;a class="wiki_link" href="/415edo"&gt;415&lt;/a&gt;, &lt;a class="wiki_link" href="/456edo"&gt;456&lt;/a&gt;, &lt;a class="wiki_link" href="/654edo"&gt;654&lt;/a&gt;, &lt;a class="wiki_link" href="/695edo"&gt;695&lt;/a&gt;&lt;br /&gt;
Badness: 0.000199&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;: 5 10976/2187 to 2.3.7&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-Uni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Uni&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 540/539, 896/891&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;, |16/11 6/11 1/11 0 -3/11&amp;gt;, &lt;br /&gt;
|0 0 1 0 0&amp;gt;, |19/11 14/11 6/11 0 -7/11&amp;gt;, &lt;br /&gt;
|32/11 -10/11 2/11 0 5/11&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;
Map: [&amp;lt;1 0 2 -1 6|, &amp;lt;0 1 2 3 -1|, &amp;lt;0 0 -3 -1 -1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 27/14&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;, &lt;a class="wiki_link" href="/80edo"&gt;80&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo"&gt;121&lt;/a&gt;&lt;br /&gt;
Badness: 0.000702&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Uni-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h3&gt;
Commas: 352/351, 364/363, 540/539&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 2 -1 6 11|, &amp;lt;0 1 2 3 -1 -4|, &amp;lt;0 0 -3 -1 -1 -1|]&lt;br /&gt;
EDOs: 22, 41, 58, 80, 121&lt;br /&gt;
Badness: 0.00106&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Uni-Tin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Tin&lt;/h3&gt;
Commas: 144/143, 196/195, 729/728&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 2 -1 6 -2|, &amp;lt;0 1 2 3 -1 3|, &amp;lt;0 0 -3 -1 -1 1|]&lt;br /&gt;
EDOs: 19, 36, 41, 58&lt;br /&gt;
Badness: 0.00107&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="x-Turan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Turan&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 10976/10935, 441/440&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;, |19/12 -2/3 1/12 0 1/4&amp;gt;, &lt;br /&gt;
|19/6 -10/3 7/6 0 1/2&amp;gt;, &lt;br /&gt;
|37/12 -8/3 7/12 0 3/4&amp;gt;, &lt;br /&gt;
|19/6 -10/3 1/6 0 3/2&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 10/9, 11/9&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 2 -1 -7|, &amp;lt;0 1 2 3 6|, &amp;lt;0 0 -3 -1 1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 27/14&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/217edo"&gt;217&lt;/a&gt;, &lt;a class="wiki_link" href="/335edo"&gt;335&lt;/a&gt;&lt;br /&gt;
Badness: 0.000936&lt;/body&gt;&lt;/html&gt;</pre></div>