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Kleismic rank three family: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 166297969 - Original comment: **
Wikispaces>xenwolf
**Imported revision 166519265 - Original comment: some links added**
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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 02:37:51 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-29 17:02:01 UTC</tt>.<br>
: The original revision id was <tt>166297969</tt>.<br>
: The original revision id was <tt>166519265</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>some links added</tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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>
<h4>Original Wikitext content:</h4>
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7 and 9 limit minimax
7 and 9 limit minimax
[|1 0 0 0&gt;, |0 1 0 0&gt;, |1 5/6 0 0&gt;, |0 0 0 1&gt;]
[|1 0 0 0&gt;, |0 1 0 0&gt;, |1 5/6 0 0&gt;, |0 0 0 1&gt;]
Eigenmonzos: 2, 7/6, 4/3
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3


Map: [&lt;1 0 1 0|, &lt;0 6 5 0|, &lt;0 0 0 1|]
Map: [&lt;1 0 1 0|, &lt;0 6 5 0|, &lt;0 0 0 1|]
Generators: 2, 6/5, 7
[[Generator|Generators]]: 2, 6/5, 7
Edos: 15, 19, 23, 34, 53, 68, 72, 87, 121, 125, 140, 212, 333, 405
[[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[23edo|23]], [[34edo|34]], [[53edo|53]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[121edo|121]], [[125edo|125]], [[140edo|140]], [[212edo|212]], 333, 405


===Enlil===
===Enlil===
Commas: 15625/15552, 385/384
[[Comma|Commas]]: 15625/15552, 385/384


Minimax tuning
[[Minimax tuning]]
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1 5/6 0 0 0&gt;,  
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1 5/6 0 0 0&gt;,  
|3 1/12 0 1/2 -1/2&gt;, |3 1/12 0 -1/2 1/2&gt;]
|3 1/12 0 1/2 -1/2&gt;, |3 1/12 0 -1/2 1/2&gt;]
Eigenmonzos: 2, 4/3, 14/11
[[Eigenmonzo|Eigenmonzos]]: 2, 4/3, 14/11


Map: [&lt;1 0 1 0 6|, &lt;0 6 5 0 1|, &lt;0 0 0 1 -1|]
Map: [&lt;1 0 1 0 6|, &lt;0 6 5 0 1|, &lt;0 0 0 1 -1|]
Generators: 2, 6/5, 7
[[Generator|Generators]]: 2, 6/5, 7


13-limit
13-limit
Commas: 15625/15552, 385/384, 325/324
[[Comma|Commas]]: 15625/15552, 385/384, 325/324


13 and 15 limit minimax tuning
13 and 15 limit minimax tuning
Line 36: Line 36:
|28/9 0 0 -14/27 13/27 1/27&gt;,  
|28/9 0 0 -14/27 13/27 1/27&gt;,  
|28/9 0 0 -14/27 -14/27 28/27&gt;]
|28/9 0 0 -14/27 -14/27 28/27&gt;]
Eigenmonzos: 2, 13/11, 14/11
[[Eigenmonzo|Eigenmonzos]]: 2, 13/11, 14/11


Map: [&lt;1 0 1 0 6 0|, &lt;0 6 5 0 1 14|, &lt;0 0 0 1 -1 0|]
Map: [&lt;1 0 1 0 6 0|, &lt;0 6 5 0 1 14|, &lt;0 0 0 1 -1 0|]
Generators: 2, 6/5, 7
[[Generator|Generators]]: 2, 6/5, 7
Edos: 15, 19, 34, 53, 57, 68, 72, 87, 159, 212, 284, 299
[[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[57edo|57]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[212edo|212]], 284, 299


===Enki===
===Enki===
Commas: 15625/15552, 3025/3024
[[Comma|Commas]]: 15625/15552, 3025/3024


Minimax tuning
[[Minimax tuning]]
[|1 0 0 0 0&gt;, |-18/13 0 6/13 -6/13 12/13&gt;,  
[|1 0 0 0 0&gt;, |-18/13 0 6/13 -6/13 12/13&gt;,  
|-2/13 0 5/13 -5/13 10/13&gt;,  
|-2/13 0 5/13 -5/13 10/13&gt;,  
|-2/13 0 -8/13 8/13 10/13&gt;, |0 0 0 0 1&gt;]
|-2/13 0 -8/13 8/13 10/13&gt;, |0 0 0 0 1&gt;]
Eigenmonzos: 2, 11/8, 7/5
[[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 7/5


Map: [&lt;1 0 1 0 1|, &lt;0 6 5 0 4|, &lt;0 0 0 2 1|]
Map: [&lt;1 0 1 0 1|, &lt;0 6 5 0 4|, &lt;0 0 0 2 1|]
Generators: 2, 6/5, 66/25
[[Generator|Generators]]: 2, 6/5, 66/25
Edos: 15, 49, 57, 72, 87, 159, 193, 231, 265, 280, 337, 352, 439  
[[edo|Edos]]: [[15edo|15]], [[49edo|49]], [[57edo|57]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], [[231|231]], 265, 280, 337, 352, 439  


13-limit
13-limit
Commas: 15625/15552, 3025/3024, 325/324
[[Comma|Commas]]: 15625/15552, 3025/3024, 325/324


13 and 15 limit
13 and 15 limit
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|13/9 0 -4/9 1/2 0 4/9&gt;,  
|13/9 0 -4/9 1/2 0 4/9&gt;,  
|14/9 0 -14/9 0 0 14/9&gt;]
|14/9 0 -14/9 0 0 14/9&gt;]
Eigenmonzos: 2, 8/7 13/10
[[Eigenmonzo|Eigenmonzos]]: 2, 8/7 13/10


Map: [&lt;1 0 1 0 1 0|, &lt;0 6 5 0 4 14|, &lt;0 0 0 2 1 0|]
Map: [&lt;1 0 1 0 1 0|, &lt;0 6 5 0 4 14|, &lt;0 0 0 2 1 0|]
Generators: 2, 6/5, 66/25
[[Generator|Generators]]: 2, 6/5, 66/25
Edos: 15, 72, 87, 159, 193, 280, 439</pre></div>
[[edo|Edos]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], 280, 439</pre></div>
<h4>Original HTML content:</h4>
<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;Kleismic rank three family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.&lt;br /&gt;
<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;Kleismic rank three family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.&lt;br /&gt;
Line 73: Line 73:
7 and 9 limit minimax&lt;br /&gt;
7 and 9 limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |1 5/6 0 0&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |1 5/6 0 0&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 7/6, 4/3&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 7/6, 4/3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 0|, &amp;lt;0 6 5 0|, &amp;lt;0 0 0 1|]&lt;br /&gt;
Map: [&amp;lt;1 0 1 0|, &amp;lt;0 6 5 0|, &amp;lt;0 0 0 1|]&lt;br /&gt;
Generators: 2, 6/5, 7&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 7&lt;br /&gt;
Edos: 15, 19, 23, 34, 53, 68, 72, 87, 121, 125, 140, 212, 333, 405&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo"&gt;121&lt;/a&gt;, &lt;a class="wiki_link" href="/125edo"&gt;125&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212&lt;/a&gt;, 333, 405&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Enlil"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Enlil&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Enlil"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Enlil&lt;/h3&gt;
Commas: 15625/15552, 385/384&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Minimax tuning&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;, |0 1 0 0 0&amp;gt;, |1 5/6 0 0 0&amp;gt;, &lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |0 1 0 0 0&amp;gt;, |1 5/6 0 0 0&amp;gt;, &lt;br /&gt;
|3 1/12 0 1/2 -1/2&amp;gt;, |3 1/12 0 -1/2 1/2&amp;gt;]&lt;br /&gt;
|3 1/12 0 1/2 -1/2&amp;gt;, |3 1/12 0 -1/2 1/2&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 4/3, 14/11&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 4/3, 14/11&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 6|, &amp;lt;0 6 5 0 1|, &amp;lt;0 0 0 1 -1|]&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 6|, &amp;lt;0 6 5 0 1|, &amp;lt;0 0 0 1 -1|]&lt;br /&gt;
Generators: 2, 6/5, 7&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
13-limit&lt;br /&gt;
13-limit&lt;br /&gt;
Commas: 15625/15552, 385/384, 325/324&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 385/384, 325/324&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
13 and 15 limit minimax tuning&lt;br /&gt;
13 and 15 limit minimax tuning&lt;br /&gt;
Line 99: Line 99:
|28/9 0 0 -14/27 13/27 1/27&amp;gt;, &lt;br /&gt;
|28/9 0 0 -14/27 13/27 1/27&amp;gt;, &lt;br /&gt;
|28/9 0 0 -14/27 -14/27 28/27&amp;gt;]&lt;br /&gt;
|28/9 0 0 -14/27 -14/27 28/27&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 13/11, 14/11&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 13/11, 14/11&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 6 0|, &amp;lt;0 6 5 0 1 14|, &amp;lt;0 0 0 1 -1 0|]&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 6 0|, &amp;lt;0 6 5 0 1 14|, &amp;lt;0 0 0 1 -1 0|]&lt;br /&gt;
Generators: 2, 6/5, 7&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 7&lt;br /&gt;
Edos: 15, 19, 34, 53, 57, 68, 72, 87, 159, 212, 284, 299&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/57edo"&gt;57&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212&lt;/a&gt;, 284, 299&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Enki"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Enki&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Enki"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Enki&lt;/h3&gt;
Commas: 15625/15552, 3025/3024&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 3025/3024&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Minimax tuning&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;, |-18/13 0 6/13 -6/13 12/13&amp;gt;, &lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |-18/13 0 6/13 -6/13 12/13&amp;gt;, &lt;br /&gt;
|-2/13 0 5/13 -5/13 10/13&amp;gt;, &lt;br /&gt;
|-2/13 0 5/13 -5/13 10/13&amp;gt;, &lt;br /&gt;
|-2/13 0 -8/13 8/13 10/13&amp;gt;, |0 0 0 0 1&amp;gt;]&lt;br /&gt;
|-2/13 0 -8/13 8/13 10/13&amp;gt;, |0 0 0 0 1&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 11/8, 7/5&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/8, 7/5&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 1|, &amp;lt;0 6 5 0 4|, &amp;lt;0 0 0 2 1|]&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 1|, &amp;lt;0 6 5 0 4|, &amp;lt;0 0 0 2 1|]&lt;br /&gt;
Generators: 2, 6/5, 66/25&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 66/25&lt;br /&gt;
Edos: 15, 49, 57, 72, 87, 159, 193, 231, 265, 280, 337, 352, 439 &lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49&lt;/a&gt;, &lt;a class="wiki_link" href="/57edo"&gt;57&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/193edo"&gt;193&lt;/a&gt;, &lt;a class="wiki_link" href="/231"&gt;231&lt;/a&gt;, 265, 280, 337, 352, 439 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
13-limit&lt;br /&gt;
13-limit&lt;br /&gt;
Commas: 15625/15552, 3025/3024, 325/324&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 3025/3024, 325/324&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
13 and 15 limit&lt;br /&gt;
13 and 15 limit&lt;br /&gt;
Line 126: Line 126:
|13/9 0 -4/9 1/2 0 4/9&amp;gt;, &lt;br /&gt;
|13/9 0 -4/9 1/2 0 4/9&amp;gt;, &lt;br /&gt;
|14/9 0 -14/9 0 0 14/9&amp;gt;]&lt;br /&gt;
|14/9 0 -14/9 0 0 14/9&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 8/7 13/10&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 8/7 13/10&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 1 0|, &amp;lt;0 6 5 0 4 14|, &amp;lt;0 0 0 2 1 0|]&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 1 0|, &amp;lt;0 6 5 0 4 14|, &amp;lt;0 0 0 2 1 0|]&lt;br /&gt;
Generators: 2, 6/5, 66/25&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 66/25&lt;br /&gt;
Edos: 15, 72, 87, 159, 193, 280, 439&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/193edo"&gt;193&lt;/a&gt;, 280, 439&lt;/body&gt;&lt;/html&gt;</pre></div>
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