Kleismic rank three family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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~~-12-~~13 15~~:59:16 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-03 22:09:50 UTC</tt>.<br>

: The original revision id was <tt>~~187834711~~</tt>.<br>

: The original revision id was <tt>190776398</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>

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[[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==

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

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[[Generator|Generators]]: 2, 6/5, 7

EDOs: 53, 68, 72, 140, 159, 212, 284

Badness: 0.000798

13-limit

===13-limit===

[[Comma|Commas]]: ~~15625~~/~~15552~~, 385/384, ~~325~~/~~324~~

[[Comma|Commas]]: 325/324, 385/384, 625/624

13 and 15 limit minimax tuning

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[[Generator|Generators]]: 2, 6/5, 7

[[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[57edo|57]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[212edo|212]], 284, 299

Badness: 0.000680

Scales: [[enlil19_13]]

===Enki===

==Enki==

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

[[Comma|Commas]]: 3025/3024, 4375/4356

[[Minimax tuning]]

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[[Generator|Generators]]: 2, 6/5, 66/25

[[edo|Edos]]: [[15edo|15]], [[49edo|49]], [[57edo|57]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], [[231|231]], 265, 280, 337, 352, 439

Badness: 0.00109

13-limit

===13-limit===

[[Comma|Commas]]: ~~15625~~/~~15552~~, ~~3025~~/~~3024~~, ~~325~~/~~324~~

[[Comma|Commas]]: 325/324, 364/363, 625/624

13 and 15 limit

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

[[Generator|Generators]]: 2, 6/5, 66/25

[[edo|Edos]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], 280, 439</pre></div>

[[edo|Edos]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], 280, 439

Badness: 0.000874</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"><html><head><title>Kleismic rank three family</title></head><body>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.<br />

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<br />

<h3 id="toc0"><a name="x--Enlil"></a>Enlil</h3>

<h2 id="toc0"><a name="x-Enlil"></a>Enlil</h2>

<a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 385/384<br />

<br />

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<a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br />

EDOs: 53, 68, 72, 140, 159, 212, 284<br />

Badness: 0.000798<br />

<br />

13-limit<br />

<h3 id="toc1"><a name="x-Enlil-13-limit"></a>13-limit</h3>

<a class="wiki_link" href="/Comma">Commas</a>: ~~15625~~/~~15552~~, 385/384, ~~325~~/~~324~~<br />

<a class="wiki_link" href="/Comma">Commas</a>: 325/324, 385/384, 625/624<br />

<br />

13 and 15 limit minimax tuning<br />

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<a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br />

Badness: 0.000680<br />

<br />

Scales: <a class="wiki_link" href="/enlil19_13">enlil19_13</a><br />

<br />

<h3 id="~~toc1~~"><a name="x--Enki"></a>Enki</h3>

<h2 id="toc2"><a name="x-Enki"></a>Enki</h2>

<a class="wiki_link" href="/Comma">Commas</a>: ~~15625~~/~~15552~~, ~~3025~~/~~3024~~<br />

<a class="wiki_link" href="/Comma">Commas</a>: 3025/3024, 4375/4356<br />

<br />

<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br />

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<a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 66/25<br />

Badness: 0.00109<br />

<br />

13-limit<br />

<h3 id="toc3"><a name="x-Enki-13-limit"></a>13-limit</h3>

<a class="wiki_link" href="/Comma">Commas</a>: ~~15625~~/~~15552~~, ~~3025~~/~~3024~~, ~~325~~/~~324~~<br />

<a class="wiki_link" href="/Comma">Commas</a>: 325/324, 364/363, 625/624<br />

<br />

13 and 15 limit<br />

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Map: [&lt;1 0 1 0 1 0|, &lt;0 6 5 0 4 14|, &lt;0 0 0 2 1 0|]<br />

<a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 66/25<br />

Badness: 0.000874</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2010-12-13 15:59:16 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-03 22:09:50 UTC</tt>.<br>
-: The original revision id was <tt>187834711</tt>.<br>
+: The original revision id was <tt>190776398</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>
@@ Line 16: / Line 16: @@
 [[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==
 [[Comma|Commas]]: 15625/15552, 385/384
@@ Line 27: / Line 27: @@
 [[Generator|Generators]]: 2, 6/5, 7
 EDOs: 53, 68, 72, 140, 159, 212, 284
+Badness: 0.000798
--limit
+===13-limit===
-[[Comma|Commas]]: 15625/15552, 385/384, 325/324
+[[Comma|Commas]]: 325/324, 385/384, 625/624
 and 15 limit minimax tuning
@@ Line 42: / Line 43: @@
 [[Generator|Generators]]: 2, 6/5, 7
 [[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[57edo|57]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[212edo|212]], 284, 299
+Badness: 0.000680
 Scales: [[enlil19_13]]
-===Enki===
+==Enki==
-[[Comma|Commas]]: 15625/15552, 3025/3024
+[[Comma|Commas]]: 3025/3024, 4375/4356
 [[Minimax tuning]]
@@ Line 56: / Line 59: @@
 [[Generator|Generators]]: 2, 6/5, 66/25
 [[edo|Edos]]: [[15edo|15]], [[49edo|49]], [[57edo|57]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], [[231|231]], 265, 280, 337, 352, 439
+Badness: 0.00109
--limit
+===13-limit===
-[[Comma|Commas]]: 15625/15552, 3025/3024, 325/324
+[[Comma|Commas]]: 325/324, 364/363, 625/624
 and 15 limit
@@ Line 69: / Line 73: @@
 Map: [&lt;1 0 1 0 1 0|, &lt;0 6 5 0 4 14|, &lt;0 0 0 2 1 0|]
 [[Generator|Generators]]: 2, 6/5, 66/25
-[[edo|Edos]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], 280, 439</pre></div>
+[[edo|Edos]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], 280, 439
+Badness: 0.000874</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;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 81: / Line 86: @@
 &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;!-- 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;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Enlil"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Enlil&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 92: / Line 97: @@
 &lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 7&lt;br /&gt;
 EDOs: 53, 68, 72, 140, 159, 212, 284&lt;br /&gt;
+Badness: 0.000798&lt;br /&gt;
 &lt;br /&gt;
--limit&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Enlil-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h3&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 385/384, 325/324&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 325/324, 385/384, 625/624&lt;br /&gt;
 &lt;br /&gt;
 and 15 limit minimax tuning&lt;br /&gt;
@@ Line 107: / Line 113: @@
 &lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 7&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;
+Badness: 0.000680&lt;br /&gt;
+&lt;br /&gt;
 Scales: &lt;a class="wiki_link" href="/enlil19_13"&gt;enlil19_13&lt;/a&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:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Enki"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Enki&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 3025/3024&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 3025/3024, 4375/4356&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
@@ Line 121: / Line 129: @@
 &lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 66/25&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;
+Badness: 0.00109&lt;br /&gt;
 &lt;br /&gt;
--limit&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Enki-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h3&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 3025/3024, 325/324&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 325/324, 364/363, 625/624&lt;br /&gt;
 &lt;br /&gt;
 and 15 limit&lt;br /&gt;
@@ Line 134: / Line 143: @@
 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;
 &lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 66/25&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="/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>
+&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;br /&gt;
+Badness: 0.000874&lt;/body&gt;&lt;/html&gt;</pre></div>