Lehmerismic temperaments: Difference between revisions

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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>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-20 20:30:02 UTC</tt>.<br>
: The original revision id was <tt>277502570</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|flat]]
 
These are rank three temperaments tempering out 3025/3024, but we can began by looking at the rank four temperament.
These are rank three temperaments tempering out 3025/3024, but we can began by looking at the rank four temperament.


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Map: [&lt;1 0 0 0 2|, &lt;0 1 0 1 2|, &lt;0 0 1 0 -1|, &lt;0 0 0 2 1|]
Map: [&lt;1 0 0 0 2|, &lt;0 1 0 1 2|, &lt;0 0 1 0 -1|, &lt;0 0 0 2 1|]
Generators: 2, 3, 5, 55/36
Generators: 2, 3, 5, 55/36
EDOs: 5, 10, 15, 26, 31, 41, 72, 118, 224, 270, 342, 612, 836, 1106, 1448, 2554
EDOs: 5, 10, 15, 26, 31, 41, 72, 118, 224, 270, 342, 612, 836, 1106, 1448, 2554


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Map: [&lt;3 0 0 4 8|, &lt;0 2 0 -4 1|, &lt;0 0 1 2 0|]
Map: [&lt;3 0 0 4 8|, &lt;0 2 0 -4 1|, &lt;0 0 1 2 0|]
Generators: 63/50, 400/231, 5
Generators: 63/50, 400/231, 5
EDOs: 15, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566
EDOs: 15, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566
Badness: 0.000259
Badness: 0.000259


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Map: [&lt;1 0 5 8 1|, &lt;0 1 1 3 2|, &lt;0 0 -6 -14 -1|]
Map: [&lt;1 0 5 8 1|, &lt;0 1 1 3 2|, &lt;0 0 -6 -14 -1|]
Generators: 2, 3, 18/11
Generators: 2, 3, 18/11
EDOs: 31, 97, 121, 152, 311, 342, 836, 1178, 2014
EDOs: 31, 97, 121, 152, 311, 342, 836, 1178, 2014
Badness: 0.000349
Badness: 0.000349


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Map: [&lt;1 0 0 -22 -9|, &lt;0 1 0 1 2|, &lt;0 0 1 10 4|]
Map: [&lt;1 0 0 -22 -9|, &lt;0 1 0 1 2|, &lt;0 0 1 10 4|]
Generators: 2, 3, 5
Generators: 2, 3, 5
EDOs: 31, 87, 118, 152, 239, 270, 962, 1232, 1502
EDOs: 31, 87, 118, 152, 239, 270, 962, 1232, 1502
Badness: 0.000390
Badness: 0.000390


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Map: [&lt;1 2 0 -8 1|, &lt;0 -3 0 11 1|, &lt;0 0 1 4 1|]
Map: [&lt;1 2 0 -8 1|, &lt;0 -3 0 11 1|, &lt;0 0 1 4 1|]
Generators: 2, 11/10, 5
Generators: 2, 11/10, 5
EDOs: 15, 57, 72, 152, 224, 311, 463, 535, 998, 1533ce, 2307ce, 2531cde, 2842bce
EDOs: 15, 57, 72, 152, 224, 311, 463, 535, 998, 1533ce, 2307ce, 2531cde, 2842bce
Badness: 0.000500
Badness: 0.000500


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Map: [&lt;1 2 0 -8 1 -6|, &lt;0 -3 0 11 1 3|, &lt;0 0 1 4 1 4|]
Map: [&lt;1 2 0 -8 1 -6|, &lt;0 -3 0 11 1 3|, &lt;0 0 1 4 1 4|]
Generators: 2, 11/10, 5
Generators: 2, 11/10, 5
EDOs: 15, 72, 87, 137, 159, 224, 311, 535, 918c, 1142c, 1453c
EDOs: 15, 72, 87, 137, 159, 224, 311, 535, 918c, 1142c, 1453c
Badness: 0.000653</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000653
<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;Lehmerismic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:10:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;a href="#Tyr"&gt;Tyr&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt; | &lt;a href="#Skadi"&gt;Skadi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt; | &lt;a href="#Ganesha"&gt;Ganesha&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Hanuman"&gt;Hanuman&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;br /&gt;
These are rank three temperaments tempering out 3025/3024, but we can began by looking at the rank four temperament.&lt;br /&gt;
&lt;br /&gt;
Comma: 3025/3024&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 2|, &amp;lt;0 1 0 1 2|, &amp;lt;0 0 1 0 -1|, &amp;lt;0 0 0 2 1|]&lt;br /&gt;
Generators: 2, 3, 5, 55/36&lt;br /&gt;
EDOs: 5, 10, 15, 26, 31, 41, 72, 118, 224, 270, 342, 612, 836, 1106, 1448, 2554&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="Tyr"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Tyr&lt;/h1&gt;
Commas: 3025/3024, 102487/102400&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 0 4 8|, &amp;lt;0 2 0 -4 1|, &amp;lt;0 0 1 2 0|]&lt;br /&gt;
Generators: 63/50, 400/231, 5&lt;br /&gt;
EDOs: 15, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566&lt;br /&gt;
Badness: 0.000259&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="Skadi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Skadi&lt;/h1&gt;
Commas: 3025/3024, 703125/702464&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 5 8 1|, &amp;lt;0 1 1 3 2|, &amp;lt;0 0 -6 -14 -1|]&lt;br /&gt;
Generators: 2, 3, 18/11&lt;br /&gt;
EDOs: 31, 97, 121, 152, 311, 342, 836, 1178, 2014&lt;br /&gt;
Badness: 0.000349&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Ganesha"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Ganesha&lt;/h1&gt;
Commas: 3025/3024, 5632/5625&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -22 -9|, &amp;lt;0 1 0 1 2|, &amp;lt;0 0 1 10 4|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
EDOs: 31, 87, 118, 152, 239, 270, 962, 1232, 1502&lt;br /&gt;
Badness: 0.000390&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Hanuman"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Hanuman&lt;/h1&gt;
Commas: 4000/3993, 3025/3024&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 0 -8 1|, &amp;lt;0 -3 0 11 1|, &amp;lt;0 0 1 4 1|]&lt;br /&gt;
Generators: 2, 11/10, 5&lt;br /&gt;
EDOs: 15, 57, 72, 152, 224, 311, 463, 535, 998, 1533ce, 2307ce, 2531cde, 2842bce&lt;br /&gt;
Badness: 0.000500&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="Hanuman-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
Commas: 625/624, 1575/1573, 2080/2079&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 0 -8 1 -6|, &amp;lt;0 -3 0 11 1 3|, &amp;lt;0 0 1 4 1 4|]&lt;br /&gt;
Generators: 2, 11/10, 5&lt;br /&gt;
EDOs: 15, 72, 87, 137, 159, 224, 311, 535, 918c, 1142c, 1453c&lt;br /&gt;
Badness: 0.000653&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

These are rank three temperaments tempering out 3025/3024, but we can began by looking at the rank four temperament.

Comma: 3025/3024

Map: [<1 0 0 0 2|, <0 1 0 1 2|, <0 0 1 0 -1|, <0 0 0 2 1|]

Generators: 2, 3, 5, 55/36

EDOs: 5, 10, 15, 26, 31, 41, 72, 118, 224, 270, 342, 612, 836, 1106, 1448, 2554

Tyr

Commas: 3025/3024, 102487/102400

Map: [<3 0 0 4 8|, <0 2 0 -4 1|, <0 0 1 2 0|]

Generators: 63/50, 400/231, 5

EDOs: 15, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566

Badness: 0.000259

Skadi

Commas: 3025/3024, 703125/702464

Map: [<1 0 5 8 1|, <0 1 1 3 2|, <0 0 -6 -14 -1|]

Generators: 2, 3, 18/11

EDOs: 31, 97, 121, 152, 311, 342, 836, 1178, 2014

Badness: 0.000349

Ganesha

Commas: 3025/3024, 5632/5625

Map: [<1 0 0 -22 -9|, <0 1 0 1 2|, <0 0 1 10 4|]

Generators: 2, 3, 5

EDOs: 31, 87, 118, 152, 239, 270, 962, 1232, 1502

Badness: 0.000390

Hanuman

Commas: 4000/3993, 3025/3024

Map: [<1 2 0 -8 1|, <0 -3 0 11 1|, <0 0 1 4 1|]

Generators: 2, 11/10, 5

EDOs: 15, 57, 72, 152, 224, 311, 463, 535, 998, 1533ce, 2307ce, 2531cde, 2842bce

Badness: 0.000500

13-limit

Commas: 625/624, 1575/1573, 2080/2079

Map: [<1 2 0 -8 1 -6|, <0 -3 0 11 1 3|, <0 0 1 4 1 4|]

Generators: 2, 11/10, 5

EDOs: 15, 72, 87, 137, 159, 224, 311, 535, 918c, 1142c, 1453c

Badness: 0.000653

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