Swetismic 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>2012-02-20 21:13:05 UTC</tt>.<br>
: The original revision id was <tt>303510594</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]]
 
These are rank three temperaments tempering out 540/539, but we can began by looking at the rank four temperament.
These are rank three temperaments tempering out 540/539, 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 0 3|, &lt;0 0 0 1 -2|]
Map: [&lt;1 0 0 0 2|, &lt;0 1 0 0 3|, &lt;0 0 0 1 -2|]
Generators: 2, 3, 5, 7
Generators: 2, 3, 5, 7
EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578
EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578


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Map: [&lt;2 1 0 2 3|, &lt;0 3 0 5 -1|, &lt;0 0 1 0 1|]
Map: [&lt;2 1 0 2 3|, &lt;0 3 0 5 -1|, &lt;0 0 1 0 1|]
Generators: 99/70, 9/7, 5
Generators: 99/70, 9/7, 5
EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578
EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578
Badness: 0.000361
Badness: 0.000361


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Map: [&lt;2 1 0 2 3 -2 |, &lt;0 3 0 5 -1 13|, &lt;0 0 1 0 1 0|]
Map: [&lt;2 1 0 2 3 -2 |, &lt;0 3 0 5 -1 13|, &lt;0 0 1 0 1 0|]
Generators: 99/70, 9/7, 5
Generators: 99/70, 9/7, 5
EDOs: 36, 58, 72, 130, 224, 354, 578
EDOs: 36, 58, 72, 130, 224, 354, 578
Badness: 0.000535
Badness: 0.000535


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Map: [&lt;2 1 0 2 3 1|, &lt;0 3 0 5 -1 -4|, &lt;0 0 1 0 1 2|]
Map: [&lt;2 1 0 2 3 1|, &lt;0 3 0 5 -1 -4|, &lt;0 0 1 0 1 2|]
Generators: 55/39.9/7.5
Generators: 55/39.9/7.5
EDOs: 22, 50, 58, 72, 130
EDOs: 22, 50, 58, 72, 130
Badness: 0.000766
Badness: 0.000766


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Map: [&lt;1 0 2 1 2|, &lt;0 2 4 3 4|, &lt;0 0 -5 -1 -3|]
Map: [&lt;1 0 2 1 2|, &lt;0 2 4 3 4|, &lt;0 0 -5 -1 -3|]
Generators: 2.121/70.49/33
Generators: 2.121/70.49/33
EDOs: 9, 49, 58, 72, 130, 193, 202, 467
EDOs: 9, 49, 58, 72, 130, 193, 202, 467
Badness: 0.000886
Badness: 0.000886


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Map: [&lt;1 0 2 1 2 1|, &lt;0 2 4 3 4 7|, &lt;0 0 -5 -1 -3 -5|]
Map: [&lt;1 0 2 1 2 1|, &lt;0 2 4 3 4 7|, &lt;0 0 -5 -1 -3 -5|]
Generators: 2.26/15.49/33
Generators: 2.26/15.49/33
EDOs: 9, 54, 58, 72, 121, 130, 193
EDOs: 9, 54, 58, 72, 121, 130, 193
Badness: 0.000724
Badness: 0.000724


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Map: [&lt;1 0 4 -2 10|, &lt;0 1 4 0 7|, &lt;0 0 -5 3 -11|]
Map: [&lt;1 0 4 -2 10|, &lt;0 1 4 0 7|, &lt;0 0 -5 3 -11|]
EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde
EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde
Badness: 0.002015
Badness: 0.002015


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Map: [&lt;1 0 4 -2 10 7|, &lt;0 1 4 0 7 5|, &lt;0 0 -5 3 -11 -7|]
Map: [&lt;1 0 4 -2 10 7|, &lt;0 1 4 0 7 5|, &lt;0 0 -5 3 -11 -7|]
EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef
EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef
Badness: 0.000997
Badness: 0.000997


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Map: [&lt;1 0 0 -3 8|, &lt;0 3 0 11 -13|, &lt;0 0 1 0 1|]
Map: [&lt;1 0 0 -3 8|, &lt;0 3 0 11 -13|, &lt;0 0 1 0 1|]
EDOs: 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce
EDOs: 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce
Badness: 0.001629
Badness: 0.001629


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Map: [&lt;1 0 0 -3 8 0|, &lt;0 3 0 11 -13 7|, &lt;0 0 1 0 1 0|]
Map: [&lt;1 0 0 -3 8 0|, &lt;0 3 0 11 -13 7|, &lt;0 0 1 0 1 0|]
EDOs: 19, 36, 53, 72, 125f, 197ef
EDOs: 19, 36, 53, 72, 125f, 197ef
Badness: 0.001439
Badness: 0.001439
</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;Swetismic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:18:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hades"&gt;Hades&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hades-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hades-Cerberus"&gt;Cerberus&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Minos"&gt;Minos&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Minos-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Persephone"&gt;Persephone&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Persephone-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hypnos"&gt;Hypnos&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hypnos-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;br /&gt;
These are rank three temperaments tempering out 540/539, but we can began by looking at the rank four temperament.&lt;br /&gt;
&lt;br /&gt;
Comma: 540/539&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 2|, &amp;lt;0 1 0 0 3|, &amp;lt;0 0 0 1 -2|]&lt;br /&gt;
Generators: 2, 3, 5, 7&lt;br /&gt;
EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578&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="Hades"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Hades&lt;/h1&gt;
Commas: 540/539, 4000/3993&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 0 2 3|, &amp;lt;0 3 0 5 -1|, &amp;lt;0 0 1 0 1|]&lt;br /&gt;
Generators: 99/70, 9/7, 5&lt;br /&gt;
EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578&lt;br /&gt;
Badness: 0.000361&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="Hades-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h2&gt;
Commas: 540/539, 729/728, 1575/1573&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 0 2 3 -2 |, &amp;lt;0 3 0 5 -1 13|, &amp;lt;0 0 1 0 1 0|]&lt;br /&gt;
Generators: 99/70, 9/7, 5&lt;br /&gt;
EDOs: 36, 58, 72, 130, 224, 354, 578&lt;br /&gt;
Badness: 0.000535&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Hades-Cerberus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Cerberus&lt;/h2&gt;
Commas: 351/350, 364/363, 540/539&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 0 2 3 1|, &amp;lt;0 3 0 5 -1 -4|, &amp;lt;0 0 1 0 1 2|]&lt;br /&gt;
Generators: 55/39.9/7.5&lt;br /&gt;
EDOs: 22, 50, 58, 72, 130&lt;br /&gt;
Badness: 0.000766&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="Minos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Minos&lt;/h1&gt;
Commas: 540/539, 12005/11979&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 2 1 2|, &amp;lt;0 2 4 3 4|, &amp;lt;0 0 -5 -1 -3|]&lt;br /&gt;
Generators: 2.121/70.49/33&lt;br /&gt;
EDOs: 9, 49, 58, 72, 130, 193, 202, 467&lt;br /&gt;
Badness: 0.000886&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="Minos-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
Commas: 364/363, 540/539, 676/675&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 2 1 2 1|, &amp;lt;0 2 4 3 4 7|, &amp;lt;0 0 -5 -1 -3 -5|]&lt;br /&gt;
Generators: 2.26/15.49/33&lt;br /&gt;
EDOs: 9, 54, 58, 72, 121, 130, 193&lt;br /&gt;
Badness: 0.000724&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Persephone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Persephone&lt;/h1&gt;
Commas: 540/539, 88209/87500&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 4 -2 10|, &amp;lt;0 1 4 0 7|, &amp;lt;0 0 -5 3 -11|]&lt;br /&gt;
EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde&lt;br /&gt;
Badness: 0.002015&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Persephone-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
Commas: 351/350, 540/539, 847/845&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 4 -2 10 7|, &amp;lt;0 1 4 0 7 5|, &amp;lt;0 0 -5 3 -11 -7|]&lt;br /&gt;
EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef&lt;br /&gt;
Badness: 0.000997&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Hypnos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Hypnos&lt;/h1&gt;
Commas: 540/539, 72171/71680&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 8|, &amp;lt;0 3 0 11 -13|, &amp;lt;0 0 1 0 1|]&lt;br /&gt;
EDOs: 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce&lt;br /&gt;
Badness: 0.001629&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Hypnos-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 540/539, 729/728&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 8 0|, &amp;lt;0 3 0 11 -13 7|, &amp;lt;0 0 1 0 1 0|]&lt;br /&gt;
EDOs: 19, 36, 53, 72, 125f, 197ef&lt;br /&gt;
Badness: 0.001439&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

These are rank three temperaments tempering out 540/539, but we can began by looking at the rank four temperament.

Comma: 540/539

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

Generators: 2, 3, 5, 7

EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578

Hades

Commas: 540/539, 4000/3993

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

Generators: 99/70, 9/7, 5

EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578

Badness: 0.000361

13-limit

Commas: 540/539, 729/728, 1575/1573

Map: [<2 1 0 2 3 -2 |, <0 3 0 5 -1 13|, <0 0 1 0 1 0|]

Generators: 99/70, 9/7, 5

EDOs: 36, 58, 72, 130, 224, 354, 578

Badness: 0.000535

Cerberus

Commas: 351/350, 364/363, 540/539

Map: [<2 1 0 2 3 1|, <0 3 0 5 -1 -4|, <0 0 1 0 1 2|]

Generators: 55/39.9/7.5

EDOs: 22, 50, 58, 72, 130

Badness: 0.000766

Minos

Commas: 540/539, 12005/11979

Map: [<1 0 2 1 2|, <0 2 4 3 4|, <0 0 -5 -1 -3|]

Generators: 2.121/70.49/33

EDOs: 9, 49, 58, 72, 130, 193, 202, 467

Badness: 0.000886

13-limit

Commas: 364/363, 540/539, 676/675

Map: [<1 0 2 1 2 1|, <0 2 4 3 4 7|, <0 0 -5 -1 -3 -5|]

Generators: 2.26/15.49/33

EDOs: 9, 54, 58, 72, 121, 130, 193

Badness: 0.000724

Persephone

Commas: 540/539, 88209/87500

Map: [<1 0 4 -2 10|, <0 1 4 0 7|, <0 0 -5 3 -11|]

EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde

Badness: 0.002015

13-limit

Commas: 351/350, 540/539, 847/845

Map: [<1 0 4 -2 10 7|, <0 1 4 0 7 5|, <0 0 -5 3 -11 -7|]

EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef

Badness: 0.000997

Hypnos

Commas: 540/539, 72171/71680

Map: [<1 0 0 -3 8|, <0 3 0 11 -13|, <0 0 1 0 1|]

EDOs: 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce

Badness: 0.001629

13-limit

Commas: 169/168, 540/539, 729/728

Map: [<1 0 0 -3 8 0|, <0 3 0 11 -13 7|, <0 0 1 0 1 0|]

EDOs: 19, 36, 53, 72, 125f, 197ef

Badness: 0.001439

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