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Subgroup temperaments: Difference between revisions

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**Imported revision 475378890 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 490758546 - Original comment: **
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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>2013-12-06 20:27:54 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-20 10:59:25 UTC</tt>.<br>
: The original revision id was <tt>475378890</tt>.<br>
: The original revision id was <tt>490758546</tt>.<br>
: The revision comment was: <tt></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>
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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=2.3.7.11.13=  
=2.3.7.11.13=  
==Suhajira (13 limit)==
Commas: 64/63, 78/77, 144/143
Gencom: [2 11/9; 64/63 78/77 144/143]
Gencom map: [&lt;1 1 0 4 2 4|, &lt;0 2 0 -4 5 -1|]
[[Tp tuning|POT2 generator]]: ~11/9 = 353.775
Map: [&lt;1 1 4 2 4|, &lt;0 2 -4 5 -1|]
EDOs: 7, 10, 17, 24d, 27e, 34d, 61de
[[Tp tuning#T2%20tuning|RMS error]]: 1.953


==Hemif (13 limit)==  
==Hemif (13 limit)==  
Subgroup: 2.3.7.11.13
Commas: 144/143, 243/242, 364/363
Commas: 144/143, 243/242, 364/363
Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]], namo
Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]], namo
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EDOs: 7, 10, 17, 24, 41, 58
EDOs: 7, 10, 17, 24, 41, 58
[[Tp tuning#T2%20tuning|RMS error]]: 0.7167 cents
[[Tp tuning#T2%20tuning|RMS error]]: 0.7167 cents
==Parapyth (Rank 3)==
Commas: 352/351, 364/363
[[Lp tuning|POL2 tuning]]: &lt;1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|
The gencom below gives [[Margo Schulter]]'s favored basis
Gencom: [2 3/2 28/27; 352/351 364/363]
Gencom mapping: [&lt;1 1 0 1 4 6|, &lt;0 1 0 3 -1 -4|, &lt;0 0 0 1 1 1|]
Sval map: [&lt;1 0 0 7 12|, &lt;0 1 0 -4 -7|, &lt;0 0 1 1 1|]
EDOs: 17, 41, 46, 58, 87, 104
[[Tp tuning#T2%20tuning|RMS error]]: 0.3789 cents


==Leapfrog==  
==Leapfrog==  
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EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]]
EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]]
[[Tp tuning#T2%20tuning|RMS error]]: 1.752 cents
[[Tp tuning#T2%20tuning|RMS error]]: 1.752 cents
==Parapyth (Rank 3)==
Commas: 352/351, 364/363
[[Lp tuning|POL2 tuning]]: &lt;1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|
The gencom below gives [[Margo Schulter]]'s favored basis
Gencom: [2 3/2 28/27; 352/351 364/363]
Gencom mapping: [&lt;1 1 0 1 4 6|, &lt;0 1 0 3 -1 -4|, &lt;0 0 0 1 1 1|]
Sval map: [&lt;1 0 0 7 12|, &lt;0 1 0 -4 -7|, &lt;0 0 1 1 1|]
EDOs: 17, 41, 46, 58, 87, 104
[[Tp tuning#T2%20tuning|RMS error]]: 0.3789 cents


=2.3.5.11=  
=2.3.5.11=  
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[[Tp tuning#T2%20tuning|RMS error]]: 0.5379 cents</pre></div>
[[Tp tuning#T2%20tuning|RMS error]]: 0.5379 cents</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;Subgroup temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:72:&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:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;a href="#x2.3.7"&gt;2.3.7&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#x2.3.11"&gt;2.3.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt; | &lt;a href="#x2.3.5.11"&gt;2.3.5.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt; | &lt;a href="#x2.3.7.11"&gt;2.3.7.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt; | &lt;a href="#x2.3.7.11.13"&gt;2.3.7.11.13&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt; | &lt;a href="#x2.3.5.11"&gt;2.3.5.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt; | &lt;a href="#x2.9.7.11"&gt;2.9.7.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt; | &lt;a href="#x2.9.15.7.11.13"&gt;2.9.15.7.11.13&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt; | &lt;a href="#x2.9.21"&gt;2.9.21&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt; | &lt;a href="#x2.3.7/5.11/5.13/5"&gt;2.3.7/5.11/5.13/5&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt; | &lt;a href="#x2.3.7.11/5.13"&gt;2.3.7.11/5.13&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&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;Subgroup temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:74:&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:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;a href="#x2.3.7"&gt;2.3.7&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt; | &lt;a href="#x2.3.11"&gt;2.3.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt; | &lt;a href="#x2.3.5.11"&gt;2.3.5.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt; | &lt;a href="#x2.3.7.11"&gt;2.3.7.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt; | &lt;a href="#x2.3.7.11.13"&gt;2.3.7.11.13&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt; | &lt;a href="#x2.3.5.11"&gt;2.3.5.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt; | &lt;a href="#x2.9.7.11"&gt;2.9.7.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt; | &lt;a href="#x2.9.15.7.11.13"&gt;2.9.15.7.11.13&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt;&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt; | &lt;a href="#x2.9.21"&gt;2.9.21&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt; | &lt;a href="#x2.3.7/5.11/5.13/5"&gt;2.3.7/5.11/5.13/5&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt; | &lt;a href="#x2.3.7.11/5.13"&gt;2.3.7.11/5.13&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;
&lt;!-- ws:end:WikiTextTocRule:109 --&gt;Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on &lt;a class="wiki_link" href="/Chromatic%20pairs"&gt;Chromatic pairs&lt;/a&gt;.&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:112 --&gt;Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on &lt;a class="wiki_link" href="/Chromatic%20pairs"&gt;Chromatic pairs&lt;/a&gt;.&lt;br /&gt;
&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="x2.3.7"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;2.3.7&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x2.3.7"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;2.3.7&lt;/h1&gt;
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  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="x2.3.7.11.13-Hemif (13 limit)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Hemif (13 limit)&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="x2.3.7.11.13-Suhajira (13 limit)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Suhajira (13 limit)&lt;/h2&gt;
Subgroup: 2.3.7.11.13&lt;br /&gt;
Commas: 64/63, 78/77, 144/143&lt;br /&gt;
Commas: 144/143, 243/242, 364/363&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 11/9; 64/63 78/77 144/143]&lt;br /&gt;
Gencom map: [&amp;lt;1 1 0 4 2 4|, &amp;lt;0 2 0 -4 5 -1|]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning"&gt;POT2 generator&lt;/a&gt;: ~11/9 = 353.775&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 4 2 4|, &amp;lt;0 2 -4 5 -1|]&lt;br /&gt;
EDOs: 7, 10, 17, 24d, 27e, 34d, 61de&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.953&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="x2.3.7.11.13-Hemif (13 limit)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Hemif (13 limit)&lt;/h2&gt;
Commas: 144/143, 243/242, 364/363&lt;br /&gt;
Related temperament: &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments"&gt;Hemififths&lt;/a&gt;, namo&lt;br /&gt;
Related temperament: &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments"&gt;Hemififths&lt;/a&gt;, namo&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 7, 10, 17, 24, 41, 58&lt;br /&gt;
EDOs: 7, 10, 17, 24, 41, 58&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.7167 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.7167 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="x2.3.7.11.13-Parapyth (Rank 3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Parapyth (Rank 3)&lt;/h2&gt;
Commas: 352/351, 364/363&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 tuning&lt;/a&gt;: &amp;lt;1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|&lt;br /&gt;
&lt;br /&gt;
The gencom below gives &lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt;'s favored basis&lt;br /&gt;
Gencom: [2 3/2 28/27; 352/351 364/363]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 1 4 6|, &amp;lt;0 1 0 3 -1 -4|, &amp;lt;0 0 0 1 1 1|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 0 0 7 12|, &amp;lt;0 1 0 -4 -7|, &amp;lt;0 0 1 1 1|]&lt;br /&gt;
EDOs: 17, 41, 46, 58, 87, 104&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3789 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="x2.3.7.11.13-Leapfrog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Leapfrog&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="x2.3.7.11.13-Leapfrog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Leapfrog&lt;/h2&gt;
Line 531: Line 542:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.752 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.752 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="x2.3.5.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;2.3.5.11&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="x2.3.7.11.13-Parapyth (Rank 3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Parapyth (Rank 3)&lt;/h2&gt;
Commas: 352/351, 364/363&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 tuning&lt;/a&gt;: &amp;lt;1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|&lt;br /&gt;
&lt;br /&gt;
The gencom below gives &lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt;'s favored basis&lt;br /&gt;
Gencom: [2 3/2 28/27; 352/351 364/363]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 1 4 6|, &amp;lt;0 1 0 3 -1 -4|, &amp;lt;0 0 0 1 1 1|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 0 0 7 12|, &amp;lt;0 1 0 -4 -7|, &amp;lt;0 0 1 1 1|]&lt;br /&gt;
EDOs: 17, 41, 46, 58, 87, 104&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3789 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="x2.3.5.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;2.3.5.11&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="x2.3.5.11-Larry"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Larry&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="x2.3.5.11-Larry"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Larry&lt;/h2&gt;
  Commas: 243/242, 4000/3993&lt;br /&gt;
  Commas: 243/242, 4000/3993&lt;br /&gt;
Related temperaments: &lt;a class="wiki_link" href="/Gravity%20family#Gravity"&gt;gravity&lt;/a&gt;, &lt;a class="wiki_link" href="/Gravity%20family#Harry"&gt;harry&lt;/a&gt;&lt;br /&gt;
Related temperaments: &lt;a class="wiki_link" href="/Gravity%20family#Gravity"&gt;gravity&lt;/a&gt;, &lt;a class="wiki_link" href="/Gravity%20family#Harry"&gt;harry&lt;/a&gt;&lt;br /&gt;
Line 546: Line 570:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3025 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3025 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="x2.9.7.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;2.9.7.11&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="x2.9.7.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;2.9.7.11&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="x2.9.7.11-Machine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Machine&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="x2.9.7.11-Machine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Machine&lt;/h2&gt;
  Commas: 64/63, 99/98&lt;br /&gt;
  Commas: 64/63, 99/98&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 560: Line 584:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.977 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.977 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="x2.9.7.11-Apparatus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Apparatus&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="x2.9.7.11-Apparatus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Apparatus&lt;/h2&gt;
  Commas: 41503/41472, 322102/321489&lt;br /&gt;
  Commas: 41503/41472, 322102/321489&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 572: Line 596:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.0673 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.0673 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="x2.9.7.11-Mechanism"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Mechanism&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="x2.9.7.11-Mechanism"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Mechanism&lt;/h2&gt;
  Commas: 896/891, 26411/26244&lt;br /&gt;
  Commas: 896/891, 26411/26244&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 584: Line 608:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.4262 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.4262 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="x2.9.15.7.11.13"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;2.9.15.7.11.13&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="x2.9.15.7.11.13"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;2.9.15.7.11.13&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="x2.9.15.7.11.13-Stacks (aka 2magic)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Stacks (aka 2magic)&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="x2.9.15.7.11.13-Stacks (aka 2magic)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Stacks (aka 2magic)&lt;/h2&gt;
  Commas: 100/99, 105/104, 144/143, 196/195&lt;br /&gt;
  Commas: 100/99, 105/104, 144/143, 196/195&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 598: Line 622:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.540 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.540 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc28"&gt;&lt;a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7.11 stacks"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;2.9.15.7.11 stacks&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc29"&gt;&lt;a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7.11 stacks"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;2.9.15.7.11 stacks&lt;/h3&gt;
  Commas: 100/99, 225/224, 245/243&lt;br /&gt;
  Commas: 100/99, 225/224, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 610: Line 634:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.226 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.226 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc29"&gt;&lt;a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7 stacks"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;2.9.15.7 stacks&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc30"&gt;&lt;a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7 stacks"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;2.9.15.7 stacks&lt;/h3&gt;
  Commas: 225/224, 245/243&lt;br /&gt;
  Commas: 225/224, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 622: Line 646:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.074 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.074 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="x2.9.21"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;2.9.21&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc31"&gt;&lt;a name="x2.9.21"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;2.9.21&lt;/h1&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="x2.9.21-A-team"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;A-team&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="x2.9.21-A-team"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;A-team&lt;/h2&gt;
  Commas: 1029/1024&lt;br /&gt;
  Commas: 1029/1024&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 635: Line 659:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3202 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3202 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc32"&gt;&lt;a name="x2.3.7/5.11/5.13/5"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;2.3.7/5.11/5.13/5&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc33"&gt;&lt;a name="x2.3.7/5.11/5.13/5"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;2.3.7/5.11/5.13/5&lt;/h1&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="x2.3.7/5.11/5.13/5-Historical"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;Historical&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="x2.3.7/5.11/5.13/5-Historical"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Historical&lt;/h2&gt;
  Subgroup: 2.3.7/5.11/5.13/5&lt;br /&gt;
  Subgroup: 2.3.7/5.11/5.13/5&lt;br /&gt;
Commas: 364/363, 441/440, 1001/1000&lt;br /&gt;
Commas: 364/363, 441/440, 1001/1000&lt;br /&gt;
Line 649: Line 673:
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.2562 cents&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.2562 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc34"&gt;&lt;a name="x2.3.7.11/5.13"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;2.3.7.11/5.13&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="x2.3.7.11/5.13"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;2.3.7.11/5.13&lt;/h1&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc35"&gt;&lt;a name="x2.3.7.11/5.13-Hypnosis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Hypnosis&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="x2.3.7.11/5.13-Hypnosis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;Hypnosis&lt;/h2&gt;
  Subgroup: 2.3.7.11/5.13&lt;br /&gt;
  Subgroup: 2.3.7.11/5.13&lt;br /&gt;
Commas: 169/168, 540/539, 729/728&lt;br /&gt;
Commas: 169/168, 540/539, 729/728&lt;br /&gt;
Retrieved from "https://en.xen.wiki/w/Subgroup_temperaments"