Subgroup temperaments: Difference between revisions

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[[toc|flat]]
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 [[Chromatic pairs]].

=2.3.7= 

==[[Semaphore and Godzilla|Semaphore]]== 
Comma: 49/48

[[Lp tuning|POL2 generator]]: ~8/7~7/6 = 250.385

[[Gencom]]: [2 8/7; 49/48]
Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|]

Map: [<1 2 3|, <0 -2 -1|]
EDOs: 5, 14, 19, 24, 67c, 91c
[[Lp tuning#L2 tuning|L2 error]]: 5.046 cents

==Archy== 
Archy can be thought of as "no-5's [[dominant]]" or "no-5's [[superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma.

Comma: 64/63

[[Lp tuning|POL2 generator]]: ~3/2 = 709.321

Gencom: [2 3/2; 64/63]
Gencom mapping: [<1 1 0 4|, <0 1 0 -2|]

Map: [<1 2 2|, <0 -1 2|]
EDOs: 5, 12, 17, 22, 27, 137bc
[[Lp tuning#L2 tuning|L2 error]]: 3.713 cents

==[[Slendric]]== 
Comma: 1029/1024

[[Lp tuning|POL2 generator]]: ~8/7 = 233.688

Gencom: [2 8/7; 1029/1024]
Gencom mapping: [<1 1 0 3|, <0 3 0 -1|]

Map: [<1 1 3|, <0 3 -1|]
EDOs: 5, 21, 26, 31, 36, 77, 113, 190
[[Lp tuning#L2 tuning|L2 error]]: 0.6403 cents

=2.3.11= 

==Neutraltet== 
Neutraltet can be thought of as 2.3.11 version of either [[mohajira]] or [[maqamic]], and is the temperament optimizing the [[neutral tetrad]].

Comma: 243/242

[[Lp tuning|POL2 generator]]: ~11/9 = 350.525

Gencom: [2 11/9; 243/242]
Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|]

Map: [<1 1 2|, <0 2 5|]
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380
[[Lp tuning#L2 tuning|L2 error]]: 0.6756 cents

[[xenharmonic/neutraltet7|Seven note albitonic scale]]
[[xenharmonic/neutraltet10|Ten note chromatic scale]]
[[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]]

=2.3.5.11= 

==Porcupine== 
Commas: 55/54, 100/99

[[Lp tuning|POL2 generator]]: ~10/9 = 164.078

Gencom: [2 10/9; 55/54, 100/99]
Gencom mapping: [<1 2 3 0 4|, <0 -3 -5 0 -4|]

Map: [<1 2 3 4|, <0 -3 -5 -4|]
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd
[[Lp tuning#L2 tuning|L2 error]]: 5.114 cents

==Mohaha== 
Commas: 81/80, 121/120

[[Lp tuning|POL2 generator]]: ~11/9 = 348.094

Gencom: [2 11/9; 81/80 121/120]
Gencom mapping: [<1 1 0 0 2|, <0 2 8 0 5|]

Map: [<1 1 0 2|, <0 2 8 5|]
EDOs: 7, 10, 17, 24, 31, 69d, 100d, 131bd
[[Lp tuning#L2 tuning|L2 error]]: 3.113 cents

===Music===
[[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]] by [[Billy Stiltner]]

=2.3.7.11= 

==Ennea== 
Commas: 41503/41472, 43923/43904

POTE generator: ~99/98 = 17.6258

Gencom: [2 99/98; 41503/41472, 43923/43904]
Gencom mapping: [<1 14/9 0 25/9 31/9|, <0 2 0 2 1|]

Sval map: [<9 0 11 24|, <0 2 2 1|]
EDOs: 54, 63, 72, 135, 342, 477, 1089, 1566
Badness: 0.00426

==Supra== 
Commas: 64/63, 99/98

[[POTE tuning|POTE generator]]: ~3/2 = 707.192

Gencom: [2 3/2; 64/63 99/98]
Gencom mapping: [<1 1 0 4 7|, <0 1 0 -2 -6|]

Sval map: [<1 0 6 13|, <0 1 -2 -6|]
EDOs: 5, 12, 17, 39, 56
Badness: 0.00933

==Skwares== 
Commas: 99/98, 243/242

POTE generator: ~9/7 = 425.244

Gencom: [2 9/7; 99/98 243/242]
Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10]]

Sval map: [<1 3 6 7|, <0 -4 -9 -10|]
EDOs: 14, 17, 31, 48, 79, 127, 206
Badness: 0.0107

==Hemif== 
Commas: 243/242, 896/891

POTE generator: ~11/9 = 351.535

Gencom: [2 11/9; 243/242 896/891]
Gencom mapping: [<1 1 0 -1 2|, <0 2 0 13 5|]

Sval map: [<1 1 -1 2|, <0 2 13 5|]
EDOs: 7, 17, 41, 58, 99
Badness: 0.0109

=2.5.7.11= 

==Larry== 
Commas: 243/242, 4000/3993
Related temperaments: [[Gravity family#Gravity|gravity]], [[Gravity family#Harry|harry]]

POTE generator: ~40/27 = 683.166

Gencom: [2 40/27; 243/242 4000/3993]
Gencom mapping: [<1 5 12 0 12|, <0 -6 -17 0 -15|]

Map: [<1 5 12 12|, <0 -6 -17 -15|]
EDOs: 7, 58, 65, 137, 202
Badness: 0.0125

=2.9.7.11= 

==Machine== 
Commas: 64/63, 99/98

[[POTE tuning|POTE generator]]: ~8/7 = 214.384

Gencom: [2 8/7; 64/63 99/98]
Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]

[[Smonzos and Svals|Sval map]]: [<1 0 6 13|, <0 1 -1 -3|]
EDOs: 5, 6, 11, 17, 28
Badness: 0.00233

==Apparatus== 
Commas: 41503/41472, 322102/321489

[[POTE tuning|POTE generator]]: ~77/72 = 115.570

Gencom: [2 77/72; 41503/41472 322102/321489]
Gencom mapping: [<1 5/2 0 3 5|, <0 -19/2 0 -2 -16|]

[[Smonzos and Svals|Sval map]]: [<1 5 3 5|, <0 -19 -2 -16|]
EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623
Badness: 0.00263

==Mechanism== 
Commas: 896/891, 26411/26244

[[POTE tuning|POTE generator]]: ~9/7 = 438.465

Gencom: [2 9/7; 896/891 26411/26244]
Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]

[[Smonzos and Svals|Sval map]]: [<1 5 5 2|, <0 -5 -6 4|]
EDOs: 8, 11, 30, 41, 52
Badness: 0.00439

=2.9.15.7.11.13= 

==Stacks (aka 2magic)== 
Commas: 100/99, 105/104, 144/143, 196/195

POTE generator: ~9/7 = 438.977

Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|] 

Sval map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]
EDOs: 11, 30, 41
Badness: 0.00602

===2.9.15.7.11 stacks=== 
Commas: 100/99, 225/224, 245/243

POTE generator: ~9/7 =438.443

Gencom: [2 9/7; 100/99 225/224 245/243]
Gencom mapping: [<1 5/2 5/2 5 2|, <0 -5/2 -1/2 -6 4|]

Sval map: [<1 0 2 -1 6|, <0 5 3 6 -4|]
EDOs: 8, 11, 30, 41, 52
Badness: 0.00371

===2.9.15.7 stacks=== 
Commas: 225/224, 245/243

POTE generator: ~9/7 = 438.850

Gencom: [2 9/7; 225/224 245/243]
Gencom mapping: [<1 5/2 5/2 5|, <0 -5/2 -1/2 -6|]

Sval map: [<1 0 2 -1|, <0 5 3 6|]
EDOs: 8, 11, 30, 41, 93, 134c, 175c
Badness: 0.00245

=2.9.21= 
==A-team== 
Commas: 1029/1024

POTE generator: ~21/16 = 467.756

Gencom: [2 21/16; 1029/1024]
Gencom mapping: [<1 1 0 3|, <0 3/2 0 -1/2|]

Sval map: [<1 2 4|, <0 3 1|]
EDOs: 5, 13, 18, 41, 59, 254c, 313c, 372c, 472c, 490c
Badness: 0.000246

Original HTML content:

<html><head><title>Subgroup temperaments</title></head><body><!-- ws:start:WikiTextTocRule:54:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><a href="#x2.3.7">2.3.7</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#x2.3.11">2.3.11</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#x2.3.5.11">2.3.5.11</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#x2.3.7.11">2.3.7.11</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#x2.5.7.11">2.5.7.11</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#x2.9.7.11">2.9.7.11</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | <a href="#x2.9.15.7.11.13">2.9.15.7.11.13</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#x2.9.21">2.9.21</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: -->
<!-- ws:end:WikiTextTocRule:82 -->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 <a class="wiki_link" href="/Chromatic%20pairs">Chromatic pairs</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x2.3.7"></a><!-- ws:end:WikiTextHeadingRule:0 -->2.3.7</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x2.3.7-Semaphore"></a><!-- ws:end:WikiTextHeadingRule:2 --><a class="wiki_link" href="/Semaphore%20and%20Godzilla">Semaphore</a></h2>
 Comma: 49/48<br />
<br />
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7~7/6 = 250.385<br />
<br />
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 49/48]<br />
Gencom mapping: [&lt;1 2 0 3|, &lt;0 -2 0 -1|]<br />
<br />
Map: [&lt;1 2 3|, &lt;0 -2 -1|]<br />
EDOs: 5, 14, 19, 24, 67c, 91c<br />
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 5.046 cents<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x2.3.7-Archy"></a><!-- ws:end:WikiTextHeadingRule:4 -->Archy</h2>
 Archy can be thought of as &quot;no-5's <a class="wiki_link" href="/dominant">dominant</a>&quot; or &quot;no-5's <a class="wiki_link" href="/superpyth">superpyth</a>&quot;. The name comes from the fact that it tempers out 64/63, the Archytas comma.<br />
<br />
Comma: 64/63<br />
<br />
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 709.321<br />
<br />
Gencom: [2 3/2; 64/63]<br />
Gencom mapping: [&lt;1 1 0 4|, &lt;0 1 0 -2|]<br />
<br />
Map: [&lt;1 2 2|, &lt;0 -1 2|]<br />
EDOs: 5, 12, 17, 22, 27, 137bc<br />
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.713 cents<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x2.3.7-Slendric"></a><!-- ws:end:WikiTextHeadingRule:6 --><a class="wiki_link" href="/Slendric">Slendric</a></h2>
 Comma: 1029/1024<br />
<br />
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7 = 233.688<br />
<br />
Gencom: [2 8/7; 1029/1024]<br />
Gencom mapping: [&lt;1 1 0 3|, &lt;0 3 0 -1|]<br />
<br />
Map: [&lt;1 1 3|, &lt;0 3 -1|]<br />
EDOs: 5, 21, 26, 31, 36, 77, 113, 190<br />
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6403 cents<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="x2.3.11"></a><!-- ws:end:WikiTextHeadingRule:8 -->2.3.11</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x2.3.11-Neutraltet"></a><!-- ws:end:WikiTextHeadingRule:10 -->Neutraltet</h2>
 Neutraltet can be thought of as 2.3.11 version of either <a class="wiki_link" href="/mohajira">mohajira</a> or <a class="wiki_link" href="/maqamic">maqamic</a>, and is the temperament optimizing the <a class="wiki_link" href="/neutral%20tetrad">neutral tetrad</a>.<br />
<br />
Comma: 243/242<br />
<br />
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 350.525<br />
<br />
Gencom: [2 11/9; 243/242]<br />
Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]<br />
<br />
Map: [&lt;1 1 2|, &lt;0 2 5|]<br />
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380<br />
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6756 cents<br />
<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet10">Ten note chromatic scale</a><br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet17">Seventeen note mega chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x2.3.5.11"></a><!-- ws:end:WikiTextHeadingRule:12 -->2.3.5.11</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x2.3.5.11-Porcupine"></a><!-- ws:end:WikiTextHeadingRule:14 -->Porcupine</h2>
 Commas: 55/54, 100/99<br />
<br />
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~10/9 = 164.078<br />
<br />
Gencom: [2 10/9; 55/54, 100/99]<br />
Gencom mapping: [&lt;1 2 3 0 4|, &lt;0 -3 -5 0 -4|]<br />
<br />
Map: [&lt;1 2 3 4|, &lt;0 -3 -5 -4|]<br />
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd<br />
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 5.114 cents<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x2.3.5.11-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:16 -->Mohaha</h2>
 Commas: 81/80, 121/120<br />
<br />
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 348.094<br />
<br />
Gencom: [2 11/9; 81/80 121/120]<br />
Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 8 0 5|]<br />
<br />
Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]<br />
EDOs: 7, 10, 17, 24, 31, 69d, 100d, 131bd<br />
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.113 cents<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x2.3.5.11-Mohaha-Music"></a><!-- ws:end:WikiTextHeadingRule:18 -->Music</h3>
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3" rel="nofollow">Mohaha10ping2</a> by <a class="wiki_link" href="/Billy%20Stiltner">Billy Stiltner</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="x2.3.7.11"></a><!-- ws:end:WikiTextHeadingRule:20 -->2.3.7.11</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x2.3.7.11-Ennea"></a><!-- ws:end:WikiTextHeadingRule:22 -->Ennea</h2>
 Commas: 41503/41472, 43923/43904<br />
<br />
POTE generator: ~99/98 = 17.6258<br />
<br />
Gencom: [2 99/98; 41503/41472, 43923/43904]<br />
Gencom mapping: [&lt;1 14/9 0 25/9 31/9|, &lt;0 2 0 2 1|]<br />
<br />
Sval map: [&lt;9 0 11 24|, &lt;0 2 2 1|]<br />
EDOs: 54, 63, 72, 135, 342, 477, 1089, 1566<br />
Badness: 0.00426<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="x2.3.7.11-Supra"></a><!-- ws:end:WikiTextHeadingRule:24 -->Supra</h2>
 Commas: 64/63, 99/98<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 707.192<br />
<br />
Gencom: [2 3/2; 64/63 99/98]<br />
Gencom mapping: [&lt;1 1 0 4 7|, &lt;0 1 0 -2 -6|]<br />
<br />
Sval map: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]<br />
EDOs: 5, 12, 17, 39, 56<br />
Badness: 0.00933<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="x2.3.7.11-Skwares"></a><!-- ws:end:WikiTextHeadingRule:26 -->Skwares</h2>
 Commas: 99/98, 243/242<br />
<br />
POTE generator: ~9/7 = 425.244<br />
<br />
Gencom: [2 9/7; 99/98 243/242]<br />
Gencom mapping: [&lt;1 3 0 6 7|, &lt;0 -4 0 -9 -10]]<br />
<br />
Sval map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]<br />
EDOs: 14, 17, 31, 48, 79, 127, 206<br />
Badness: 0.0107<br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x2.3.7.11-Hemif"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hemif</h2>
 Commas: 243/242, 896/891<br />
<br />
POTE generator: ~11/9 = 351.535<br />
<br />
Gencom: [2 11/9; 243/242 896/891]<br />
Gencom mapping: [&lt;1 1 0 -1 2|, &lt;0 2 0 13 5|]<br />
<br />
Sval map: [&lt;1 1 -1 2|, &lt;0 2 13 5|]<br />
EDOs: 7, 17, 41, 58, 99<br />
Badness: 0.0109<br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="x2.5.7.11"></a><!-- ws:end:WikiTextHeadingRule:30 -->2.5.7.11</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="x2.5.7.11-Larry"></a><!-- ws:end:WikiTextHeadingRule:32 -->Larry</h2>
 Commas: 243/242, 4000/3993<br />
Related temperaments: <a class="wiki_link" href="/Gravity%20family#Gravity">gravity</a>, <a class="wiki_link" href="/Gravity%20family#Harry">harry</a><br />
<br />
POTE generator: ~40/27 = 683.166<br />
<br />
Gencom: [2 40/27; 243/242 4000/3993]<br />
Gencom mapping: [&lt;1 5 12 0 12|, &lt;0 -6 -17 0 -15|]<br />
<br />
Map: [&lt;1 5 12 12|, &lt;0 -6 -17 -15|]<br />
EDOs: 7, 58, 65, 137, 202<br />
Badness: 0.0125<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:34 -->2.9.7.11</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:36 -->Machine</h2>
 Commas: 64/63, 99/98<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 214.384<br />
<br />
Gencom: [2 8/7; 64/63 99/98]<br />
Gencom mapping: [&lt;1 3/2 0 3 4|, &lt;0 1/2 0 -1 -3|]<br />
<br />
<a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]<br />
EDOs: 5, 6, 11, 17, 28<br />
Badness: 0.00233<br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:38 -->Apparatus</h2>
 Commas: 41503/41472, 322102/321489<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~77/72 = 115.570<br />
<br />
Gencom: [2 77/72; 41503/41472 322102/321489]<br />
Gencom mapping: [&lt;1 5/2 0 3 5|, &lt;0 -19/2 0 -2 -16|]<br />
<br />
<a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [&lt;1 5 3 5|, &lt;0 -19 -2 -16|]<br />
EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623<br />
Badness: 0.00263<br />
<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:40 -->Mechanism</h2>
 Commas: 896/891, 26411/26244<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 438.465<br />
<br />
Gencom: [2 9/7; 896/891 26411/26244]<br />
Gencom mapping: [&lt;1 5/2 0 5 2|, &lt;0 -5/2 0 -6 4|]<br />
<br />
<a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [&lt;1 5 5 2|, &lt;0 -5 -6 4|]<br />
EDOs: 8, 11, 30, 41, 52<br />
Badness: 0.00439<br />
<br />
<!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="x2.9.15.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:42 -->2.9.15.7.11.13</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)"></a><!-- ws:end:WikiTextHeadingRule:44 -->Stacks (aka 2magic)</h2>
 Commas: 100/99, 105/104, 144/143, 196/195<br />
<br />
POTE generator: ~9/7 = 438.977<br />
<br />
Gencom: [2 9/7; 100/99 105/104 144/143 196/195]<br />
Gencom mapping: [&lt;1 5/2 5/2 5 2 7|, &lt;0 -5/2 -1/2 -6 4 -9|] <br />
<br />
Sval map: [&lt;1 0 2 -1 6 -2|, &lt;0 5 3 6 -4 9|]<br />
EDOs: 11, 30, 41<br />
Badness: 0.00602<br />
<br />
<!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc23"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7.11 stacks"></a><!-- ws:end:WikiTextHeadingRule:46 -->2.9.15.7.11 stacks</h3>
 Commas: 100/99, 225/224, 245/243<br />
<br />
POTE generator: ~9/7 =438.443<br />
<br />
Gencom: [2 9/7; 100/99 225/224 245/243]<br />
Gencom mapping: [&lt;1 5/2 5/2 5 2|, &lt;0 -5/2 -1/2 -6 4|]<br />
<br />
Sval map: [&lt;1 0 2 -1 6|, &lt;0 5 3 6 -4|]<br />
EDOs: 8, 11, 30, 41, 52<br />
Badness: 0.00371<br />
<br />
<!-- ws:start:WikiTextHeadingRule:48:&lt;h3&gt; --><h3 id="toc24"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7 stacks"></a><!-- ws:end:WikiTextHeadingRule:48 -->2.9.15.7 stacks</h3>
 Commas: 225/224, 245/243<br />
<br />
POTE generator: ~9/7 = 438.850<br />
<br />
Gencom: [2 9/7; 225/224 245/243]<br />
Gencom mapping: [&lt;1 5/2 5/2 5|, &lt;0 -5/2 -1/2 -6|]<br />
<br />
Sval map: [&lt;1 0 2 -1|, &lt;0 5 3 6|]<br />
EDOs: 8, 11, 30, 41, 93, 134c, 175c<br />
Badness: 0.00245<br />
<br />
<!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="x2.9.21"></a><!-- ws:end:WikiTextHeadingRule:50 -->2.9.21</h1>
 <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="x2.9.21-A-team"></a><!-- ws:end:WikiTextHeadingRule:52 -->A-team</h2>
 Commas: 1029/1024<br />
<br />
POTE generator: ~21/16 = 467.756<br />
<br />
Gencom: [2 21/16; 1029/1024]<br />
Gencom mapping: [&lt;1 1 0 3|, &lt;0 3/2 0 -1/2|]<br />
<br />
Sval map: [&lt;1 2 4|, &lt;0 3 1|]<br />
EDOs: 5, 13, 18, 41, 59, 254c, 313c, 372c, 472c, 490c<br />
Badness: 0.000246</body></html>

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