Gamelismic family: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 463337328 - Original comment: **
Wikispaces>Gedankenwelt
**Imported revision 488195934 - 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>2013-10-26 13:48:20 UTC</tt>.<br>
: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2014-02-08 20:13:15 UTC</tt>.<br>
: The original revision id was <tt>463337328</tt>.<br>
: The original revision id was <tt>488195934</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>
<h4>Original Wikitext content:</h4>
<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]]
<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]]
 
=Gamelan=  
=Gamelan=
//Gamelan temperament// is the rank three [[Harmonic Limit|7-limit]] [[Regular Temperaments|temperament]] tempering out 1029/1024.
//Gamelan temperament// is the rank three [[Harmonic Limit|7-limit]] [[Regular Temperaments|temperament]] tempering out 1029/1024.  




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[[Minkowski lattice basis]]: 8/7 length 0.5192, 5/4 length = log2(5)
[[Minkowski lattice basis]]: 8/7 length 0.5192, 5/4 length = log2(5)
Angle(8/7, 5/4) = 90 degrees
Angle(8/7, 5/4) = 90 degrees
Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|]  
Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|]


Map: [&lt;1 1 0 3|, &lt;0 3 0 -1|,&lt;0 0 1 0|]
Map: [&lt;1 1 0 3|, &lt;0 3 0 -1|,&lt;0 0 1 0|]
[[edo|EDOs]]: 5, 10, 15, 26, 31, 41, 72, 118, [[118edo|118]], [[159edo|159]], [[190edo|190]]
[[edo|EDOs]]: 5, 10, 15, 26, 31, 41, 72, [[118edo|118]], [[159edo|159]], [[190edo|190]]
Badness: 0.000176
Badness: 0.000176


[[Projection pair]]: 3 1024/343 to 2.5.7
[[Projection pair]]: 3 1024/343 to 2.5.7


=Portent=
=Portent=  
Portent has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.  
Portent has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.


[[Comma|Commas]]: c = 1029/1024, e = 385/384
[[Comma|Commas]]: c = 1029/1024, e = 385/384


Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat
Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat
[|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;,  
[|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;,
|39/14 4/7 1/2 -2/7 -1/2&gt;,
|39/14 4/7 1/2 -2/7 -1/2&gt;,
|20/7 -2/7 0 1/7 0&gt;,  
|20/7 -2/7 0 1/7 0&gt;,
|39/14 4/7 -1/2 -2/7 1/2&gt;]
|39/14 4/7 -1/2 -2/7 1/2&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7
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Map: [&lt;1 1 0 3 5|, &lt;0 3 0 -1 4| &lt;0 0 1 0 -1|]
Map: [&lt;1 1 0 3 5|, &lt;0 3 0 -1 4| &lt;0 0 1 0 -1|]
[[Generator|Generators]]: 2, 8/7, 5
[[Generator|Generators]]: 2, 8/7, 5
Edos: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190
EDOs: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190
Badness: 0.000234
Badness: 0.000234


Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7
Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7


==Portending==
==Portending==  
Commas: 325/324, 364/363, 441/440
Commas: 325/324, 364/363, 441/440


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Badness: 0.000627
Badness: 0.000627


==Portentous==
==Portentous==  
Commas: 385/384, 441/440, 625/624
Commas: 385/384, 441/440, 625/624


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Badness: 0.000662
Badness: 0.000662


==Ominous==
==Ominous==  
Commas: 351/350, 385/384, 441/440
Commas: 351/350, 385/384, 441/440


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Badness: 0.000751
Badness: 0.000751


===17-limit===
===17-limit===  
Commas: 273/272, 351/350, 441/440, 561/560
Commas: 273/272, 351/350, 441/440, 561/560


Minimax tuning
Minimax tuning
[|1 0 0 0 0 0 0&gt;,  
[|1 0 0 0 0 0 0&gt;,
|7/4 9/10 0 0 -3/10 -3/20 0&gt;,  
|7/4 9/10 0 0 -3/10 -3/20 0&gt;,
|5/2 7/5 0 0 -4/5 1/10 0&gt;,  
|5/2 7/5 0 0 -4/5 1/10 0&gt;,
|11/4 -3/10 0 0 1/10 1/20 0&gt;,  
|11/4 -3/10 0 0 1/10 1/20 0&gt;,
|7/2 -1/5 0 0 2/5 -3/10 0&gt;,  
|7/2 -1/5 0 0 2/5 -3/10 0&gt;,
|7/2 -1/5 0 0 -3/5 7/10 0&gt;,  
|7/2 -1/5 0 0 -3/5 7/10 0&gt;,
|4 2/5 0 0 -4/5 3/5 0&gt;]
|4 2/5 0 0 -4/5 3/5 0&gt;]
Eigenmonzos: 2, 13/11, 11/9
Eigenmonzos: 2, 13/11, 11/9
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Map to lattice: [&lt;0 1 1 0 0 -1 0|, &lt;0 -1 -1 0 -1 2 1|]
Map to lattice: [&lt;0 1 1 0 0 -1 0|, &lt;0 -1 -1 0 -1 2 1|]


Map: [&lt;1 1 0 3 5 1 1|, &lt;0 3 0 -1 4 -10 -8|,  
Map: [&lt;1 1 0 3 5 1 1|, &lt;0 3 0 -1 4 -10 -8|,
&lt;0 0 1 0 -1 2 2|]
&lt;0 0 1 0 -1 2 2|]
Generators: 2, 8/7, 5
Generators: 2, 8/7, 5
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Badness: 0.000612
Badness: 0.000612


==Momentous==
==Momentous==  
Commas: 196/195, 352/351, 385/384
Commas: 196/195, 352/351, 385/384


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Badness: 0.000832
Badness: 0.000832


==Foreboding==
==Foreboding==  
Commas: 105/104, 144/143, 275/273
Commas: 105/104, 144/143, 275/273


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Badness: 0.000873
Badness: 0.000873


=Gamel=
=Gamel=  
Commas: 1029/1024, 540/539
Commas: 1029/1024, 540/539


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<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;Gamelismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:18:&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:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;a href="#Gamelan"&gt;Gamelan&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Portent"&gt;Portent&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#Gamel"&gt;Gamel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&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;Gamelismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:18:&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:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;a href="#Gamelan"&gt;Gamelan&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Portent"&gt;Portent&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#Gamel"&gt;Gamel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Gamelan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Gamelan&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Gamelan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Gamelan&lt;/h1&gt;
&lt;em&gt;Gamelan temperament&lt;/em&gt; is the rank three &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;temperament&lt;/a&gt; tempering out 1029/1024.&lt;br /&gt;
&lt;em&gt;Gamelan temperament&lt;/em&gt; is the rank three &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;temperament&lt;/a&gt; tempering out 1029/1024. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;a class="wiki_link" href="/Minkowski%20lattice%20basis"&gt;Minkowski lattice basis&lt;/a&gt;: 8/7 length 0.5192, 5/4 length = log2(5)&lt;br /&gt;
&lt;a class="wiki_link" href="/Minkowski%20lattice%20basis"&gt;Minkowski lattice basis&lt;/a&gt;: 8/7 length 0.5192, 5/4 length = log2(5)&lt;br /&gt;
Angle(8/7, 5/4) = 90 degrees&lt;br /&gt;
Angle(8/7, 5/4) = 90 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 3 0 -1|, &amp;lt;0 0 1 0|] &lt;br /&gt;
Map to lattice: [&amp;lt;0 3 0 -1|, &amp;lt;0 0 1 0|]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3|, &amp;lt;0 3 0 -1|,&amp;lt;0 0 1 0|]&lt;br /&gt;
Map: [&amp;lt;1 1 0 3|, &amp;lt;0 3 0 -1|,&amp;lt;0 0 1 0|]&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: 5, 10, 15, 26, 31, 41, 72, 118, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/190edo"&gt;190&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: 5, 10, 15, 26, 31, 41, 72, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/190edo"&gt;190&lt;/a&gt;&lt;br /&gt;
Badness: 0.000176&lt;br /&gt;
Badness: 0.000176&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&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="Portent"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Portent&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Portent"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Portent&lt;/h1&gt;
Portent has a &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; [1029/1024, 385/384] and also tempers out 441/440. &lt;br /&gt;
Portent has a &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; [1029/1024, 385/384] and also tempers out 441/440.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: c = 1029/1024, e = 385/384&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: c = 1029/1024, e = 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat&lt;br /&gt;
Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |10/7 6/7 0 -3/7 0&amp;gt;, &lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |10/7 6/7 0 -3/7 0&amp;gt;,&lt;br /&gt;
|39/14 4/7 1/2 -2/7 -1/2&amp;gt;,&lt;br /&gt;
|39/14 4/7 1/2 -2/7 -1/2&amp;gt;,&lt;br /&gt;
|20/7 -2/7 0 1/7 0&amp;gt;, &lt;br /&gt;
|20/7 -2/7 0 1/7 0&amp;gt;,&lt;br /&gt;
|39/14 4/7 -1/2 -2/7 1/2&amp;gt;]&lt;br /&gt;
|39/14 4/7 -1/2 -2/7 1/2&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/10, 9/7&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/10, 9/7&lt;br /&gt;
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Map: [&amp;lt;1 1 0 3 5|, &amp;lt;0 3 0 -1 4| &amp;lt;0 0 1 0 -1|]&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5|, &amp;lt;0 3 0 -1 4| &amp;lt;0 0 1 0 -1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 8/7, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 8/7, 5&lt;br /&gt;
Edos: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190&lt;br /&gt;
EDOs: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190&lt;br /&gt;
Badness: 0.000234&lt;br /&gt;
Badness: 0.000234&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&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="Portent-Portending"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Portending&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Portent-Portending"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Portending&lt;/h2&gt;
Commas: 325/324, 364/363, 441/440&lt;br /&gt;
Commas: 325/324, 364/363, 441/440&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 6|, &amp;lt;0 3 0 -1 4 12| &amp;lt;0 0 1 0 -1 -2|]&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 6|, &amp;lt;0 3 0 -1 4 12| &amp;lt;0 0 1 0 -1 -2|]&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Portent-Portentous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Portentous&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Portent-Portentous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Portentous&lt;/h2&gt;
Commas: 385/384, 441/440, 625/624&lt;br /&gt;
Commas: 385/384, 441/440, 625/624&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 -5|, &amp;lt;0 3 0 -1 4 -3| &amp;lt;0 0 1 0 -1 4|]&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 -5|, &amp;lt;0 3 0 -1 4 -3| &amp;lt;0 0 1 0 -1 4|]&lt;br /&gt;
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&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="Portent-Ominous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Ominous&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Portent-Ominous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Ominous&lt;/h2&gt;
Commas: 351/350, 385/384, 441/440&lt;br /&gt;
Commas: 351/350, 385/384, 441/440&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 1|, &amp;lt;0 3 0 -1 4 -10| &amp;lt;0 0 1 0 -1 2|]&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 1|, &amp;lt;0 3 0 -1 4 -10| &amp;lt;0 0 1 0 -1 2|]&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Portent-Ominous-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;17-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Portent-Ominous-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;17-limit&lt;/h3&gt;
Commas: 273/272, 351/350, 441/440, 561/560&lt;br /&gt;
Commas: 273/272, 351/350, 441/440, 561/560&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Minimax tuning&lt;br /&gt;
Minimax tuning&lt;br /&gt;
[|1 0 0 0 0 0 0&amp;gt;, &lt;br /&gt;
[|1 0 0 0 0 0 0&amp;gt;,&lt;br /&gt;
|7/4 9/10 0 0 -3/10 -3/20 0&amp;gt;, &lt;br /&gt;
|7/4 9/10 0 0 -3/10 -3/20 0&amp;gt;,&lt;br /&gt;
|5/2 7/5 0 0 -4/5 1/10 0&amp;gt;, &lt;br /&gt;
|5/2 7/5 0 0 -4/5 1/10 0&amp;gt;,&lt;br /&gt;
|11/4 -3/10 0 0 1/10 1/20 0&amp;gt;, &lt;br /&gt;
|11/4 -3/10 0 0 1/10 1/20 0&amp;gt;,&lt;br /&gt;
|7/2 -1/5 0 0 2/5 -3/10 0&amp;gt;, &lt;br /&gt;
|7/2 -1/5 0 0 2/5 -3/10 0&amp;gt;,&lt;br /&gt;
|7/2 -1/5 0 0 -3/5 7/10 0&amp;gt;, &lt;br /&gt;
|7/2 -1/5 0 0 -3/5 7/10 0&amp;gt;,&lt;br /&gt;
|4 2/5 0 0 -4/5 3/5 0&amp;gt;]&lt;br /&gt;
|4 2/5 0 0 -4/5 3/5 0&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 13/11, 11/9&lt;br /&gt;
Eigenmonzos: 2, 13/11, 11/9&lt;br /&gt;
Line 197: Line 195:
Map to lattice: [&amp;lt;0 1 1 0 0 -1 0|, &amp;lt;0 -1 -1 0 -1 2 1|]&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 1 0 0 -1 0|, &amp;lt;0 -1 -1 0 -1 2 1|]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 1 1|, &amp;lt;0 3 0 -1 4 -10 -8|, &lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 1 1|, &amp;lt;0 3 0 -1 4 -10 -8|,&lt;br /&gt;
&amp;lt;0 0 1 0 -1 2 2|]&lt;br /&gt;
&amp;lt;0 0 1 0 -1 2 2|]&lt;br /&gt;
Generators: 2, 8/7, 5&lt;br /&gt;
Generators: 2, 8/7, 5&lt;br /&gt;
Line 204: Line 202:
&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="Portent-Momentous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Momentous&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Portent-Momentous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Momentous&lt;/h2&gt;
Commas: 196/195, 352/351, 385/384&lt;br /&gt;
Commas: 196/195, 352/351, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 7|, &amp;lt;0 3 0 -4 1 -5|, &amp;lt;0 0 1 0 -1 -1|]&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 7|, &amp;lt;0 3 0 -4 1 -5|, &amp;lt;0 0 1 0 -1 -1|]&lt;br /&gt;
Line 211: Line 209:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Portent-Foreboding"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Foreboding&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Portent-Foreboding"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Foreboding&lt;/h2&gt;
Commas: 105/104, 144/143, 275/273&lt;br /&gt;
Commas: 105/104, 144/143, 275/273&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 1|, &amp;lt;0 3 0 -1 4 2|, &amp;lt;0 0 1 0 -1 1|]&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 1|, &amp;lt;0 3 0 -1 4 2|, &amp;lt;0 0 1 0 -1 1|]&lt;br /&gt;
Line 218: Line 216:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Gamel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Gamel&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Gamel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Gamel&lt;/h1&gt;
Commas: 1029/1024, 540/539&lt;br /&gt;
Commas: 1029/1024, 540/539&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 -1|, &amp;lt;0 3 0 -1 11|, &amp;lt;0 0 1 0 1|]&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 -1|, &amp;lt;0 3 0 -1 11|, &amp;lt;0 0 1 0 1|]&lt;br /&gt;
EDOs: 10, 31, 41, 72&lt;br /&gt;
EDOs: 10, 31, 41, 72&lt;br /&gt;
Badness: 0.000853&lt;/body&gt;&lt;/html&gt;</pre></div>
Badness: 0.000853&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 20:13, 8 February 2014

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[[toc|flat]]
=Gamelan= 
//Gamelan temperament// is the rank three [[Harmonic Limit|7-limit]] [[Regular Temperaments|temperament]] tempering out 1029/1024.


[[Comma]]: c = 1029/1024

7-limit minimax tuning: 3, 5, and 7 1/4c flat
9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat
TOP-RMS: <1200.486 1901.833 2786.314 3367.676|
[[Minkowski lattice basis]]: 8/7 length 0.5192, 5/4 length = log2(5)
Angle(8/7, 5/4) = 90 degrees
Map to lattice: [<0 3 0 -1|, <0 0 1 0|]

Map: [<1 1 0 3|, <0 3 0 -1|,<0 0 1 0|]
[[edo|EDOs]]: 5, 10, 15, 26, 31, 41, 72, [[118edo|118]], [[159edo|159]], [[190edo|190]]
Badness: 0.000176

[[Projection pair]]: 3 1024/343 to 2.5.7

=Portent= 
Portent has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.

[[Comma|Commas]]: c = 1029/1024, e = 385/384

Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat
[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>,
|39/14 4/7 1/2 -2/7 -1/2>,
|20/7 -2/7 0 1/7 0>,
|39/14 4/7 -1/2 -2/7 1/2>]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7

[[Minkowski lattice basis]]: 8/7 length 0.46467, 12/11 length 1.931
Angle(8/7, 12/11) = 86.657 degrees
Map to lattice: [<0 3 1 -1 3|, <0 0 1 0 -1|]

Map: [<1 1 0 3 5|, <0 3 0 -1 4| <0 0 1 0 -1|]
[[Generator|Generators]]: 2, 8/7, 5
EDOs: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190
Badness: 0.000234

Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7

==Portending== 
Commas: 325/324, 364/363, 441/440

Map: [<1 1 0 3 5 6|, <0 3 0 -1 4 12| <0 0 1 0 -1 -2|]
EDOs: 15, 26, 41, 46, 72, 87, 159, 477cdf
Badness: 0.000627

==Portentous== 
Commas: 385/384, 441/440, 625/624

Map: [<1 1 0 3 5 -5|, <0 3 0 -1 4 -3| <0 0 1 0 -1 4|]
EDOs: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef
Badness: 0.000662

==Ominous== 
Commas: 351/350, 385/384, 441/440

Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 -10| <0 0 1 0 -1 2|]
EDOs: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef
Badness: 0.000751

===17-limit=== 
Commas: 273/272, 351/350, 441/440, 561/560

Minimax tuning
[|1 0 0 0 0 0 0>,
|7/4 9/10 0 0 -3/10 -3/20 0>,
|5/2 7/5 0 0 -4/5 1/10 0>,
|11/4 -3/10 0 0 1/10 1/20 0>,
|7/2 -1/5 0 0 2/5 -3/10 0>,
|7/2 -1/5 0 0 -3/5 7/10 0>,
|4 2/5 0 0 -4/5 3/5 0>]
Eigenmonzos: 2, 13/11, 11/9

Lattice basis: 8/7 0.3859 6/5 1.1303
Angle(8/7, 6/5) = 98.6015
Map to lattice: [<0 1 1 0 0 -1 0|, <0 -1 -1 0 -1 2 1|]

Map: [<1 1 0 3 5 1 1|, <0 3 0 -1 4 -10 -8|,
<0 0 1 0 -1 2 2|]
Generators: 2, 8/7, 5
EDOs: 26, 31, 46, 72, 103, 149, 175f, 221ef
Badness: 0.000612

==Momentous== 
Commas: 196/195, 352/351, 385/384

Map: [<1 1 0 3 5 7|, <0 3 0 -4 1 -5|, <0 0 1 0 -1 -1|]
EDOs: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def
Badness: 0.000832

==Foreboding== 
Commas: 105/104, 144/143, 275/273

Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 2|, <0 0 1 0 -1 1|]
[[edo|EDOs]]: 5, 10, 15, 26, 31, 41, [[72edo|72f]], [[185edo|185cf]]
Badness: 0.000873

=Gamel= 
Commas: 1029/1024, 540/539

Map: [<1 1 0 3 -1|, <0 3 0 -1 11|, <0 0 1 0 1|]
EDOs: 10, 31, 41, 72
Badness: 0.000853

Original HTML content:

<html><head><title>Gamelismic family</title></head><body><!-- ws:start:WikiTextTocRule:18:&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:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#Gamelan">Gamelan</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Portent">Portent</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Gamel">Gamel</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: -->
<!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Gamelan"></a><!-- ws:end:WikiTextHeadingRule:0 -->Gamelan</h1>
 <em>Gamelan temperament</em> is the rank three <a class="wiki_link" href="/Harmonic%20Limit">7-limit</a> <a class="wiki_link" href="/Regular%20Temperaments">temperament</a> tempering out 1029/1024.<br />
<br />
<br />
<a class="wiki_link" href="/Comma">Comma</a>: c = 1029/1024<br />
<br />
7-limit minimax tuning: 3, 5, and 7 1/4c flat<br />
9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat<br />
TOP-RMS: &lt;1200.486 1901.833 2786.314 3367.676|<br />
<a class="wiki_link" href="/Minkowski%20lattice%20basis">Minkowski lattice basis</a>: 8/7 length 0.5192, 5/4 length = log2(5)<br />
Angle(8/7, 5/4) = 90 degrees<br />
Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|]<br />
<br />
Map: [&lt;1 1 0 3|, &lt;0 3 0 -1|,&lt;0 0 1 0|]<br />
<a class="wiki_link" href="/edo">EDOs</a>: 5, 10, 15, 26, 31, 41, 72, <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/190edo">190</a><br />
Badness: 0.000176<br />
<br />
<a class="wiki_link" href="/Projection%20pair">Projection pair</a>: 3 1024/343 to 2.5.7<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Portent"></a><!-- ws:end:WikiTextHeadingRule:2 -->Portent</h1>
 Portent has a <a class="wiki_link" href="/Normal%20lists">normal comma list</a> [1029/1024, 385/384] and also tempers out 441/440.<br />
<br />
<a class="wiki_link" href="/Comma">Commas</a>: c = 1029/1024, e = 385/384<br />
<br />
Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat<br />
[|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;,<br />
|39/14 4/7 1/2 -2/7 -1/2&gt;,<br />
|20/7 -2/7 0 1/7 0&gt;,<br />
|39/14 4/7 -1/2 -2/7 1/2&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/10, 9/7<br />
<br />
<a class="wiki_link" href="/Minkowski%20lattice%20basis">Minkowski lattice basis</a>: 8/7 length 0.46467, 12/11 length 1.931<br />
Angle(8/7, 12/11) = 86.657 degrees<br />
Map to lattice: [&lt;0 3 1 -1 3|, &lt;0 0 1 0 -1|]<br />
<br />
Map: [&lt;1 1 0 3 5|, &lt;0 3 0 -1 4| &lt;0 0 1 0 -1|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 8/7, 5<br />
EDOs: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190<br />
Badness: 0.000234<br />
<br />
Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Portent-Portending"></a><!-- ws:end:WikiTextHeadingRule:4 -->Portending</h2>
 Commas: 325/324, 364/363, 441/440<br />
<br />
Map: [&lt;1 1 0 3 5 6|, &lt;0 3 0 -1 4 12| &lt;0 0 1 0 -1 -2|]<br />
EDOs: 15, 26, 41, 46, 72, 87, 159, 477cdf<br />
Badness: 0.000627<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Portent-Portentous"></a><!-- ws:end:WikiTextHeadingRule:6 -->Portentous</h2>
 Commas: 385/384, 441/440, 625/624<br />
<br />
Map: [&lt;1 1 0 3 5 -5|, &lt;0 3 0 -1 4 -3| &lt;0 0 1 0 -1 4|]<br />
EDOs: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef<br />
Badness: 0.000662<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Portent-Ominous"></a><!-- ws:end:WikiTextHeadingRule:8 -->Ominous</h2>
 Commas: 351/350, 385/384, 441/440<br />
<br />
Map: [&lt;1 1 0 3 5 1|, &lt;0 3 0 -1 4 -10| &lt;0 0 1 0 -1 2|]<br />
EDOs: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef<br />
Badness: 0.000751<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Portent-Ominous-17-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->17-limit</h3>
 Commas: 273/272, 351/350, 441/440, 561/560<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0 0 0&gt;,<br />
|7/4 9/10 0 0 -3/10 -3/20 0&gt;,<br />
|5/2 7/5 0 0 -4/5 1/10 0&gt;,<br />
|11/4 -3/10 0 0 1/10 1/20 0&gt;,<br />
|7/2 -1/5 0 0 2/5 -3/10 0&gt;,<br />
|7/2 -1/5 0 0 -3/5 7/10 0&gt;,<br />
|4 2/5 0 0 -4/5 3/5 0&gt;]<br />
Eigenmonzos: 2, 13/11, 11/9<br />
<br />
Lattice basis: 8/7 0.3859 6/5 1.1303<br />
Angle(8/7, 6/5) = 98.6015<br />
Map to lattice: [&lt;0 1 1 0 0 -1 0|, &lt;0 -1 -1 0 -1 2 1|]<br />
<br />
Map: [&lt;1 1 0 3 5 1 1|, &lt;0 3 0 -1 4 -10 -8|,<br />
&lt;0 0 1 0 -1 2 2|]<br />
Generators: 2, 8/7, 5<br />
EDOs: 26, 31, 46, 72, 103, 149, 175f, 221ef<br />
Badness: 0.000612<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Portent-Momentous"></a><!-- ws:end:WikiTextHeadingRule:12 -->Momentous</h2>
 Commas: 196/195, 352/351, 385/384<br />
<br />
Map: [&lt;1 1 0 3 5 7|, &lt;0 3 0 -4 1 -5|, &lt;0 0 1 0 -1 -1|]<br />
EDOs: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def<br />
Badness: 0.000832<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Portent-Foreboding"></a><!-- ws:end:WikiTextHeadingRule:14 -->Foreboding</h2>
 Commas: 105/104, 144/143, 275/273<br />
<br />
Map: [&lt;1 1 0 3 5 1|, &lt;0 3 0 -1 4 2|, &lt;0 0 1 0 -1 1|]<br />
<a class="wiki_link" href="/edo">EDOs</a>: 5, 10, 15, 26, 31, 41, <a class="wiki_link" href="/72edo">72f</a>, <a class="wiki_link" href="/185edo">185cf</a><br />
Badness: 0.000873<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Gamel"></a><!-- ws:end:WikiTextHeadingRule:16 -->Gamel</h1>
 Commas: 1029/1024, 540/539<br />
<br />
Map: [&lt;1 1 0 3 -1|, &lt;0 3 0 -1 11|, &lt;0 0 1 0 1|]<br />
EDOs: 10, 31, 41, 72<br />
Badness: 0.000853</body></html>
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