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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-11 17:54:31 UTC</tt>.<br>
: The original revision id was <tt>274515178</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
 
 
=Vital statistics=
=Vital statistics=
[[Comma]] c = 5120/5103
[[Comma|Comma]] c = 5120/5103


7-limit minimax: 3 and 7 1/7c sharp, 5 just
7-limit minimax: 3 and 7 1/7c sharp, 5 just
[|1 0 0 0&gt;, |10/7 1/7 1/7 -1/7&gt;,  
[|1 0 0 0&gt;, |10/7 1/7 1/7 -1/7&gt;,  
|0 0 1 0&gt;, |10/7 -6/7 1/7 6/7&gt;]
|0 0 1 0&gt;, |10/7 -6/7 1/7 6/7&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 7/6
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 7/6


9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp
9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp
[|1 0 0 0&gt;, |5/4 1/4 1/8 -1/8&gt;,  
[|1 0 0 0&gt;, |5/4 1/4 1/8 -1/8&gt;,  
|0 0 1 0&gt;, |5/2 -3/2 1/4 3/4&gt;]
|0 0 1 0&gt;, |5/2 -3/2 1/4 3/4&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 9/7
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 9/7


Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063
Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063
Angle(3/2, 10/9) = 82.112 degrees
Angle(3/2, 10/9) = 82.112 degrees
Map to lattice: [&lt;0 1 2 -4|, &lt;0 0 1 1|]
Map to lattice: [&lt;0 1 2 -4|, &lt;0 0 1 1|]


Map: [&lt;1 0 0 10|, &lt;0 1 0 -6|, &lt;0 0 1 1|]
Map: [&lt;1 0 0 10|, &lt;0 1 0 -6|, &lt;0 0 1 1|]
Generators: 2, 3, 5
Generators: 2, 3, 5
[[edo|EDOs]]: [[99edo|99]], [[140edo|140]], [[239edo|239]], [[292edo|292]], [[391edo|391]], [[490edo|490]], [[881edo|881bd]]
 
[[EDO|EDOs]]: [[99edo|99]], [[140edo|140]], [[239edo|239]], [[292edo|292]], [[391edo|391]], [[490edo|490]], [[881edo|881bd]]
 
Badness: 0.000153
Badness: 0.000153


[[Projection pair]]s: 7 5120/729
[[Projection_pair|Projection pair]]s: 7 5120/729


==Music==
==Music==
By Gene Ward Smith
By Gene Ward Smith
[[http://www.archive.org/details/Choraled|Choraled]] [[http://www.archive.org/download/Choraled/Genewardsmith-Choraled.mp3|play]]
 
[http://www.archive.org/details/Choraled Choraled] [http://www.archive.org/download/Choraled/Genewardsmith-Choraled.mp3 play]
 
By Chris Vaisvil
By Chris Vaisvil
[[http://clones.soonlabel.com/public/micro/hemifamity27/hemifamity27-IF-20100917.mp3|Hemifamity27]]
 
[http://clones.soonlabel.com/public/micro/hemifamity27/hemifamity27-IF-20100917.mp3 Hemifamity27]


=Pele=
=Pele=
[[Comma|Commas]]: 441/440, 896/891
[[Comma|Commas]]: 441/440, 896/891


[[Minimax tuning]]
[[Minimax_tuning|Minimax tuning]]
 
[|1 0 0 0 0&gt;, |17/10 0 1/10 0 -1/10&gt;,  
[|1 0 0 0 0&gt;, |17/10 0 1/10 0 -1/10&gt;,  
|17/5 -2 6/5 0 -1/5&gt;,
|17/5 -2 6/5 0 -1/5&gt;,
|16/5 -2 3/5 0 2/5&gt;, |17/5 -2 1/5 0 4/5&gt;]
|16/5 -2 3/5 0 2/5&gt;, |17/5 -2 1/5 0 4/5&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 11/9
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 11/9


Lattice basis: 3/2 length 0.3812 56/55 length 1.5893
Lattice basis: 3/2 length 0.3812 56/55 length 1.5893
Angle(3/2, 56/55) = 90.4578 degrees
Angle(3/2, 56/55) = 90.4578 degrees
Map to lattice: [&lt;0 1 4 -2 -6|, &lt;0 0 -1 -1 -1|]
Map to lattice: [&lt;0 1 4 -2 -6|, &lt;0 0 -1 -1 -1|]


Map: [&lt;1 0 0 10 17|, &lt;0 1 0 -6 -10|, &lt;0 0 1 1 1|]
Map: [&lt;1 0 0 10 17|, &lt;0 1 0 -6 -10|, &lt;0 0 1 1 1|]
[[Generator|Generators]]: 2, 3, 5
 
[[edo|Edos]]: [[41edo|41]], [[46edo|46]], [[77edo|77e]], [[87edo|87]], [[99edo|99e]], [[128edo|128]], [[145edo|145]], [[186edo|186e]], [[232edo|232]], [[285edo|285e]], [[331edo|331e]]
[[generator|Generators]]: 2, 3, 5
 
[[EDO|Edos]]: [[41edo|41]], [[46edo|46]], [[77edo|77e]], [[87edo|87]], [[99edo|99e]], [[128edo|128]], [[145edo|145]], [[186edo|186e]], [[232edo|232]], [[285edo|285e]], [[331edo|331e]]
 
Badness: 0.000648
Badness: 0.000648


Line 63: Line 73:


13-limit minimax
13-limit minimax
Eigenmonzos: 2, 10/9, 13/10
Eigenmonzos: 2, 10/9, 13/10


15-limit minimax
15-limit minimax
Eigenmonzos: 2, 15/13, 6/5
Eigenmonzos: 2, 15/13, 6/5


Map: [&lt;1 0 0 10 17 22|, &lt;0 1 0 -6 -10 -13|, &lt;0 0 1 1 1 1|]
Map: [&lt;1 0 0 10 17 22|, &lt;0 1 0 -6 -10 -13|, &lt;0 0 1 1 1 1|]
EDOs: 29, 41, 46, 58, 87, 145, 232, 377cef
EDOs: 29, 41, 46, 58, 87, 145, 232, 377cef
Badness: 0.000703
Badness: 0.000703


Line 75: Line 89:
[[Comma|Commas]]: 5120/5103, 540/539
[[Comma|Commas]]: 5120/5103, 540/539


[[Minimax tuning]]
[[Minimax_tuning|Minimax tuning]]
 
[|1 0 0 0 0&gt;, |4/3 0 2/21 -1/21 1/21&gt;,  
[|1 0 0 0 0&gt;, |4/3 0 2/21 -1/21 1/21&gt;,  
|0 0 1 0 0&gt;, |2 0 3/7 2/7 -2/7&gt;,  
|0 0 1 0 0&gt;, |2 0 3/7 2/7 -2/7&gt;,  
|2 0 3/7 -5/7 5/7&gt;]
|2 0 3/7 -5/7 5/7&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 14/11
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 14/11


Line 84: Line 100:


Map: [&lt;1 0 0 10 -18|, &lt;0 1 0 -6 15|, &lt;0 0 1 1 -1|]
Map: [&lt;1 0 0 10 -18|, &lt;0 1 0 -6 15|, &lt;0 0 1 1 -1|]
EDOs: 84, 97, 99e, 111, 121, 130, 152, 555de, 707de, 859bde
EDOs: 84, 97, 99e, 111, 121, 130, 152, 555de, 707de, 859bde


Line 90: Line 107:


13 and 15 limit minimax tuning
13 and 15 limit minimax tuning
[|1 0 0 0 0 0&gt;, |13/8 -1/2 1/8 0 0 1/8&gt;,  
[|1 0 0 0 0 0&gt;, |13/8 -1/2 1/8 0 0 1/8&gt;,  
|13/4 -3 5/4 0 0 1/4&gt;, |7/2 0 1/2 0 0 -1/2&gt;,  
|13/4 -3 5/4 0 0 1/4&gt;, |7/2 0 1/2 0 0 -1/2&gt;,  
|25/8 -9/2 5/8 0 0 13/8&gt;,  
|25/8 -9/2 5/8 0 0 13/8&gt;,  
|13/4 -3 1/4 0 0 5/4&gt;]
|13/4 -3 1/4 0 0 5/4&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 14/13
[[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 14/13


Line 100: Line 119:


17-limit minimax
17-limit minimax
[|1 0 0 0 0 0 0&gt;,  
[|1 0 0 0 0 0 0&gt;,  
|13/12 0 0 1/12 1/6 -1/12 0&gt;,  
|13/12 0 0 1/12 1/6 -1/12 0&gt;,  
Line 107: Line 127:
|7/4 0 0 -1/4 1/2 1/4 0&gt;,  
|7/4 0 0 -1/4 1/2 1/4 0&gt;,  
|35/12 0 0 23/12 5/6 -23/12 0&gt;]
|35/12 0 0 23/12 5/6 -23/12 0&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 14/13
[[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 14/13


Map: [&lt;1 0 0 10 -18 -13 32|,  
Map: [&lt;1 0 0 10 -18 -13 32|,  
&lt;0 1 0 -6 15 12 -22|, &lt;0 0 1 1 -1 -1 3|]
&lt;0 1 0 -6 15 12 -22|, &lt;0 0 1 1 -1 -1 3|]
[[Generator|Generators]]: 2, 3, 5
 
[[edo|Edos]]: [[94edo|94]], [[111edo|111]], [[152edo|152]], [[205edo|205]], [[345edo|345]]
[[generator|Generators]]: 2, 3, 5
 
[[EDO|Edos]]: [[94edo|94]], [[111edo|111]], [[152edo|152]], [[205edo|205]], [[345edo|345]]


=Akea=
=Akea=
[[Comma|Commas]]: 385/384, 2200/2187
[[Comma|Commas]]: 385/384, 2200/2187


[[Minimax tuning]]
[[Minimax_tuning|Minimax tuning]]
 
[|1 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0&gt;,  
[|1 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0&gt;,  
|26/9 0 13/18 -7/18 -1/3&gt;,
|26/9 0 13/18 -7/18 -1/3&gt;,
|26/9 0 -5/18 11/18 -1/3&gt;,  
|26/9 0 -5/18 11/18 -1/3&gt;,  
|26/9 0 -5/18 -7/18 2/3&gt;]
|26/9 0 -5/18 -7/18 2/3&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 14/11, 7/5
[[Eigenmonzo|Eigenmonzos]]: 2, 14/11, 7/5


Map: [&lt;1 0 0 10 -3|, &lt;0 1 0 -6 7|, &lt;0 0 1 1 -2|]
Map: [&lt;1 0 0 10 -3|, &lt;0 1 0 -6 7|, &lt;0 0 1 1 -2|]
[[Generator|Generators]]: 2, 3, 5
 
[[generator|Generators]]: 2, 3, 5
 
EDOs: 34, 41, 53, 87, 140, 181, 321
EDOs: 34, 41, 53, 87, 140, 181, 321
Badness: 0.000998
Badness: 0.000998


Line 133: Line 162:


13 and 15 limit minimax
13 and 15 limit minimax
[|1 0 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0 0&gt;,  
[|1 0 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0 0&gt;,  
|26/9 0 13/18 -7/18 -1/3 0&gt;,  
|26/9 0 13/18 -7/18 -1/3 0&gt;,  
Line 138: Line 168:
|26/9 0 -5/18 -7/18 2/3 0&gt;,  
|26/9 0 -5/18 -7/18 2/3 0&gt;,  
|26/9 0 -7/9 1/9 2/3 0&gt;]
|26/9 0 -7/9 1/9 2/3 0&gt;]
Eigenmonzos: 2, 14/11, 7/5
Eigenmonzos: 2, 14/11, 7/5


Lattice basis: 3/2 length 0.5354 27/20 length 1.0463
Lattice basis: 3/2 length 0.5354 27/20 length 1.0463
Angle(3/2, 27/20) = 80.5628 degrees
Angle(3/2, 27/20) = 80.5628 degrees
Map to lattice: [&lt;0 1 3 -3 1 -2|, &lt;0 0 -1 -1 2 2|]
Map to lattice: [&lt;0 1 3 -3 1 -2|, &lt;0 0 -1 -1 2 2|]


Map: [&lt;1 0 0 10 -3 2|, &lt;0 1 0 -6 7 4|, &lt;0 0 1 1 -2 -2|]
Map: [&lt;1 0 0 10 -3 2|, &lt;0 1 0 -6 7 4|, &lt;0 0 1 1 -2 -2|]
Generators: 2, 3, 5
Generators: 2, 3, 5
[[edo|EDOs]]: 7, 41, 46, 53, 87, [[94edo|94]], [[140edo|140]], [[181edo|181]], [[321edo|321]], [[408edo|408]]
 
[[EDO|EDOs]]: 7, 41, 46, 53, 87, [[94edo|94]], [[140edo|140]], [[181edo|181]], [[321edo|321]], [[408edo|408]]
 
Badness: 0.000822
Badness: 0.000822
Scales: [[akea46_13]]
 
Scales: [[akea46_13|akea46_13]]


=Kapo=
=Kapo=
[[Comma|Commas]]: 5120/5103, 3025/3024
[[Comma|Commas]]: 5120/5103, 3025/3024


[[Minimax tuning]]
[[Minimax_tuning|Minimax tuning]]
 
[|1 0 0 0 0&gt;, |8/5 2/5 0 -1/15 -2/15&gt;,  
[|1 0 0 0 0&gt;, |8/5 2/5 0 -1/15 -2/15&gt;,  
|14/5 6/5 0 7/15 -16/15&gt;,  
|14/5 6/5 0 7/15 -16/15&gt;,  
|16/5 -6/5 0 13/15 -4/15&gt;,  
|16/5 -6/5 0 13/15 -4/15&gt;,  
|16/5 -6/5 0 -2/15 11/15&gt;]
|16/5 -6/5 0 -2/15 11/15&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 9/7
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 9/7


Map: [&lt;1 0 0 10 7|, &lt;0 1 1 -5 -2|, &lt;0 0 2 2 -1|]
Map: [&lt;1 0 0 10 7|, &lt;0 1 1 -5 -2|, &lt;0 0 2 2 -1|]
[[Generator|Generators]]: 2, 3, 128/99
 
[[edo|EDOs]]: [[152edo|152]], [[198edo|198]], [[239edo|239]], [[350edo|350]], [[391edo|391]], [[478edo|478]], [[589edo|589]]
[[generator|Generators]]: 2, 3, 128/99
 
[[EDO|EDOs]]: [[152edo|152]], [[198edo|198]], [[239edo|239]], [[350edo|350]], [[391edo|391]], [[478edo|478]], [[589edo|589]]
 
EDOs: 41, 87, 111, 152, 239, 391
EDOs: 41, 87, 111, 152, 239, 391
Badness: 0.000994
Badness: 0.000994


Line 170: Line 213:


Map: [&lt;1 0 0 10 6|, &lt;0 1 0 -6 -6|, &lt;0 0 1 1 3|]
Map: [&lt;1 0 0 10 6|, &lt;0 1 0 -6 -6|, &lt;0 0 1 1 3|]
EDOs: 7, 12, 39, 46, 53, 58, 99, 111
EDOs: 7, 12, 39, 46, 53, 58, 99, 111
Badness: 0.00118
Badness: 0.00118


Line 177: Line 222:


Map: [&lt;1 0 0 10 -6|, &lt;0 2 0 -12 9|, &lt;0 0 1 1 1|]
Map: [&lt;1 0 0 10 -6|, &lt;0 2 0 -12 9|, &lt;0 0 1 1 1|]
EDOs: 29, 53, 58, 87, 111, 140, 198
EDOs: 29, 53, 58, 87, 111, 140, 198
Badness: 0.00174
Badness: 0.00174


Line 184: Line 231:


Map: [&lt;1 0 0 10 -6 -1|, &lt;0 2 0 -12 9 3|, &lt;0 0 1 1 1 1|]
Map: [&lt;1 0 0 10 -6 -1|, &lt;0 2 0 -12 9 3|, &lt;0 0 1 1 1 1|]
EDOs: 29, 53, 58, 87, 111, 140, 198
EDOs: 29, 53, 58, 87, 111, 140, 198
Badness: 0.000781</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000781
<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;Hemifamity family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:26:&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:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;a href="#Vital statistics"&gt;Vital statistics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Pele"&gt;Pele&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Laka"&gt;Laka&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#Akea"&gt;Akea&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#Kapo"&gt;Kapo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt; | &lt;a href="#Lono"&gt;Lono&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Namaka"&gt;Namaka&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;
[[Category:family]]
&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;br /&gt;
[[Category:hemifamity]]
&lt;br /&gt;
[[Category:planar]]
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Vital statistics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Vital statistics&lt;/h1&gt;
[[Category:theory]]
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt; c = 5120/5103&lt;br /&gt;
&lt;br /&gt;
7-limit minimax: 3 and 7 1/7c sharp, 5 just&lt;br /&gt;
[|1 0 0 0&amp;gt;, |10/7 1/7 1/7 -1/7&amp;gt;, &lt;br /&gt;
|0 0 1 0&amp;gt;, |10/7 -6/7 1/7 6/7&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 5/4, 7/6&lt;br /&gt;
&lt;br /&gt;
9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp&lt;br /&gt;
[|1 0 0 0&amp;gt;, |5/4 1/4 1/8 -1/8&amp;gt;, &lt;br /&gt;
|0 0 1 0&amp;gt;, |5/2 -3/2 1/4 3/4&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 5/4, 9/7&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063&lt;br /&gt;
Angle(3/2, 10/9) = 82.112 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 2 -4|, &amp;lt;0 0 1 1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10|, &amp;lt;0 1 0 -6|, &amp;lt;0 0 1 1|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/99edo"&gt;99&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/239edo"&gt;239&lt;/a&gt;, &lt;a class="wiki_link" href="/292edo"&gt;292&lt;/a&gt;, &lt;a class="wiki_link" href="/391edo"&gt;391&lt;/a&gt;, &lt;a class="wiki_link" href="/490edo"&gt;490&lt;/a&gt;, &lt;a class="wiki_link" href="/881edo"&gt;881bd&lt;/a&gt;&lt;br /&gt;
Badness: 0.000153&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 5120/729&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="Vital statistics-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Music&lt;/h2&gt;
By Gene Ward Smith&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Choraled" rel="nofollow"&gt;Choraled&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/Choraled/Genewardsmith-Choraled.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
By Chris Vaisvil&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/hemifamity27/hemifamity27-IF-20100917.mp3" rel="nofollow"&gt;Hemifamity27&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Pele"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pele&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 441/440, 896/891&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |17/10 0 1/10 0 -1/10&amp;gt;, &lt;br /&gt;
|17/5 -2 6/5 0 -1/5&amp;gt;,&lt;br /&gt;
|16/5 -2 3/5 0 2/5&amp;gt;, |17/5 -2 1/5 0 4/5&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 10/9, 11/9&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 3/2 length 0.3812 56/55 length 1.5893&lt;br /&gt;
Angle(3/2, 56/55) = 90.4578 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 4 -2 -6|, &amp;lt;0 0 -1 -1 -1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 17|, &amp;lt;0 1 0 -6 -10|, &amp;lt;0 0 1 1 1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/77edo"&gt;77e&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99e&lt;/a&gt;, &lt;a class="wiki_link" href="/128edo"&gt;128&lt;/a&gt;, &lt;a class="wiki_link" href="/145edo"&gt;145&lt;/a&gt;, &lt;a class="wiki_link" href="/186edo"&gt;186e&lt;/a&gt;, &lt;a class="wiki_link" href="/232edo"&gt;232&lt;/a&gt;, &lt;a class="wiki_link" href="/285edo"&gt;285e&lt;/a&gt;, &lt;a class="wiki_link" href="/331edo"&gt;331e&lt;/a&gt;&lt;br /&gt;
Badness: 0.000648&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 5120/729 11 655360/59049&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="Pele-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 196/195, 352/351, 364/363&lt;br /&gt;
&lt;br /&gt;
13-limit minimax&lt;br /&gt;
Eigenmonzos: 2, 10/9, 13/10&lt;br /&gt;
&lt;br /&gt;
15-limit minimax&lt;br /&gt;
Eigenmonzos: 2, 15/13, 6/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 17 22|, &amp;lt;0 1 0 -6 -10 -13|, &amp;lt;0 0 1 1 1 1|]&lt;br /&gt;
EDOs: 29, 41, 46, 58, 87, 145, 232, 377cef&lt;br /&gt;
Badness: 0.000703&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Laka"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Laka&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 5120/5103, 540/539&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |4/3 0 2/21 -1/21 1/21&amp;gt;, &lt;br /&gt;
|0 0 1 0 0&amp;gt;, |2 0 3/7 2/7 -2/7&amp;gt;, &lt;br /&gt;
|2 0 3/7 -5/7 5/7&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 5/4, 14/11&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 5120/729 11 14348907/1310720&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 -18|, &amp;lt;0 1 0 -6 15|, &amp;lt;0 0 1 1 -1|]&lt;br /&gt;
EDOs: 84, 97, 99e, 111, 121, 130, 152, 555de, 707de, 859bde&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Laka-13 limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13 limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 352/351, 540/539, 847/845&lt;br /&gt;
&lt;br /&gt;
13 and 15 limit minimax tuning&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |13/8 -1/2 1/8 0 0 1/8&amp;gt;, &lt;br /&gt;
|13/4 -3 5/4 0 0 1/4&amp;gt;, |7/2 0 1/2 0 0 -1/2&amp;gt;, &lt;br /&gt;
|25/8 -9/2 5/8 0 0 13/8&amp;gt;, &lt;br /&gt;
|13/4 -3 1/4 0 0 5/4&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/8, 14/13&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="Laka-17 limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;17 limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 352/351, 540/539, 847/845, 442/441&lt;br /&gt;
&lt;br /&gt;
17-limit minimax&lt;br /&gt;
[|1 0 0 0 0 0 0&amp;gt;, &lt;br /&gt;
|13/12 0 0 1/12 1/6 -1/12 0&amp;gt;, &lt;br /&gt;
|-7/4 0 0 5/4 3/2 -5/4 0&amp;gt;, &lt;br /&gt;
|7/4 0 0 3/4 1/2 -3/4 0&amp;gt;, &lt;br /&gt;
|0 0 0 0 1 0 0&amp;gt;, &lt;br /&gt;
|7/4 0 0 -1/4 1/2 1/4 0&amp;gt;, &lt;br /&gt;
|35/12 0 0 23/12 5/6 -23/12 0&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/8, 14/13&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 -18 -13 32|, &lt;br /&gt;
&amp;lt;0 1 0 -6 15 12 -22|, &amp;lt;0 0 1 1 -1 -1 3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/111edo"&gt;111&lt;/a&gt;, &lt;a class="wiki_link" href="/152edo"&gt;152&lt;/a&gt;, &lt;a class="wiki_link" href="/205edo"&gt;205&lt;/a&gt;, &lt;a class="wiki_link" href="/345edo"&gt;345&lt;/a&gt;&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="Akea"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Akea&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 385/384, 2200/2187&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |5/3 0 1/6 -1/6 0&amp;gt;, &lt;br /&gt;
|26/9 0 13/18 -7/18 -1/3&amp;gt;,&lt;br /&gt;
|26/9 0 -5/18 11/18 -1/3&amp;gt;, &lt;br /&gt;
|26/9 0 -5/18 -7/18 2/3&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 14/11, 7/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 -3|, &amp;lt;0 1 0 -6 7|, &amp;lt;0 0 1 1 -2|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
EDOs: 34, 41, 53, 87, 140, 181, 321&lt;br /&gt;
Badness: 0.000998&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="Akea-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
Commas: 325/324, 352/351, 385/384&lt;br /&gt;
&lt;br /&gt;
13 and 15 limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |5/3 0 1/6 -1/6 0 0&amp;gt;, &lt;br /&gt;
|26/9 0 13/18 -7/18 -1/3 0&amp;gt;, &lt;br /&gt;
|26/9 0 -5/18 11/18 -1/3 0&amp;gt;, &lt;br /&gt;
|26/9 0 -5/18 -7/18 2/3 0&amp;gt;, &lt;br /&gt;
|26/9 0 -7/9 1/9 2/3 0&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 14/11, 7/5&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 3/2 length 0.5354 27/20 length 1.0463&lt;br /&gt;
Angle(3/2, 27/20) = 80.5628 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 3 -3 1 -2|, &amp;lt;0 0 -1 -1 2 2|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 -3 2|, &amp;lt;0 1 0 -6 7 4|, &amp;lt;0 0 1 1 -2 -2|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: 7, 41, 46, 53, 87, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/181edo"&gt;181&lt;/a&gt;, &lt;a class="wiki_link" href="/321edo"&gt;321&lt;/a&gt;, &lt;a class="wiki_link" href="/408edo"&gt;408&lt;/a&gt;&lt;br /&gt;
Badness: 0.000822&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/akea46_13"&gt;akea46_13&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Kapo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Kapo&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 5120/5103, 3025/3024&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |8/5 2/5 0 -1/15 -2/15&amp;gt;, &lt;br /&gt;
|14/5 6/5 0 7/15 -16/15&amp;gt;, &lt;br /&gt;
|16/5 -6/5 0 13/15 -4/15&amp;gt;, &lt;br /&gt;
|16/5 -6/5 0 -2/15 11/15&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/9, 9/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 7|, &amp;lt;0 1 1 -5 -2|, &amp;lt;0 0 2 2 -1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 128/99&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/152edo"&gt;152&lt;/a&gt;, &lt;a class="wiki_link" href="/198edo"&gt;198&lt;/a&gt;, &lt;a class="wiki_link" href="/239edo"&gt;239&lt;/a&gt;, &lt;a class="wiki_link" href="/350edo"&gt;350&lt;/a&gt;, &lt;a class="wiki_link" href="/391edo"&gt;391&lt;/a&gt;, &lt;a class="wiki_link" href="/478edo"&gt;478&lt;/a&gt;, &lt;a class="wiki_link" href="/589edo"&gt;589&lt;/a&gt;&lt;br /&gt;
EDOs: 41, 87, 111, 152, 239, 391&lt;br /&gt;
Badness: 0.000994&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Lono"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Lono&lt;/h1&gt;
Commas: 176/175, 5120/5103&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 6|, &amp;lt;0 1 0 -6 -6|, &amp;lt;0 0 1 1 3|]&lt;br /&gt;
EDOs: 7, 12, 39, 46, 53, 58, 99, 111&lt;br /&gt;
Badness: 0.00118&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Namaka"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Namaka&lt;/h1&gt;
Commas: 3388/3375, 5120/5103&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 -6|, &amp;lt;0 2 0 -12 9|, &amp;lt;0 0 1 1 1|]&lt;br /&gt;
EDOs: 29, 53, 58, 87, 111, 140, 198&lt;br /&gt;
Badness: 0.00174&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Namaka-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h2&gt;
Commas: 352/351, 676/675, 847/845&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 10 -6 -1|, &amp;lt;0 2 0 -12 9 3|, &amp;lt;0 0 1 1 1 1|]&lt;br /&gt;
EDOs: 29, 53, 58, 87, 111, 140, 198&lt;br /&gt;
Badness: 0.000781&lt;/body&gt;&lt;/html&gt;</pre></div>
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