Hemifamity family: Difference between revisions

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**Imported revision 189809278 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 190464070 - 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>2010-12-22 23:12:41 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-02 03:43:11 UTC</tt>.<br>
: The original revision id was <tt>189809278</tt>.<br>
: The original revision id was <tt>190464070</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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Generators: 2, 3, 5
Generators: 2, 3, 5
[[edo|EDOs]]: [[99edo|99]], [[140edo|140]], [[239edo|239]], [[292edo|292]], [[490edo|490]], [[531edo|531]]
[[edo|EDOs]]: [[99edo|99]], [[140edo|140]], [[239edo|239]], [[292edo|292]], [[490edo|490]], [[531edo|531]]
Badness: 0.000153


Music
Music
Line 33: Line 34:
http://tinyurl.com/2d6k6xo
http://tinyurl.com/2d6k6xo


==11-limit children==
==Pele==
 
===Pele===
[[Comma|Commas]]: 441/440, 896/891
[[Comma|Commas]]: 441/440, 896/891


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[[Generator|Generators]]: 2, 3, 5
[[Generator|Generators]]: 2, 3, 5
[[edo|Edos]]: [[87edo|87]], [[128edo|128]], [[145edo|145]], [[232edo|232]]
[[edo|Edos]]: [[87edo|87]], [[128edo|128]], [[145edo|145]], [[232edo|232]]
Badness: 0.000648


13-limit
===13-limit===
Commas: 196/195, 352/351, 364/363
Commas: 196/195, 352/351, 364/363


Line 60: Line 60:
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|]
EDOs: 29, 41, 46, 58, 87, 145, 232
Badness: 0.000703


===Laka===
===Laka===
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Generators: 2, 3, 5&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="/490edo"&gt;490&lt;/a&gt;, &lt;a class="wiki_link" href="/531edo"&gt;531&lt;/a&gt;&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="/490edo"&gt;490&lt;/a&gt;, &lt;a class="wiki_link" href="/531edo"&gt;531&lt;/a&gt;&lt;br /&gt;
Badness: 0.000153&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Music&lt;br /&gt;
Music&lt;br /&gt;
By Gene Ward Smith&lt;br /&gt;
By Gene Ward Smith&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:198:http://www.archive.org/details/Choraled --&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Choraled" rel="nofollow"&gt;http://www.archive.org/details/Choraled&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:198 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:202:http://www.archive.org/details/Choraled --&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Choraled" rel="nofollow"&gt;http://www.archive.org/details/Choraled&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:202 --&gt;&lt;br /&gt;
By Chris Vaisvil&lt;br /&gt;
By Chris Vaisvil&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:199:http://tinyurl.com/2d6k6xo --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/2d6k6xo" rel="nofollow"&gt;http://tinyurl.com/2d6k6xo&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:199 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:203:http://tinyurl.com/2d6k6xo --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/2d6k6xo" rel="nofollow"&gt;http://tinyurl.com/2d6k6xo&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:203 --&gt;&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="x-11-limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit children&lt;/h2&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-11-limit children-Pele"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pele&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Pele"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Pele&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 441/440, 896/891&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 441/440, 896/891&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&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="/87edo"&gt;87&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="/232edo"&gt;232&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/87edo"&gt;87&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="/232edo"&gt;232&lt;/a&gt;&lt;br /&gt;
Badness: 0.000648&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
13-limit&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Pele-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h3&gt;
Commas: 196/195, 352/351, 364/363&lt;br /&gt;
Commas: 196/195, 352/351, 364/363&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Eigenmonzos: 2, 15/13, 6/5&lt;br /&gt;
Eigenmonzos: 2, 15/13, 6/5&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-11-limit children-Laka"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Laka&lt;/h3&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&lt;br /&gt;
Badness: 0.000703&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Pele-Laka"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Laka&lt;/h3&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 5120/5103, 540/539&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 5120/5103, 540/539&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&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;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;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-11-limit children-Akea"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Akea&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Pele-Akea"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Akea&lt;/h3&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 385/384, 2200/2187&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 385/384, 2200/2187&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Scales: &lt;a class="wiki_link" href="/akea46_13"&gt;akea46_13&lt;/a&gt;&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;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-11-limit children-Kapo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Kapo&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Pele-Kapo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Kapo&lt;/h3&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 5120/5103, 3025/3024&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 5120/5103, 3025/3024&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;

Revision as of 03:43, 2 January 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2011-01-02 03:43:11 UTC.
The original revision id was 190464070.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

===Vital statistics===
[[Comma]] c = 5120/5103

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

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

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

Map: [<1 0 0 10|, <0 1 0 -6|, <0 0 1 1|]
Generators: 2, 3, 5
[[edo|EDOs]]: [[99edo|99]], [[140edo|140]], [[239edo|239]], [[292edo|292]], [[490edo|490]], [[531edo|531]]
Badness: 0.000153

Music
By Gene Ward Smith
http://www.archive.org/details/Choraled
By Chris Vaisvil
http://tinyurl.com/2d6k6xo

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

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

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

Map: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|]
[[Generator|Generators]]: 2, 3, 5
[[edo|Edos]]: [[87edo|87]], [[128edo|128]], [[145edo|145]], [[232edo|232]]
Badness: 0.000648

===13-limit===
Commas: 196/195, 352/351, 364/363

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

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

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

===Laka===
[[Comma|Commas]]: 5120/5103, 540/539

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

13 limit
[[Comma|Commas]]: 352/351, 540/539, 847/845

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

17 limit
[[Comma|Commas]]: 352/351, 540/539, 847/845, 442/441

17-limit minimax
[|1 0 0 0 0 0 0>, 
|13/12 0 0 1/12 1/6 -1/12 0>, 
|-7/4 0 0 5/4 3/2 -5/4 0>, 
|7/4 0 0 3/4 1/2 -3/4 0>, 
|0 0 0 0 1 0 0>, 
|7/4 0 0 -1/4 1/2 1/4 0>, 
|35/12 0 0 23/12 5/6 -23/12 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 14/13

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

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

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

Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]
[[Generator|Generators]]: 2, 3, 5

13-limit
Commas: 325/324, 352/351, 385/384

13 and 15 limit minimax
[|1 0 0 0 0 0>, |5/3 0 1/6 -1/6 0 0>, 
|26/9 0 13/18 -7/18 -1/3 0>, 
|26/9 0 -5/18 11/18 -1/3 0>, 
|26/9 0 -5/18 -7/18 2/3 0>, 
|26/9 0 -7/9 1/9 2/3 0>]
Eigenmonzos: 2, 14/11, 7/5

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

Map: [<1 0 0 10 -3 2|, <0 1 0 -6 7 4|, <0 0 1 1 -2 -2|]
Generators: 2, 3, 5
[[edo|EDOs]]: [[94edo|94]], [[140edo|140]], [[181edo|181]], [[408edo|408]]
Scales: [[akea46_13]]

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

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

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

Original HTML content:

<html><head><title>Hemifamity family</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3>
<a class="wiki_link" href="/Comma">Comma</a> c = 5120/5103<br />
<br />
7-limit minimax: 3 and 7 1/7c sharp, 5 just<br />
[|1 0 0 0&gt;, |10/7 1/7 1/7 -1/7&gt;, <br />
|0 0 1 0&gt;, |10/7 -6/7 1/7 6/7&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4, 7/6<br />
<br />
9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp<br />
[|1 0 0 0&gt;, |5/4 1/4 1/8 -1/8&gt;, <br />
|0 0 1 0&gt;, |5/2 -3/2 1/4 3/4&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4, 9/7<br />
<br />
Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063<br />
Angle(3/2, 10/9) = 82.112 degrees<br />
Map to lattice: [&lt;0 1 2 -4|, &lt;0 0 1 1|]<br />
<br />
Map: [&lt;1 0 0 10|, &lt;0 1 0 -6|, &lt;0 0 1 1|]<br />
Generators: 2, 3, 5<br />
<a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/99edo">99</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/292edo">292</a>, <a class="wiki_link" href="/490edo">490</a>, <a class="wiki_link" href="/531edo">531</a><br />
Badness: 0.000153<br />
<br />
Music<br />
By Gene Ward Smith<br />
<!-- ws:start:WikiTextUrlRule:202:http://www.archive.org/details/Choraled --><a class="wiki_link_ext" href="http://www.archive.org/details/Choraled" rel="nofollow">http://www.archive.org/details/Choraled</a><!-- ws:end:WikiTextUrlRule:202 --><br />
By Chris Vaisvil<br />
<!-- ws:start:WikiTextUrlRule:203:http://tinyurl.com/2d6k6xo --><a class="wiki_link_ext" href="http://tinyurl.com/2d6k6xo" rel="nofollow">http://tinyurl.com/2d6k6xo</a><!-- ws:end:WikiTextUrlRule:203 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Pele"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pele</h2>
<a class="wiki_link" href="/Comma">Commas</a>: 441/440, 896/891<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br />
[|1 0 0 0 0&gt;, |17/10 0 1/10 0 -1/10&gt;, <br />
|17/5 -2 6/5 0 -1/5&gt;,<br />
|16/5 -2 3/5 0 2/5&gt;, |17/5 -2 1/5 0 4/5&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9, 11/9<br />
<br />
Lattice basis: 3/2 length 0.3812 56/55 length 1.5893<br />
Angle(3/2, 56/55) = 90.4578 degrees<br />
Map to lattice: [&lt;0 1 4 -2 -6|, &lt;0 0 -1 -1 -1|]<br />
<br />
Map: [&lt;1 0 0 10 17|, &lt;0 1 0 -6 -10|, &lt;0 0 1 1 1|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/128edo">128</a>, <a class="wiki_link" href="/145edo">145</a>, <a class="wiki_link" href="/232edo">232</a><br />
Badness: 0.000648<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Pele-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h3>
Commas: 196/195, 352/351, 364/363<br />
<br />
13-limit minimax<br />
Eigenmonzos: 2, 10/9, 13/10<br />
<br />
15-limit minimax<br />
Eigenmonzos: 2, 15/13, 6/5<br />
<br />
Map: [&lt;1 0 0 10 17 22|, &lt;0 1 0 -6 -10 -13|, &lt;0 0 1 1 1 1|]<br />
EDOs: 29, 41, 46, 58, 87, 145, 232<br />
Badness: 0.000703<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Pele-Laka"></a><!-- ws:end:WikiTextHeadingRule:6 -->Laka</h3>
<a class="wiki_link" href="/Comma">Commas</a>: 5120/5103, 540/539<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br />
[|1 0 0 0 0&gt;, |4/3 0 2/21 -1/21 1/21&gt;, <br />
|0 0 1 0 0&gt;, |2 0 3/7 2/7 -2/7&gt;, <br />
|2 0 3/7 -5/7 5/7&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4, 14/11<br />
<br />
13 limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: 352/351, 540/539, 847/845<br />
<br />
13 and 15 limit minimax tuning<br />
[|1 0 0 0 0 0&gt;, |13/8 -1/2 1/8 0 0 1/8&gt;, <br />
|13/4 -3 5/4 0 0 1/4&gt;, |7/2 0 1/2 0 0 -1/2&gt;, <br />
|25/8 -9/2 5/8 0 0 13/8&gt;, <br />
|13/4 -3 1/4 0 0 5/4&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/8, 14/13<br />
<br />
17 limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: 352/351, 540/539, 847/845, 442/441<br />
<br />
17-limit minimax<br />
[|1 0 0 0 0 0 0&gt;, <br />
|13/12 0 0 1/12 1/6 -1/12 0&gt;, <br />
|-7/4 0 0 5/4 3/2 -5/4 0&gt;, <br />
|7/4 0 0 3/4 1/2 -3/4 0&gt;, <br />
|0 0 0 0 1 0 0&gt;, <br />
|7/4 0 0 -1/4 1/2 1/4 0&gt;, <br />
|35/12 0 0 23/12 5/6 -23/12 0&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/8, 14/13<br />
<br />
Map: [&lt;1 0 0 10 -18 -13 32|, <br />
&lt;0 1 0 -6 15 12 -22|, &lt;0 0 1 1 -1 -1 3|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/111edo">111</a>, <a class="wiki_link" href="/152edo">152</a>, <a class="wiki_link" href="/205edo">205</a>, <a class="wiki_link" href="/345edo">345</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Pele-Akea"></a><!-- ws:end:WikiTextHeadingRule:8 -->Akea</h3>
<a class="wiki_link" href="/Comma">Commas</a>: 385/384, 2200/2187<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br />
[|1 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0&gt;, <br />
|26/9 0 13/18 -7/18 -1/3&gt;,<br />
|26/9 0 -5/18 11/18 -1/3&gt;, <br />
|26/9 0 -5/18 -7/18 2/3&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 14/11, 7/5<br />
<br />
Map: [&lt;1 0 0 10 -3|, &lt;0 1 0 -6 7|, &lt;0 0 1 1 -2|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br />
<br />
13-limit<br />
Commas: 325/324, 352/351, 385/384<br />
<br />
13 and 15 limit minimax<br />
[|1 0 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0 0&gt;, <br />
|26/9 0 13/18 -7/18 -1/3 0&gt;, <br />
|26/9 0 -5/18 11/18 -1/3 0&gt;, <br />
|26/9 0 -5/18 -7/18 2/3 0&gt;, <br />
|26/9 0 -7/9 1/9 2/3 0&gt;]<br />
Eigenmonzos: 2, 14/11, 7/5<br />
<br />
Lattice basis: 3/2 length 0.5354 27/20 length 1.0463<br />
Angle(3/2, 27/20) = 80.5628 degrees<br />
Map to lattice: [&lt;0 1 3 -3 1 -2|, &lt;0 0 -1 -1 2 2|]<br />
<br />
Map: [&lt;1 0 0 10 -3 2|, &lt;0 1 0 -6 7 4|, &lt;0 0 1 1 -2 -2|]<br />
Generators: 2, 3, 5<br />
<a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/181edo">181</a>, <a class="wiki_link" href="/408edo">408</a><br />
Scales: <a class="wiki_link" href="/akea46_13">akea46_13</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Pele-Kapo"></a><!-- ws:end:WikiTextHeadingRule:10 -->Kapo</h3>
<a class="wiki_link" href="/Comma">Commas</a>: 5120/5103, 3025/3024<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br />
[|1 0 0 0 0&gt;, |8/5 2/5 0 -1/15 -2/15&gt;, <br />
|14/5 6/5 0 7/15 -16/15&gt;, <br />
|16/5 -6/5 0 13/15 -4/15&gt;, <br />
|16/5 -6/5 0 -2/15 11/15&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9, 9/7<br />
<br />
Map: [&lt;1 0 0 10 7|, &lt;0 1 1 -5 -2|, &lt;0 0 2 2 -1|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 128/99<br />
<a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/152edo">152</a>, <a class="wiki_link" href="/198edo">198</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/350edo">350</a>, <a class="wiki_link" href="/391edo">391</a>, <a class="wiki_link" href="/478edo">478</a>, <a class="wiki_link" href="/589edo">589</a></body></html>