Aberschismic family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 190464070 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 193574288 - 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>2011-01- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-16 01:04:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>193574288</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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[[edo|Edos]]: [[94edo|94]], [[111edo|111]], [[152edo|152]], [[205edo|205]], [[345edo|345]] | [[edo|Edos]]: [[94edo|94]], [[111edo|111]], [[152edo|152]], [[205edo|205]], [[345edo|345]] | ||
==Akea== | |||
[[Comma|Commas]]: 385/384, 2200/2187 | [[Comma|Commas]]: 385/384, 2200/2187 | ||
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Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|] | Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|] | ||
[[Generator|Generators]]: 2, 3, 5 | [[Generator|Generators]]: 2, 3, 5 | ||
EDOs: 34, 41, 53, 87, 140, 181, 321 | |||
Badness: 0.000998 | |||
13-limit | ===13-limit=== | ||
Commas: 325/324, 352/351, 385/384 | Commas: 325/324, 352/351, 385/384 | ||
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Generators: 2, 3, 5 | Generators: 2, 3, 5 | ||
[[edo|EDOs]]: [[94edo|94]], [[140edo|140]], [[181edo|181]], [[408edo|408]] | [[edo|EDOs]]: [[94edo|94]], [[140edo|140]], [[181edo|181]], [[408edo|408]] | ||
Badness: 0.000822 | |||
Scales: [[akea46_13]] | Scales: [[akea46_13]] | ||
==Kapo== | |||
[[Comma|Commas]]: 5120/5103, 3025/3024 | [[Comma|Commas]]: 5120/5103, 3025/3024 | ||
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Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|] | Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|] | ||
[[Generator|Generators]]: 2, 3, 128/99 | [[Generator|Generators]]: 2, 3, 128/99 | ||
[[edo|EDOs]]: [[152edo|152]], [[198edo|198]], [[239edo|239]], [[350edo|350]], [[391edo|391]], [[478edo|478]], [[589edo|589]]</pre></div> | [[edo|EDOs]]: [[152edo|152]], [[198edo|198]], [[239edo|239]], [[350edo|350]], [[391edo|391]], [[478edo|478]], [[589edo|589]] | ||
EDOs: 41, 87, 111, 152, 239, 391 | |||
Badness: 0.000994 | |||
==Lono== | |||
Commas: 176/175, 5120/5103 | |||
Map: [<1 0 0 10 6|, <0 1 0 -6 -6|, <0 0 1 1 3|] | |||
EDOs: 7, 12, 39, 46, 53, 58, 99, 111 | |||
Badness: 0.00118 | |||
</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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> | <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"><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> | ||
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Music<br /> | Music<br /> | ||
By Gene Ward Smith<br /> | By Gene Ward Smith<br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:216: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:216 --><br /> | ||
By Chris Vaisvil<br /> | By Chris Vaisvil<br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:217:http://tinyurl.com/2d6k6xo --><a class="wiki_link_ext" href="http://tinyurl.com/2d6k6xo" rel="nofollow">http://tinyurl.com/2d6k6xo</a><!-- ws:end:WikiTextUrlRule:217 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Pele"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pele</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Pele"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pele</h2> | ||
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<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 /> | <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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt; | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Akea"></a><!-- ws:end:WikiTextHeadingRule:8 -->Akea</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 385/384, 2200/2187<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 2200/2187<br /> | ||
<br /> | <br /> | ||
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Map: [&lt;1 0 0 10 -3|, &lt;0 1 0 -6 7|, &lt;0 0 1 1 -2|]<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 /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br /> | ||
EDOs: 34, 41, 53, 87, 140, 181, 321<br /> | |||
Badness: 0.000998<br /> | |||
<br /> | <br /> | ||
13-limit< | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Akea-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h3> | ||
Commas: 325/324, 352/351, 385/384<br /> | Commas: 325/324, 352/351, 385/384<br /> | ||
<br /> | <br /> | ||
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Generators: 2, 3, 5<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 /> | <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 /> | ||
Badness: 0.000822<br /> | |||
Scales: <a class="wiki_link" href="/akea46_13">akea46_13</a><br /> | Scales: <a class="wiki_link" href="/akea46_13">akea46_13</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Kapo"></a><!-- ws:end:WikiTextHeadingRule:12 -->Kapo</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 5120/5103, 3025/3024<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 5120/5103, 3025/3024<br /> | ||
<br /> | <br /> | ||
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Map: [&lt;1 0 0 10 7|, &lt;0 1 1 -5 -2|, &lt;0 0 2 2 -1|]<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="/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></pre></div> | <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><br /> | ||
EDOs: 41, 87, 111, 152, 239, 391<br /> | |||
Badness: 0.000994<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Lono"></a><!-- ws:end:WikiTextHeadingRule:14 -->Lono</h2> | |||
Commas: 176/175, 5120/5103<br /> | |||
<br /> | |||
Map: [&lt;1 0 0 10 6|, &lt;0 1 0 -6 -6|, &lt;0 0 1 1 3|]<br /> | |||
EDOs: 7, 12, 39, 46, 53, 58, 99, 111<br /> | |||
Badness: 0.00118</body></html></pre></div> | |||
Revision as of 01:04, 16 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 2011-01-16 01:04:26 UTC.
- The original revision id was 193574288.
- 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 EDOs: 34, 41, 53, 87, 140, 181, 321 Badness: 0.000998 ===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]] Badness: 0.000822 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]] EDOs: 41, 87, 111, 152, 239, 391 Badness: 0.000994 ==Lono== Commas: 176/175, 5120/5103 Map: [<1 0 0 10 6|, <0 1 0 -6 -6|, <0 0 1 1 3|] EDOs: 7, 12, 39, 46, 53, 58, 99, 111 Badness: 0.00118
Original HTML content:
<html><head><title>Hemifamity family</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h3> --><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>, |10/7 1/7 1/7 -1/7>, <br /> |0 0 1 0>, |10/7 -6/7 1/7 6/7>]<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>, |5/4 1/4 1/8 -1/8>, <br /> |0 0 1 0>, |5/2 -3/2 1/4 3/4>]<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: [<0 1 2 -4|, <0 0 1 1|]<br /> <br /> Map: [<1 0 0 10|, <0 1 0 -6|, <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:216: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:216 --><br /> By Chris Vaisvil<br /> <!-- ws:start:WikiTextUrlRule:217:http://tinyurl.com/2d6k6xo --><a class="wiki_link_ext" href="http://tinyurl.com/2d6k6xo" rel="nofollow">http://tinyurl.com/2d6k6xo</a><!-- ws:end:WikiTextUrlRule:217 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><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>, |17/10 0 1/10 0 -1/10>, <br /> |17/5 -2 6/5 0 -1/5>,<br /> |16/5 -2 3/5 0 2/5>, |17/5 -2 1/5 0 4/5>]<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: [<0 1 4 -2 -6|, <0 0 -1 -1 -1|]<br /> <br /> Map: [<1 0 0 10 17|, <0 1 0 -6 -10|, <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:<h3> --><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: [<1 0 0 10 17 22|, <0 1 0 -6 -10 -13|, <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:<h3> --><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>, |4/3 0 2/21 -1/21 1/21>, <br /> |0 0 1 0 0>, |2 0 3/7 2/7 -2/7>, <br /> |2 0 3/7 -5/7 5/7>]<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>, |13/8 -1/2 1/8 0 0 1/8>, <br /> |13/4 -3 5/4 0 0 1/4>, |7/2 0 1/2 0 0 -1/2>, <br /> |25/8 -9/2 5/8 0 0 13/8>, <br /> |13/4 -3 1/4 0 0 5/4>]<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>, <br /> |13/12 0 0 1/12 1/6 -1/12 0>, <br /> |-7/4 0 0 5/4 3/2 -5/4 0>, <br /> |7/4 0 0 3/4 1/2 -3/4 0>, <br /> |0 0 0 0 1 0 0>, <br /> |7/4 0 0 -1/4 1/2 1/4 0>, <br /> |35/12 0 0 23/12 5/6 -23/12 0>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/8, 14/13<br /> <br /> Map: [<1 0 0 10 -18 -13 32|, <br /> <0 1 0 -6 15 12 -22|, <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:<h2> --><h2 id="toc4"><a name="x-Akea"></a><!-- ws:end:WikiTextHeadingRule:8 -->Akea</h2> <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>, |5/3 0 1/6 -1/6 0>, <br /> |26/9 0 13/18 -7/18 -1/3>,<br /> |26/9 0 -5/18 11/18 -1/3>, <br /> |26/9 0 -5/18 -7/18 2/3>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 14/11, 7/5<br /> <br /> Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br /> EDOs: 34, 41, 53, 87, 140, 181, 321<br /> Badness: 0.000998<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="x-Akea-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h3> Commas: 325/324, 352/351, 385/384<br /> <br /> 13 and 15 limit minimax<br /> [|1 0 0 0 0 0>, |5/3 0 1/6 -1/6 0 0>, <br /> |26/9 0 13/18 -7/18 -1/3 0>, <br /> |26/9 0 -5/18 11/18 -1/3 0>, <br /> |26/9 0 -5/18 -7/18 2/3 0>, <br /> |26/9 0 -7/9 1/9 2/3 0>]<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: [<0 1 3 -3 1 -2|, <0 0 -1 -1 2 2|]<br /> <br /> Map: [<1 0 0 10 -3 2|, <0 1 0 -6 7 4|, <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 /> Badness: 0.000822<br /> Scales: <a class="wiki_link" href="/akea46_13">akea46_13</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x-Kapo"></a><!-- ws:end:WikiTextHeadingRule:12 -->Kapo</h2> <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>, |8/5 2/5 0 -1/15 -2/15>, <br /> |14/5 6/5 0 7/15 -16/15>, <br /> |16/5 -6/5 0 13/15 -4/15>, <br /> |16/5 -6/5 0 -2/15 11/15>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9, 9/7<br /> <br /> Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <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><br /> EDOs: 41, 87, 111, 152, 239, 391<br /> Badness: 0.000994<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x-Lono"></a><!-- ws:end:WikiTextHeadingRule:14 -->Lono</h2> Commas: 176/175, 5120/5103<br /> <br /> Map: [<1 0 0 10 6|, <0 1 0 -6 -6|, <0 0 1 1 3|]<br /> EDOs: 7, 12, 39, 46, 53, 58, 99, 111<br /> Badness: 0.00118</body></html>