Hemifamity family

Revision as of 16:01, 23 September 2010 by Wikispaces>xenwolf (**Imported revision 164978201 - Original comment: links added, some of them should describe the terminology**)

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This revision was by author xenwolf and made on 2010-09-23 16:01:44 UTC.
The original revision id was 164978201.
The revision comment was: links added, some of them should describe the terminology

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===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|]
[[edo|EDOs]]: [[99edo|99]], [[140edo|140]], [[239edo|239]], [[292edo|292]], [[490edo|490]], [[531edo|531]]

==11-limit children==

===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

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

===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>, |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, 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
[[edo|EDOs]]: [[94edo|94]], [[140edo|140]], [[181edo|181]], [[408edo|408]]

===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 />
<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 />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-11-limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit children</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-11-limit children-Pele"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pele</h3>
<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 />
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="/128edo">128</a>, <a class="wiki_link" href="/145edo">145</a>, <a class="wiki_link" href="/232edo">232</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-11-limit children-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], [[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-11-limit children-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;, |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, 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 />
<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 />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-11-limit children-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>