Sensamagic family
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- This revision was by author genewardsmith and made on 2011-12-28 03:13:14 UTC.
- The original revision id was 288626852.
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Original Wikitext content:
[[toc]]
=Sensamagic=
[[Comma]]: 245/243
[[7-limit]] [[minimax]]
[|1 0 0 0>, |0 0 1/5 2/5>, |0 0 1 0>, |0 0 0 1>]
[[Eigenmonzo]]s: 2, 8/7, 5/4
[[9-limit]] minimax
[|1 0 0 0>, |0 1 0 0>, |0 5/3 2/3 -2/3>, |0 5/3 -1/3 1/3>]
Eigenmonzos: 2, 4/3, 7/5
Lattice basis: 3/2 0.9644 9/7 1.0807
Angle(3/2, 9/7) = 86.5288
Map to lattice: [<0 1 1 2|, <0 0 2 -1|]
Map: [<1 0 0 0|, <0 1 1 2|, <0 0 2 -1|]
Generators: 2, 3, 9/7
Edos: [[17edo|,17]] [[19edo|19]], [[22edo|22]], [[24edo|24]], [[27edo|27]], [[41edo|41]], [[46edo|46]], [[60edo|60]], [[68edo|68]], [[87edo|87]], [[109edo|109]], [[128edo|128]], [[169edo|169]], [[177edo|177]], [[237edo|237]]
[[Badness]]: 0.000129
[[Projection pair]]: 5 243/49 to 2.3.7
===[[Minkowski blocks]]===
{2, 3, 7} subgroup
12: 729/686, 64/63
17: 64/63, 19683/19208
19: 49/48, 177147/175616
22: 64/63, 537824/531441
24: 64/63, 15059072/14348907
==Undecimal sensamagic==
Commas: 245/243, 385/384
[[11-limit]] minimax
[|1 0 0 0 0>, |21/13 6/13 -1/13 1/13 -3/13>,
|35/13 10/13 7/13 -7/13 -5/13>,
|35/13 10/13 -6/13 6/13 -5/13>,
|42/13 -14/13 -2/13 2/13 7/13>]
Eigenmonzos: 2, 11/9, 7/5
Map: [<1 0 0 0 7|, <0 1 1 2 -2|, <0 0 2 -1 -1|]
Generators: 2, 3, 9/7
EDOs: [[5edo|5]], 17, 19, 22, 41, 68, 87, [[196edo|196]], [[283edo|283]], 607bd, 694bd
Badness: 0.000722
Projection pairs: 5 243/49 11 896/81 to 2.3.7
==13-limit==
Commas: 245/243, 352/351, 385/384
Map: [<1 0 0 0 7 12|, <0 1 1 2 -2 -5|, <0 0 2 -1 -1 -1|]
Generators: 2, 3, 9/7
EDOs: 17, 22, 41, 46, 63, 87, 237, 283, 324d, 370bd, 411bd, 607bd, 694bd
Badness: 0.00120
=Sensawer=
Commas: 245/243, 441/440
Map: [<1 0 0 0 -3|, <0 1 1 2 5|, <0 0 2 -1 -4|]
EDOs: 41, 87, 302d, 389d, 476bd
Badness: 0.000796
==13-limit==
Commas: 196/195, 245/243, 352/351
Map: [<1 0 0 0 -3 2|, <0 1 1 2 5 2|, <0 0 2 -1 -4 -4|]
EDOs: 41, 46, 87, 522bd
Badness: 0.000928
=Octarod=
Commas: 100/99, 245/243
Map: [<1 0 0 0 2|, <0 1 1 2 0|, <0 0 2 -1 4|]
EDOs: 19, 22, 41, 63, 104, 109e, 131e, 172e
Badness: 0.000581
Original HTML content:
<html><head><title>Sensamagic family</title></head><body><!-- ws:start:WikiTextTocRule:14:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 1em;"><a href="#Sensamagic">Sensamagic</a></div>
<!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 3em;"><a href="#Sensamagic--Minkowski blocks">Minkowski blocks</a></div>
<!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 2em;"><a href="#Sensamagic-Undecimal sensamagic">Undecimal sensamagic</a></div>
<!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 2em;"><a href="#Sensamagic-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><div style="margin-left: 1em;"><a href="#Sensawer">Sensawer</a></div>
<!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><div style="margin-left: 2em;"><a href="#Sensawer-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><div style="margin-left: 1em;"><a href="#Octarod">Octarod</a></div>
<!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --></div>
<!-- ws:end:WikiTextTocRule:22 --><br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Sensamagic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Sensamagic</h1>
<a class="wiki_link" href="/Comma">Comma</a>: 245/243<br />
<br />
<a class="wiki_link" href="/7-limit">7-limit</a> <a class="wiki_link" href="/minimax">minimax</a><br />
[|1 0 0 0>, |0 0 1/5 2/5>, |0 0 1 0>, |0 0 0 1>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 8/7, 5/4<br />
<br />
<a class="wiki_link" href="/9-limit">9-limit</a> minimax<br />
[|1 0 0 0>, |0 1 0 0>, |0 5/3 2/3 -2/3>, |0 5/3 -1/3 1/3>]<br />
Eigenmonzos: 2, 4/3, 7/5 <br />
<br />
Lattice basis: 3/2 0.9644 9/7 1.0807<br />
Angle(3/2, 9/7) = 86.5288<br />
Map to lattice: [<0 1 1 2|, <0 0 2 -1|]<br />
<br />
Map: [<1 0 0 0|, <0 1 1 2|, <0 0 2 -1|]<br />
Generators: 2, 3, 9/7<br />
Edos: <a class="wiki_link" href="/17edo">,17</a> <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/60edo">60</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/109edo">109</a>, <a class="wiki_link" href="/128edo">128</a>, <a class="wiki_link" href="/169edo">169</a>, <a class="wiki_link" href="/177edo">177</a>, <a class="wiki_link" href="/237edo">237</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.000129<br />
<br />
<a class="wiki_link" href="/Projection%20pair">Projection pair</a>: 5 243/49 to 2.3.7<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="Sensamagic--Minkowski blocks"></a><!-- ws:end:WikiTextHeadingRule:2 --><a class="wiki_link" href="/Minkowski%20blocks">Minkowski blocks</a></h3>
{2, 3, 7} subgroup<br />
<br />
12: 729/686, 64/63<br />
17: 64/63, 19683/19208<br />
19: 49/48, 177147/175616<br />
22: 64/63, 537824/531441<br />
24: 64/63, 15059072/14348907<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Sensamagic-Undecimal sensamagic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Undecimal sensamagic</h2>
Commas: 245/243, 385/384<br />
<br />
<a class="wiki_link" href="/11-limit">11-limit</a> minimax<br />
[|1 0 0 0 0>, |21/13 6/13 -1/13 1/13 -3/13>, <br />
|35/13 10/13 7/13 -7/13 -5/13>, <br />
|35/13 10/13 -6/13 6/13 -5/13>, <br />
|42/13 -14/13 -2/13 2/13 7/13>]<br />
Eigenmonzos: 2, 11/9, 7/5<br />
<br />
Map: [<1 0 0 0 7|, <0 1 1 2 -2|, <0 0 2 -1 -1|]<br />
Generators: 2, 3, 9/7<br />
EDOs: <a class="wiki_link" href="/5edo">5</a>, 17, 19, 22, 41, 68, 87, <a class="wiki_link" href="/196edo">196</a>, <a class="wiki_link" href="/283edo">283</a>, 607bd, 694bd<br />
Badness: 0.000722<br />
<br />
Projection pairs: 5 243/49 11 896/81 to 2.3.7<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Sensamagic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2>
Commas: 245/243, 352/351, 385/384<br />
<br />
Map: [<1 0 0 0 7 12|, <0 1 1 2 -2 -5|, <0 0 2 -1 -1 -1|]<br />
Generators: 2, 3, 9/7<br />
EDOs: 17, 22, 41, 46, 63, 87, 237, 283, 324d, 370bd, 411bd, 607bd, 694bd<br />
Badness: 0.00120<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Sensawer"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensawer</h1>
Commas: 245/243, 441/440<br />
<br />
Map: [<1 0 0 0 -3|, <0 1 1 2 5|, <0 0 2 -1 -4|]<br />
EDOs: 41, 87, 302d, 389d, 476bd<br />
Badness: 0.000796<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Sensawer-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h2>
Commas: 196/195, 245/243, 352/351<br />
<br />
Map: [<1 0 0 0 -3 2|, <0 1 1 2 5 2|, <0 0 2 -1 -4 -4|]<br />
EDOs: 41, 46, 87, 522bd<br />
Badness: 0.000928<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Octarod"></a><!-- ws:end:WikiTextHeadingRule:12 -->Octarod</h1>
Commas: 100/99, 245/243<br />
<br />
Map: [<1 0 0 0 2|, <0 1 1 2 0|, <0 0 2 -1 4|]<br />
EDOs: 19, 22, 41, 63, 104, 109e, 131e, 172e <br />
Badness: 0.000581</body></html>