Keenanismic family
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- This revision was by author genewardsmith and made on 2011-09-08 16:20:33 UTC.
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[[toc|flat]] The keenanismic family of rank four temperaments tempers out the [[385_384|keenanisma]], the 11-limit comma 385/384 = |-7 -1 1 1 1> of 4.503 cents. =Keenamismic= Comma: 385/384 Minimax tuning [|1 0 0 0 0>, |0 1 0 0 0>, |7/3 1/3 2/3 -1/3 -1/3>, |7/3 1/3 -1/3 2/3 -1/3>, |7/3 1/3 -1/3 -1/3 2/3>] Eigenmonzos: 2, 3, 7/5, 11/5 Map: [<1 0 0 0 7|, <0 1 0 0 1|, <0 0 1 0 -1|, <0 0 0 1 -1|] Transpose: [2 3 5 7 385/35] EDOs: [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[53edo|53]], [[68edo|53]], [[72edo|72]], [[118edo|118]], [[159edo|159]], [[190edo|190]], [[212edo|212]] and [[284edo|284]] 10^9*Badness: 15.159 =Martwin= Commas: 385/384, 325/324 Minimax tuning ||1 0 0 0 0 0>, |0 1 0 0 0 0>, |2/3 4/3 1/3 0 0 -1/3>, |17/3 -5/3 1/3 0 -1 2/3>, |2/3 4/3 -2/3 0 1 -1/3>, |2/3 4/3 -2/3 0 0 2/3>] Eigenmonzos: 2, 3, 11/5, 13/5 Map: [<1 0 0 0 7 2|, <0 1 0 0 1 4|, <0 0 1 0 -1 -2|, <0 0 0 1 -1 0|] Transpose: [2 3 5 7 385/35 324/25] EDOs: [[7edo|7]], [[15edo|15]], [[19edo|19]], [[26edo|26]], [[34edo|34]], [[41edo|41]], [[46edo|46]], [[53edo|53]], [[72edo|72]], [[87edo|87]], [[140edo|140]], [[159edo|159]], [[212edo|212]] and[[299edo|299]] 10^6*Badness: 2.206 =Ancient= Commas: 385/384, 625/624 Map: [<1 0 0 0 7 -4|, <0 1 0 0 1 -1|, <0 0 1 0 -1 4|, <0 0 0 1 -1 0|] Transpose: [2 3 5 7 385/35 625/48] EDOs: [[6edo|6]], [[15edo|15]], [[19edo|19]], [[22edo|22]], [31edo|31]], [[50edo|50]], [[53edo|53]], [[72edo|72]], [[87edo|87]], [[103edo|103]], [[140edo|140]], [[159edo|159]], [[190edo|190]] 10^6*Badness: 2.573
Original HTML content:
<html><head><title>Keenanismic family</title></head><body><!-- ws:start:WikiTextTocRule:6:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#Keenamismic">Keenamismic</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Martwin">Martwin</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Ancient">Ancient</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> <!-- ws:end:WikiTextTocRule:10 --><br /> The keenanismic family of rank four temperaments tempers out the <a class="wiki_link" href="/385_384">keenanisma</a>, the 11-limit comma 385/384 = |-7 -1 1 1 1> of 4.503 cents.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Keenamismic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Keenamismic</h1> Comma: 385/384<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0>, |0 1 0 0 0>, |7/3 1/3 2/3 -1/3 -1/3>, <br /> |7/3 1/3 -1/3 2/3 -1/3>, |7/3 1/3 -1/3 -1/3 2/3>]<br /> Eigenmonzos: 2, 3, 7/5, 11/5<br /> <br /> Map: [<1 0 0 0 7|, <0 1 0 0 1|, <0 0 1 0 -1|, <0 0 0 1 -1|]<br /> Transpose: [2 3 5 7 385/35]<br /> EDOs: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/68edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/190edo">190</a>, <a class="wiki_link" href="/212edo">212</a> and <a class="wiki_link" href="/284edo">284</a><br /> 10^9*Badness: 15.159<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Martwin"></a><!-- ws:end:WikiTextHeadingRule:2 -->Martwin</h1> Commas: 385/384, 325/324<br /> <br /> Minimax tuning<br /> ||1 0 0 0 0 0>, |0 1 0 0 0 0>, |2/3 4/3 1/3 0 0 -1/3>, <br /> |17/3 -5/3 1/3 0 -1 2/3>, |2/3 4/3 -2/3 0 1 -1/3>, |2/3 4/3 -2/3 0 0 2/3>]<br /> Eigenmonzos: 2, 3, 11/5, 13/5<br /> <br /> Map: [<1 0 0 0 7 2|, <0 1 0 0 1 4|, <0 0 1 0 -1 -2|, <0 0 0 1 -1 0|]<br /> Transpose: [2 3 5 7 385/35 324/25]<br /> EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/212edo">212</a> and<a class="wiki_link" href="/299edo">299</a><br /> 10^6*Badness: 2.206<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Ancient"></a><!-- ws:end:WikiTextHeadingRule:4 -->Ancient</h1> Commas: 385/384, 625/624<br /> <br /> Map: [<1 0 0 0 7 -4|, <0 1 0 0 1 -1|, <0 0 1 0 -1 4|, <0 0 0 1 -1 0|]<br /> Transpose: [2 3 5 7 385/35 625/48]<br /> EDOs: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, [31edo|31]], <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/103edo">103</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/190edo">190</a><br /> 10^6*Badness: 2.573</body></html>