Archytas family
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author xenwolf and made on 2010-09-29 16:47:24 UTC.
- The original revision id was 166515177.
- The revision comment was: links added; please would you describe Eigenmonzo? Thanks in advance :-)
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Original Wikitext content:
Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord, which is familiar from [[12edo]] and also a feature of [[22edo]] and [[27edo]]. [[Comma]]: 64/63 7-limit minimax [|1 0 0 0>, |2 1/3 0 -1/3>, |2 -2/3 1 -1/3>, |2 -2/3 0 2/3>] [[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 7/5 9-limit minimax [|1 0 0 0>, |3/2 1/2 0 -1/4>, |3/2 -1/2 1 -1/4>, |3 -1 0 1/2>] [[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 9/7 Lattice basis: 3/2 length 1.0508 5/4 length 2.3219 Angle(3/2, 5/4) = 90 degrees Map to lattice: [<0 1 0 -2|, <0 0 1 0|] Map: [<1 0 0 6|, <0 1 0 -2|, <0 0 1 0|] [[Generator|Generators]]: 2, 3, 5 [[edo|Edos]]: [[10edo|10]], [[12edo|12]], [[15edo|15]], [[22edo|22]], [[27edo|27]], [[37edo|37]], [[49edo|49]], [[59edo|59]] ==11 limit children== ===Ares=== [[Comma|Commas]]: 64/63, 100/99 [[Minimax tuning]] [|1 0 0 0 0>, |3/2 1/2 0 -1/4 0>, |2 0 0 -1/2 1/2>, |3 -1 0 1/2 0>, |3 -1 0 -1/2 1>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 9/7 Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|] [[Generator|Generators]]: 2, 3, 5 [[edo|Edos]]: [[12edo|12]], [[15edo|15]], [[22edo|22]], [[37edo|37]], [[49edo|49]]
Original HTML content:
<html><head><title>Archytas family</title></head><body>Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord, which is familiar from <a class="wiki_link" href="/12edo">12edo</a> and also a feature of <a class="wiki_link" href="/22edo">22edo</a> and <a class="wiki_link" href="/27edo">27edo</a>.<br /> <br /> <a class="wiki_link" href="/Comma">Comma</a>: 64/63<br /> <br /> 7-limit minimax<br /> [|1 0 0 0>, |2 1/3 0 -1/3>, <br /> |2 -2/3 1 -1/3>, |2 -2/3 0 2/3>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 6/5, 7/5<br /> <br /> 9-limit minimax<br /> [|1 0 0 0>, |3/2 1/2 0 -1/4>, <br /> |3/2 -1/2 1 -1/4>, |3 -1 0 1/2>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 6/5, 9/7<br /> <br /> Lattice basis: 3/2 length 1.0508 5/4 length 2.3219<br /> Angle(3/2, 5/4) = 90 degrees<br /> Map to lattice: [<0 1 0 -2|, <0 0 1 0|]<br /> <br /> Map: [<1 0 0 6|, <0 1 0 -2|, <0 0 1 0|]<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="/10edo">10</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/37edo">37</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/59edo">59</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-11 limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->11 limit children</h2> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-11 limit children-Ares"></a><!-- ws:end:WikiTextHeadingRule:2 -->Ares</h3> <a class="wiki_link" href="/Comma">Commas</a>: 64/63, 100/99<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> [|1 0 0 0 0>, |3/2 1/2 0 -1/4 0>, <br /> |2 0 0 -1/2 1/2>, |3 -1 0 1/2 0>, <br /> |3 -1 0 -1/2 1>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9, 9/7<br /> <br /> Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 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="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/37edo">37</a>, <a class="wiki_link" href="/49edo">49</a></body></html>