Archytas family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 165809979 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 165868333 - 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>2010-09-27 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-27 20:34:28 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>165868333</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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|3/2 -1/2 1 -1/4>, |3 -1 0 1/2>] | |3/2 -1/2 1 -1/4>, |3 -1 0 1/2>] | ||
Eigenmonzos: 2, 6/5, 9/7 | 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|] | Map: [<1 0 0 6|, <0 1 0 -2|, <0 0 1 0|] | ||
| Line 28: | Line 32: | ||
===Ares=== | ===Ares=== | ||
Commas: 64/63, 100/99 | Commas: 64/63, 100/99 | ||
</pre></div> | |||
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>] | |||
Eigenmonzos: 2, 11/9, 9/7 | |||
Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|] | |||
Generators: 2, 3, 5 | |||
Edos: 12, 15, 22, 37, 49</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>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 /> | <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>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 /> | ||
| Line 43: | Line 56: | ||
|3/2 -1/2 1 -1/4&gt;, |3 -1 0 1/2&gt;]<br /> | |3/2 -1/2 1 -1/4&gt;, |3 -1 0 1/2&gt;]<br /> | ||
Eigenmonzos: 2, 6/5, 9/7<br /> | Eigenmonzos: 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: [&lt;0 1 0 -2|, &lt;0 0 1 0|]<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 0 6|, &lt;0 1 0 -2|, &lt;0 0 1 0|]<br /> | Map: [&lt;1 0 0 6|, &lt;0 1 0 -2|, &lt;0 0 1 0|]<br /> | ||
| Line 51: | Line 68: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-11 limit children-Ares"></a><!-- ws:end:WikiTextHeadingRule:2 -->Ares</h3> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-11 limit children-Ares"></a><!-- ws:end:WikiTextHeadingRule:2 -->Ares</h3> | ||
Commas: 64/63, 100/99</body></html></pre></div> | Commas: 64/63, 100/99<br /> | ||
<br /> | |||
Minimax tuning<br /> | |||
[|1 0 0 0 0&gt;, |3/2 1/2 0 -1/4 0&gt;, <br /> | |||
|2 0 0 -1/2 1/2&gt;, |3 -1 0 1/2 0&gt;, <br /> | |||
|3 -1 0 -1/2 1&gt;]<br /> | |||
Eigenmonzos: 2, 11/9, 9/7<br /> | |||
<br /> | |||
Map: [&lt;1 0 0 6 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 0 2|]<br /> | |||
Generators: 2, 3, 5<br /> | |||
Edos: 12, 15, 22, 37, 49</body></html></pre></div> | |||
Revision as of 20:34, 27 September 2010
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 2010-09-27 20:34:28 UTC.
- The original revision id was 165868333.
- 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:
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>] 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>] 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|] Generators: 2, 3, 5 Edos: 10, 12, 15, 22, 27, 37, 49, 59 ==11 limit children== ===Ares=== 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>] Eigenmonzos: 2, 11/9, 9/7 Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|] Generators: 2, 3, 5 Edos: 12, 15, 22, 37, 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 /> Comma: 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 /> Eigenmonzos: 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 /> Eigenmonzos: 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 /> Generators: 2, 3, 5<br /> Edos: 10, 12, 15, 22, 27, 37, 49, 59<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> Commas: 64/63, 100/99<br /> <br /> Minimax tuning<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 /> Eigenmonzos: 2, 11/9, 9/7<br /> <br /> Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|]<br /> Generators: 2, 3, 5<br /> Edos: 12, 15, 22, 37, 49</body></html>