Archytas family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 165868333 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 166515177 - Original comment: links added; please would you describe Eigenmonzo? Thanks in advance :-)** |
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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: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-29 16:47:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>166515177</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>links added; please would you describe [[Eigenmonzo]]? Thanks in advance :-)</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">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]]. | <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;white-space: pre-wrap ! important" class="old-revision-html">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 | [[Comma]]: 64/63 | ||
7-limit minimax | 7-limit minimax | ||
[|1 0 0 0>, |2 1/3 0 -1/3>, | [|1 0 0 0>, |2 1/3 0 -1/3>, | ||
|2 -2/3 1 -1/3>, |2 -2/3 0 2/3>] | |2 -2/3 1 -1/3>, |2 -2/3 0 2/3>] | ||
Eigenmonzos: 2, 6/5, 7/5 | [[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 7/5 | ||
9-limit minimax | 9-limit minimax | ||
[|1 0 0 0>, |3/2 1/2 0 -1/4>, | [|1 0 0 0>, |3/2 1/2 0 -1/4>, | ||
|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 | [[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 9/7 | ||
Lattice basis: 3/2 length 1.0508 5/4 length 2.3219 | Lattice basis: 3/2 length 1.0508 5/4 length 2.3219 | ||
| Line 25: | Line 25: | ||
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|] | ||
Generators: 2, 3, 5 | [[Generator|Generators]]: 2, 3, 5 | ||
Edos: 10, 12, 15, 22, 27, 37, 49, 59 | [[edo|Edos]]: [[10edo|10]], [[12edo|12]], [[15edo|15]], [[22edo|22]], [[27edo|27]], [[37edo|37]], [[49edo|49]], [[59edo|59]] | ||
==11 limit children== | ==11 limit children== | ||
===Ares=== | ===Ares=== | ||
Commas: 64/63, 100/99 | [[Comma|Commas]]: 64/63, 100/99 | ||
Minimax tuning | [[Minimax tuning]] | ||
[|1 0 0 0 0>, |3/2 1/2 0 -1/4 0>, | [|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>, | |2 0 0 -1/2 1/2>, |3 -1 0 1/2 0>, | ||
|3 -1 0 -1/2 1>] | |3 -1 0 -1/2 1>] | ||
Eigenmonzos: 2, 11/9, 9/7 | [[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 9/7 | ||
Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|] | Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|] | ||
Generators: 2, 3, 5 | [[Generator|Generators]]: 2, 3, 5 | ||
Edos: 12, 15, 22, 37, 49</pre></div> | [[edo|Edos]]: [[12edo|12]], [[15edo|15]], [[22edo|22]], [[37edo|37]], [[49edo|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 /> | ||
<br /> | <br /> | ||
Comma: 64/63<br /> | <a class="wiki_link" href="/Comma">Comma</a>: 64/63<br /> | ||
<br /> | <br /> | ||
7-limit minimax<br /> | 7-limit minimax<br /> | ||
[|1 0 0 0&gt;, |2 1/3 0 -1/3&gt;, <br /> | [|1 0 0 0&gt;, |2 1/3 0 -1/3&gt;, <br /> | ||
|2 -2/3 1 -1/3&gt;, |2 -2/3 0 2/3&gt;]<br /> | |2 -2/3 1 -1/3&gt;, |2 -2/3 0 2/3&gt;]<br /> | ||
Eigenmonzos: 2, 6/5, 7/5<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 6/5, 7/5<br /> | ||
<br /> | <br /> | ||
9-limit minimax<br /> | 9-limit minimax<br /> | ||
[|1 0 0 0&gt;, |3/2 1/2 0 -1/4&gt;, <br /> | [|1 0 0 0&gt;, |3/2 1/2 0 -1/4&gt;, <br /> | ||
|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 /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 6/5, 9/7<br /> | ||
<br /> | <br /> | ||
Lattice basis: 3/2 length 1.0508 5/4 length 2.3219<br /> | Lattice basis: 3/2 length 1.0508 5/4 length 2.3219<br /> | ||
| Line 62: | Line 62: | ||
<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 /> | ||
Generators: 2, 3, 5<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br /> | ||
Edos: 10, 12, 15, 22, 27, 37, 49, 59<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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-11 limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->11 limit children</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-11 limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->11 limit children</h2> | ||
<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<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 64/63, 100/99<br /> | ||
<br /> | <br /> | ||
Minimax tuning<br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> | ||
[|1 0 0 0 0&gt;, |3/2 1/2 0 -1/4 0&gt;, <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 /> | |2 0 0 -1/2 1/2&gt;, |3 -1 0 1/2 0&gt;, <br /> | ||
|3 -1 0 -1/2 1&gt;]<br /> | |3 -1 0 -1/2 1&gt;]<br /> | ||
Eigenmonzos: 2, 11/9, 9/7<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9, 9/7<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 6 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 0 2|]<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 /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br /> | ||
Edos: 12, 15, 22, 37, 49</body></html></pre></div> | <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></pre></div> | ||