Archytas family: Difference between revisions

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**Imported revision 195703526 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 203033580 - 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>2011-01-24 18:54:18 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-18 06:59:08 UTC</tt>.<br>
: The original revision id was <tt>195703526</tt>.<br>
: The original revision id was <tt>203033580</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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Scales: [[ares12]]
Scales: [[ares12]]
</pre></div>
 
==Vulcan==
Commas: 56/55, 64/63</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Archytas family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord, which is familiar from &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and also a feature of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; and &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;.&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Archytas family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord, which is familiar from &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and also a feature of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; and &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;.&lt;br /&gt;
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Badness: 0.000469&lt;br /&gt;
Badness: 0.000469&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/ares12"&gt;ares12&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Scales: &lt;a class="wiki_link" href="/ares12"&gt;ares12&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Vulcan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Vulcan&lt;/h2&gt;
Commas: 56/55, 64/63&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 06:59, 18 February 2011

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 2011-02-18 06:59:08 UTC.
The original revision id was 203033580.
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>]
[[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]]: [[7edo|7]], [[10edo|10]], [[12edo|12]], [[15edo|15]], [[22edo|22]], [[27edo|27]], [[37edo|37]], [[49edo|49]], [[59edo|59]]
Scales: [[archytas12]]

Music: Chris Vaisvil 
[[http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3|12 archytas hobbits with ale]]
==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

Lattice basis: 3/2 0.9878 6/5 1.4312
Angle(3/2, 6/5) = 75.0475 degrees
Map to lattice: [<0 1 1 -2 0|, <0 0 -1 0 -2|]

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]]
Badness: 0.000469

Scales: [[ares12]]

==Vulcan==
Commas: 56/55, 64/63

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&gt;, |2 1/3 0 -1/3&gt;, <br />
|2 -2/3 1 -1/3&gt;, |2 -2/3 0 2/3&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 6/5, 7/5<br />
<br />
9-limit minimax<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 />
<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: [&lt;0 1 0 -2|, &lt;0 0 1 0|]<br />
<br />
Map: [&lt;1 0 0 6|, &lt;0 1 0 -2|, &lt;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="/7edo">7</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 />
Scales: <a class="wiki_link" href="/archytas12">archytas12</a><br />
<br />
Music: Chris Vaisvil <br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3" rel="nofollow">12 archytas hobbits with ale</a><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>
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Ares"></a><!-- ws:end:WikiTextHeadingRule:2 -->Ares</h2>
<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&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 />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9, 9/7<br />
<br />
Lattice basis: 3/2 0.9878 6/5 1.4312<br />
Angle(3/2, 6/5) = 75.0475 degrees<br />
Map to lattice: [&lt;0 1 1 -2 0|, &lt;0 0 -1 0 -2|]<br />
<br />
Map: [&lt;1 0 0 6 2|, &lt;0 1 0 -2 -2|, &lt;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><br />
Badness: 0.000469<br />
<br />
Scales: <a class="wiki_link" href="/ares12">ares12</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Vulcan"></a><!-- ws:end:WikiTextHeadingRule:4 -->Vulcan</h2>
Commas: 56/55, 64/63</body></html>