Diaschismic rank three family

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Revision as of 15:13, 11 December 2010 by Wikispaces>genewardsmith (**Imported revision 187368427 - Original comment: **)
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This revision was by author genewardsmith and made on 2010-12-11 15:13:01 UTC.
The original revision id was 187368427.
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:

These are the rank three temperaments tempering out the diaschisma, 2048/2025. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

==Julius==
Commas: 176/175, 896/891

Minimax tuning
[|1 0 0 0 0>, |11/8 1/2 -1/4 0 0>, |11/4 -1 1/2 0 0>, 
|-1/8 3/2 -5/4 0 1>, |11/8 -1/2 -1/4 0 1>]
Eigenmonzos: 2, 12/11, 10/9

Map: [<2 0 11 0 14|, <0 1 -2 0 -4|, <0 0 0 1 1 |]
EDOs: 58, 68, 80, 126

==Augustus==
Commas: 385/384, 1232/1215

Minimax tuning
[|1 0 0 0 0>, |11/8 1/2 -1/4 0 0>, |11/4 -1 1/2 0 0>, 
|45/16 3/4 -3/8 1/2 -1/2>, |45/16 3/4 -3/8 -1/2 1/2>]
Eigenmonzos: 2, 10/9, 14/11

Map: [<2 0 11 0 3|, <0 1 -2 0 3|, <0 0 0 1 -1|]
EDOs: 46, 68, 114, 124

Original HTML content:

<html><head><title>Diaschismic rank three family</title></head><body>These are the rank three temperaments tempering out the diaschisma, 2048/2025. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Julius"></a><!-- ws:end:WikiTextHeadingRule:0 -->Julius</h2>
Commas: 176/175, 896/891<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |11/8 1/2 -1/4 0 0&gt;, |11/4 -1 1/2 0 0&gt;, <br />
|-1/8 3/2 -5/4 0 1&gt;, |11/8 -1/2 -1/4 0 1&gt;]<br />
Eigenmonzos: 2, 12/11, 10/9<br />
<br />
Map: [&lt;2 0 11 0 14|, &lt;0 1 -2 0 -4|, &lt;0 0 0 1 1 |]<br />
EDOs: 58, 68, 80, 126<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Augustus"></a><!-- ws:end:WikiTextHeadingRule:2 -->Augustus</h2>
Commas: 385/384, 1232/1215<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |11/8 1/2 -1/4 0 0&gt;, |11/4 -1 1/2 0 0&gt;, <br />
|45/16 3/4 -3/8 1/2 -1/2&gt;, |45/16 3/4 -3/8 -1/2 1/2&gt;]<br />
Eigenmonzos: 2, 10/9, 14/11<br />
<br />
Map: [&lt;2 0 11 0 3|, &lt;0 1 -2 0 3|, &lt;0 0 0 1 -1|]<br />
EDOs: 46, 68, 114, 124</body></html>
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