Regular temperament: Difference between revisions
Wikispaces>genewardsmith **Imported revision 511016062 - Original comment: ** |
Wikispaces>clumma **Imported revision 535151684 - Original comment: GTFO** |
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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:clumma|clumma]] and made on <tt>2014-12-14 22:20:08 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>535151684</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>GTFO</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> | ||
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=Characterizing an abstract regular temperament= | =Characterizing an abstract regular temperament= | ||
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<!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Characterizing an abstract regular temperament">Characterizing an abstract regular temperament</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Translation between methods of specifying temperaments">Translation between methods of specifying temperaments</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#The Geometry of Regular Temperaments">The Geometry of Regular Temperaments</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Characterizing an abstract regular temperament">Characterizing an abstract regular temperament</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Translation between methods of specifying temperaments">Translation between methods of specifying temperaments</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#The Geometry of Regular Temperaments">The Geometry of Regular Temperaments</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Characterizing an abstract regular temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->Characterizing an abstract regular temperament</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Characterizing an abstract regular temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->Characterizing an abstract regular temperament</h1> | ||
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Grassmannians have the structure of a smooth, homogenous <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Metric_space" rel="nofollow">metric space</a>, and hence represent a distinctly geometric mathematical object. In the 5-limit, the Grassmannian <strong>Gr</strong>(2, 3), consisting of the planes through the origin in three dimensional space, may be identified with the projective plane, and hence 5-limit rank two temperaments may be pictured as points in a projective plane, as below.<br /> | Grassmannians have the structure of a smooth, homogenous <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Metric_space" rel="nofollow">metric space</a>, and hence represent a distinctly geometric mathematical object. In the 5-limit, the Grassmannian <strong>Gr</strong>(2, 3), consisting of the planes through the origin in three dimensional space, may be identified with the projective plane, and hence 5-limit rank two temperaments may be pictured as points in a projective plane, as below.<br /> | ||
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