Chordal space: Difference between revisions
Wikispaces>guest **Imported revision 149829367 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 149831565 - 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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-21 12:41:12 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>149831565</tt>.<br> | ||
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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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We can now take the twenty-four major and minor triads of equal temperament and place them on the vertices of a regular 24-gon. We then draw lines from triads separated by one step, and also from each major triad to its parallel minor triad, and obtain a geometric picture of the regular graph in question, which satisfactorily models the triadic relationships in 12 equal temperament. | We can now take the twenty-four major and minor triads of equal temperament and place them on the vertices of a regular 24-gon. We then draw lines from triads separated by one step, and also from each major triad to its parallel minor triad, and obtain a geometric picture of the regular graph in question, which satisfactorily models the triadic relationships in 12 equal temperament. | ||
[[ | [[http://tinyurl.com/277rbhd|Cyclic chordal space for 12 equal]] | ||
Cyclic chordal space for 12 equal | |||
We may obtain very similar pictures for any of the other equal temperaments supporting the use of [[meantone temperament]], including in particular [[19edo]] and [[31edo]], by drawing a 38-gon or a 62-gon respectively, and linking all chords separated by one step, and the correct half separated by seven steps. | We may obtain very similar pictures for any of the other equal temperaments supporting the use of [[meantone temperament]], including in particular [[19edo]] and [[31edo]], by drawing a 38-gon or a 62-gon respectively, and linking all chords separated by one step, and the correct half separated by seven steps. | ||
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We can now take the twenty-four major and minor triads of equal temperament and place them on the vertices of a regular 24-gon. We then draw lines from triads separated by one step, and also from each major triad to its parallel minor triad, and obtain a geometric picture of the regular graph in question, which satisfactorily models the triadic relationships in 12 equal temperament.<br /> | We can now take the twenty-four major and minor triads of equal temperament and place them on the vertices of a regular 24-gon. We then draw lines from triads separated by one step, and also from each major triad to its parallel minor triad, and obtain a geometric picture of the regular graph in question, which satisfactorily models the triadic relationships in 12 equal temperament.<br /> | ||
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<a class=" | <a class="wiki_link_ext" href="http://tinyurl.com/277rbhd" rel="nofollow">Cyclic chordal space for 12 equal</a> <br /> | ||
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We may obtain very similar pictures for any of the other equal temperaments supporting the use of <a class="wiki_link" href="/meantone%20temperament">meantone temperament</a>, including in particular <a class="wiki_link" href="/19edo">19edo</a> and <a class="wiki_link" href="/31edo">31edo</a>, by drawing a 38-gon or a 62-gon respectively, and linking all chords separated by one step, and the correct half separated by seven steps.<br /> | We may obtain very similar pictures for any of the other equal temperaments supporting the use of <a class="wiki_link" href="/meantone%20temperament">meantone temperament</a>, including in particular <a class="wiki_link" href="/19edo">19edo</a> and <a class="wiki_link" href="/31edo">31edo</a>, by drawing a 38-gon or a 62-gon respectively, and linking all chords separated by one step, and the correct half separated by seven steps.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-External links"></a><!-- ws:end:WikiTextHeadingRule:14 -->External links</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-External links"></a><!-- ws:end:WikiTextHeadingRule:14 -->External links</h2> | ||
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*[<!-- ws:start:WikiTextUrlRule: | *[<!-- ws:start:WikiTextUrlRule:284:http://66.98.148.43/~xenharmo/sevlat.htm --><a class="wiki_link_ext" href="http://66.98.148.43/~xenharmo/sevlat.htm" rel="nofollow">http://66.98.148.43/~xenharmo/sevlat.htm</a><!-- ws:end:WikiTextUrlRule:284 --> Seven-limit modulatory and chordal space]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-References"></a><!-- ws:end:WikiTextHeadingRule:16 -->References</h2> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-References"></a><!-- ws:end:WikiTextHeadingRule:16 -->References</h2> | ||