Chordal space: Difference between revisions
Wikispaces>genewardsmith **Imported revision 149831565 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 154015043 - 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>2010- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-07-26 01:51:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>154015043</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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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. | ||
[[ | [[file:Chordal12.svg]] | ||
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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< | <!-- ws:start:WikiTextFileRule:138:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/Chordal12.svg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@Chordal12.svg&quot; title=&quot;File: Chordal12.svg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/Chordal12.svg/154014593/Chordal12.svg" onclick="ws.common.trackFileLink('/file/view/Chordal12.svg/154014593/Chordal12.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="Chordal12.svg" /></a><div><a href="/file/view/Chordal12.svg/154014593/Chordal12.svg" onclick="ws.common.trackFileLink('/file/view/Chordal12.svg/154014593/Chordal12.svg');" class="filename" title="Chordal12.svg">Chordal12.svg</a><br /><ul><li><a href="/file/detail/Chordal12.svg">Details</a></li><li><a href="/file/view/Chordal12.svg/154014593/Chordal12.svg">Download</a></li><li style="color: #666">46 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:138 --> <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 /> | ||