Fokker chord: Difference between revisions
Wikispaces>genewardsmith **Imported revision 500130866 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 500311060 - 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>2014-04- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-04-03 10:30:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>500311060</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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=7-limit tetrads= | =7-limit tetrads= | ||
The major (otonal) and minor (utonal) 7-limit tetrads are Fokker blocks in eight different ways. In the table below, the chromas defining each of these arenas are listed in the first columns, and the offsets giving the otonal and utonal tetrads in the second. Hence, from the first row, we can find that the otonal tetrad is Fokblock([21/20, 15/14, 35/32], [2, 2, 2] ) and the utonal tetrad is Fokblock([21/20, 15/14, 35/32], [3, 3, 0]). The dual Fokker group basis is given in the last column in abbreviated form. Each number corresponds to a patent val, and that val, wedged with the patent val for four, gives the Fokker group element. Hence in the first row, 1, 3, 2 is shorthand for 1&4, 3&4, 2&4, and these denote the wedgies <<2 -1 1 -6 -4 5||, <<2 1 -1 -3 -7 -5||, <<0 2 2 3 3 -1||. | |||
|| | || Chroma basis || Major offsets || Minor offsets || Dual basis || | ||
|| [21/20, 15/14, 35/32] || [2, 2, 2] || [3, 3, 0] || 1, 3, 2 || | || [21/20, 15/14, 35/32] || [2, 2, 2] || [3, 3, 0] || 1, 3, 2 || | ||
|| [25/24, 15/14, 35/32] || [1, 2, 3] || [0, 3, 2] || 1, 3, 7 || | || [25/24, 15/14, 35/32] || [1, 2, 3] || [0, 3, 2] || 1, 3, 7 || | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x7-limit tetrads"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit tetrads</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x7-limit tetrads"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit tetrads</h1> | ||
The major (otonal) and minor (utonal) 7-limit tetrads are Fokker blocks in eight different ways. In the table below, the chromas defining each of these arenas are listed in the first columns, and the offsets giving the otonal and utonal tetrads in the second. Hence, from the first row, we can find that the otonal tetrad is Fokblock([21/20, 15/14, 35/32], [2, 2, 2] ) and the utonal tetrad is Fokblock([21/20, 15/14, 35/32], [3, 3, 0]). The dual Fokker group basis is given in the last column in abbreviated form. Each number corresponds to a patent val, and that val, wedged with the patent val for four, gives the Fokker group element. Hence in the first row, 1, 3, 2 is shorthand for 1&amp;4, 3&amp;4, 2&amp;4, and these denote the wedgies &lt;&lt;2 -1 1 -6 -4 5||, &lt;&lt;2 1 -1 -3 -7 -5||, &lt;&lt;0 2 2 3 3 -1||.<br /> | |||
<br /> | <br /> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td> | <td>Chroma basis<br /> | ||
</td> | </td> | ||
<td>Major | <td>Major offsets<br /> | ||
</td> | </td> | ||
<td>Minor | <td>Minor offsets<br /> | ||
</td> | </td> | ||
<td> | <td>Dual basis<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||