Graham complexity: Difference between revisions
Wikispaces>genewardsmith **Imported revision 242005839 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 242008691 - 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>2011-07-19 18: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-19 18:34:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>242008691</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //Graham complexity// of a set of pitch classes in a rank two temperament is the number of periods per octave times the difference between the maximum and minimum number of generators required to reach each pitch class.</pre></div> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //Graham complexity// of a set of pitch classes in a rank two temperament is the number of periods per octave times the difference between the maximum and minimum number of generators required to reach each pitch class. For example, consider a major triad in diaschismic temperament, with mapping [<2 0 11|, <0 1 -2|] corresponding to a generator of a '3'. That makes a 5/4 represented by [7 -2] and 3/2 by [-2 1], and 1 of course by [0 0]; so that the difference between the maximum and minimum number of generators is 1 - (-2) = 3, and so the Graham complexity of a major triad is 2*3 = 6.</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Graham complexity</title></head><body>The <em>Graham complexity</em> of a set of pitch classes in a rank two temperament is the number of periods per octave times the difference between the maximum and minimum number of generators required to reach each pitch class.</body></html></pre></div> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Graham complexity</title></head><body>The <em>Graham complexity</em> of a set of pitch classes in a rank two temperament is the number of periods per octave times the difference between the maximum and minimum number of generators required to reach each pitch class. For example, consider a major triad in diaschismic temperament, with mapping [&lt;2 0 11|, &lt;0 1 -2|] corresponding to a generator of a '3'. That makes a 5/4 represented by [7 -2] and 3/2 by [-2 1], and 1 of course by [0 0]; so that the difference between the maximum and minimum number of generators is 1 - (-2) = 3, and so the Graham complexity of a major triad is 2*3 = 6.</body></html></pre></div> | ||