Maximal harmony epimorphic scales: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 406560504 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 406993732 - 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>2013-02-12 23:03:56 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-02-14 11:34:20 UTC</tt>.<br>
: The original revision id was <tt>406560504</tt>.<br>
: The original revision id was <tt>406993732</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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==Seven notes==
==Seven notes==
[[maxsev1]]
[[maxsev1]]
[[maxsev2]]</pre></div>
[[maxsev2]]
 
=Marvel=
==Seven notes==
[[Gypsy scale]]</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Maximal harmony epimorphic scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of  a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the &lt;a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales"&gt;graph of the scale&lt;/a&gt; is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Maximal harmony epimorphic scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of  a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the &lt;a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales"&gt;graph of the scale&lt;/a&gt; is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x7 odd limit-Seven notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Seven notes&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x7 odd limit-Seven notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Seven notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/maxsev1"&gt;maxsev1&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/maxsev1"&gt;maxsev1&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/maxsev2"&gt;maxsev2&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;a class="wiki_link" href="/maxsev2"&gt;maxsev2&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Marvel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Marvel&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Marvel-Seven notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Seven notes&lt;/h2&gt;
&lt;a class="wiki_link" href="/Gypsy%20scale"&gt;Gypsy scale&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>