Graph-theoretic properties of scales: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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==Elfjove7==

[[Elfjove7]] is the seven note elf scale of jove temperament, the 11-limit temperament rank three tempering out 243/242, 441/440, 540/539 and 2401/2400. In the 202et tuning, it has steps 0, 39, 59, 84, 118, 143, 163, 202, with a consonance set {25, 28, 31, 34, 39, 45, 53, 59, 65, 70, 73, 84, 93, 98, 104, 109, 118, 129, 132, 137, 143, 149, 157, 163, 168, 171, 174, 177}. The permutation group of automorphisms is intransitive, with orbits {0}, {1, 6} and {2, 3, 4, 5}. The group is the group of the square, acting transitively on the {2, 3, 4, 5} orbit, and ~~exchanging~~ 1 and 6 ~~when~~ the ~~permutation of~~ 2345 ~~is odd~~.

[[Elfjove7]] is the seven note elf scale of jove temperament, the 11-limit temperament rank three tempering out 243/242, 441/440, 540/539 and 2401/2400. In the 202et tuning, it has steps 0, 39, 59, 84, 118, 143, 163, 202, with a consonance set {25, 28, 31, 34, 39, 45, 53, 59, 65, 70, 73, 84, 93, 98, 104, 109, 118, 129, 132, 137, 143, 149, 157, 163, 168, 171, 174, 177}. The permutation group of automorphisms is intransitive, with orbits {0}, {1, 6} and {2, 3, 4, 5}. The group is the group of the square, acting transitively on the {2, 3, 4, 5} orbit. The permuations of the {2, 3, 4, 5} square Identity, (24), (35), and (24)(35) leave 1 and 6 fixed, and the permutations (2345), (23)(45), (2543) and (25)(43) exchange the pair.

Elfjove7 has three maximal cliques, the pentad 02345 and the two tetrads 0135 and 0246. The scale is a tempering of the transversal 1-8/7-11/9-4/3-3/2-18/11-7/4-2, and so the maximal cliques are temperings of 1-11/9-4/3-3/2-18/11, 1-8/7-4/3-18/11 and 1-11/9-3/2-7/4, which are essentially tempered chords.

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<br />

<h2 id="toc13"><a name="Seven note scales-Elfjove7"></a>Elfjove7</h2>

<a class="wiki_link" href="/Elfjove7">Elfjove7</a> is the seven note elf scale of jove temperament, the 11-limit temperament rank three tempering out 243/242, 441/440, 540/539 and 2401/2400. In the 202et tuning, it has steps 0, 39, 59, 84, 118, 143, 163, 202, with a consonance set {25, 28, 31, 34, 39, 45, 53, 59, 65, 70, 73, 84, 93, 98, 104, 109, 118, 129, 132, 137, 143, 149, 157, 163, 168, 171, 174, 177}. The permutation group of automorphisms is intransitive, with orbits {0}, {1, 6} and {2, 3, 4, 5}. The group is the group of the square, acting transitively on the {2, 3, 4, 5} orbit, and ~~exchanging~~ 1 and 6 ~~when~~ the ~~permutation of~~ 2345 ~~is odd~~.<br />

<a class="wiki_link" href="/Elfjove7">Elfjove7</a> is the seven note elf scale of jove temperament, the 11-limit temperament rank three tempering out 243/242, 441/440, 540/539 and 2401/2400. In the 202et tuning, it has steps 0, 39, 59, 84, 118, 143, 163, 202, with a consonance set {25, 28, 31, 34, 39, 45, 53, 59, 65, 70, 73, 84, 93, 98, 104, 109, 118, 129, 132, 137, 143, 149, 157, 163, 168, 171, 174, 177}. The permutation group of automorphisms is intransitive, with orbits {0}, {1, 6} and {2, 3, 4, 5}. The group is the group of the square, acting transitively on the {2, 3, 4, 5} orbit. The permuations of the {2, 3, 4, 5} square Identity, (24), (35), and (24)(35) leave 1 and 6 fixed, and the permutations (2345), (23)(45), (2543) and (25)(43) exchange the pair.<br />

<br />

Elfjove7 has three maximal cliques, the pentad 02345 and the two tetrads 0135 and 0246. The scale is a tempering of the transversal 1-8/7-11/9-4/3-3/2-18/11-7/4-2, and so the maximal cliques are temperings of 1-11/9-4/3-3/2-18/11, 1-8/7-4/3-18/11 and 1-11/9-3/2-7/4, which are essentially tempered chords.<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2014-04-15 18:45:06 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-04-15 19:02:57 UTC</tt>.<br>
-: The original revision id was <tt>502721858</tt>.<br>
+: The original revision id was <tt>502724154</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>
@@ Line 100: / Line 100: @@
 ==Elfjove7==
-[[Elfjove7]] is the seven note elf scale of jove temperament, the 11-limit temperament rank three tempering out 243/242, 441/440, 540/539 and 2401/2400. In the 202et tuning, it has steps 0, 39, 59, 84, 118, 143, 163, 202, with a consonance set {25, 28, 31, 34, 39, 45, 53, 59, 65, 70, 73, 84, 93, 98, 104, 109, 118, 129, 132, 137, 143, 149, 157, 163, 168, 171, 174, 177}. The permutation group of automorphisms is intransitive, with orbits {0}, {1, 6} and {2, 3, 4, 5}. The group is the group of the square, acting transitively on the {2, 3, 4, 5} orbit, and exchanging 1 and 6 when the permutation of 2345 is odd.
+[[Elfjove7]] is the seven note elf scale of jove temperament, the 11-limit temperament rank three tempering out 243/242, 441/440, 540/539 and 2401/2400. In the 202et tuning, it has steps 0, 39, 59, 84, 118, 143, 163, 202, with a consonance set {25, 28, 31, 34, 39, 45, 53, 59, 65, 70, 73, 84, 93, 98, 104, 109, 118, 129, 132, 137, 143, 149, 157, 163, 168, 171, 174, 177}. The permutation group of automorphisms is intransitive, with orbits {0}, {1, 6} and {2, 3, 4, 5}. The group is the group of the square, acting transitively on the {2, 3, 4, 5} orbit. The permuations of the {2, 3, 4, 5} square Identity, (24), (35), and (24)(35) leave 1 and 6 fixed, and the permutations (2345), (23)(45), (2543) and (25)(43) exchange the pair.
 Elfjove7 has three maximal cliques, the pentad 02345 and the two tetrads 0135 and 0246. The scale is a tempering of the transversal 1-8/7-11/9-4/3-3/2-18/11-7/4-2, and so the maximal cliques are temperings of 1-11/9-4/3-3/2-18/11, 1-8/7-4/3-18/11 and 1-11/9-3/2-7/4, which are essentially tempered chords.
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 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Seven note scales-Elfjove7"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Elfjove7&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Elfjove7"&gt;Elfjove7&lt;/a&gt; is the seven note elf scale of jove temperament, the 11-limit temperament rank three tempering out 243/242, 441/440, 540/539 and 2401/2400. In the 202et tuning, it has steps 0, 39, 59, 84, 118, 143, 163, 202, with a consonance set {25, 28, 31, 34, 39, 45, 53, 59, 65, 70, 73, 84, 93, 98, 104, 109, 118, 129, 132, 137, 143, 149, 157, 163, 168, 171, 174, 177}. The permutation group of automorphisms is intransitive, with orbits {0}, {1, 6} and {2, 3, 4, 5}. The group is the group of the square, acting transitively on the {2, 3, 4, 5} orbit, and exchanging 1 and 6 when the permutation of 2345 is odd.&lt;br /&gt;
+&lt;a class="wiki_link" href="/Elfjove7"&gt;Elfjove7&lt;/a&gt; is the seven note elf scale of jove temperament, the 11-limit temperament rank three tempering out 243/242, 441/440, 540/539 and 2401/2400. In the 202et tuning, it has steps 0, 39, 59, 84, 118, 143, 163, 202, with a consonance set {25, 28, 31, 34, 39, 45, 53, 59, 65, 70, 73, 84, 93, 98, 104, 109, 118, 129, 132, 137, 143, 149, 157, 163, 168, 171, 174, 177}. The permutation group of automorphisms is intransitive, with orbits {0}, {1, 6} and {2, 3, 4, 5}. The group is the group of the square, acting transitively on the {2, 3, 4, 5} orbit. The permuations of the {2, 3, 4, 5} square Identity, (24), (35), and (24)(35) leave 1 and 6 fixed, and the permutations (2345), (23)(45), (2543) and (25)(43) exchange the pair.&lt;br /&gt;
 &lt;br /&gt;
 Elfjove7 has three maximal cliques, the pentad 02345 and the two tetrads 0135 and 0246. The scale is a tempering of the transversal 1-8/7-11/9-4/3-3/2-18/11-7/4-2, and so the maximal cliques are temperings of 1-11/9-4/3-3/2-18/11, 1-8/7-4/3-18/11 and 1-11/9-3/2-7/4, which are essentially tempered chords.&lt;br /&gt;