Graph-theoretic properties of scales: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-08-19 22:19:08 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-08-19 23:01:40 UTC</tt>.<br>

: The original revision id was <tt>~~445590500~~</tt>.<br>

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==Godzilla[9]==

The symmetric mode of the 9-note godzilla MOS has notes 0, 3, 4, 7, 8, 11, 12, 15, 16, 19 in [[19edo]], with 11-limit consonance set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. Its graph has 32 edges, and its automorphism group is the same as that of star and nova--the group of the 16-cell, S2≀S4, the 8T44 transitive group. The graph can be drawn in four dimensions as the eight verticies of the 16-cell, plus another vertex in the center connecting with all of the rest, and corresponding to note 0, the center note of the MOS.

The symmetric mode of the 9-note godzilla MOS has notes 0, 3, 4, 7, 8, 11, 12, 15, 16, 19 in [[19edo]], with 11-limit consonance set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. Its graph has 32 edges, and its automorphism group is the same as that of star and nova--the group of the 16-cell, S2≀S4, the 8T44 transitive group of order 384. The graph can be drawn in four dimensions as the eight verticies of the 16-cell, plus another vertex in the center connecting with all of the rest, and corresponding to note 0, the center note of the MOS. The sixteen tetrads of star or nova correspond to sixteen pentads, which each add note 0 to the choice of notes 1 or 2, 3 or 4, 5 or 6, and 7 or 8. It has algebraic, edge, and vertex connectivities all 7. Godizlla[9] is a consonant class scale in multiple ways, skipping only class 1 and class 8.

=Ten note scales=

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<br />

<h2 id="toc19"><a name="Nine note scales-Godzilla[9]"></a>Godzilla[9]</h2>

The symmetric mode of the 9-note godzilla MOS has notes 0, 3, 4, 7, 8, 11, 12, 15, 16, 19 in <a class="wiki_link" href="/19edo">19edo</a>, with 11-limit consonance set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. Its graph has 32 edges, and its automorphism group is the same as that of star and nova--the group of the 16-cell, S2≀S4, the 8T44 transitive group. The graph can be drawn in four dimensions as the eight verticies of the 16-cell, plus another vertex in the center connecting with all of the rest, and corresponding to note 0, the center note of the MOS.<br />

The symmetric mode of the 9-note godzilla MOS has notes 0, 3, 4, 7, 8, 11, 12, 15, 16, 19 in <a class="wiki_link" href="/19edo">19edo</a>, with 11-limit consonance set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. Its graph has 32 edges, and its automorphism group is the same as that of star and nova--the group of the 16-cell, S2≀S4, the 8T44 transitive group of order 384. The graph can be drawn in four dimensions as the eight verticies of the 16-cell, plus another vertex in the center connecting with all of the rest, and corresponding to note 0, the center note of the MOS. The sixteen tetrads of star or nova correspond to sixteen pentads, which each add note 0 to the choice of notes 1 or 2, 3 or 4, 5 or 6, and 7 or 8. It has algebraic, edge, and vertex connectivities all 7. Godizlla[9] is a consonant class scale in multiple ways, skipping only class 1 and class 8.<br />

<br />

<h1 id="toc20"><a name="Ten note scales"></a>Ten note scales</h1>

@@ 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>2013-08-19 22:19:08 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-08-19 23:01:40 UTC</tt>.<br>
-: The original revision id was <tt>445590500</tt>.<br>
+: The original revision id was <tt>445596820</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 143: / Line 143: @@
 ==Godzilla[9]==
-The symmetric mode of the 9-note godzilla MOS has notes 0, 3, 4, 7, 8, 11, 12, 15, 16, 19 in [[19edo]], with 11-limit consonance set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. Its graph has 32 edges, and its automorphism group is the same as that of star and nova--the group of the 16-cell,  S2≀S4, the 8T44 transitive group. The graph can be drawn in four dimensions as the eight verticies of the 16-cell, plus another vertex in the center connecting with all of the rest, and corresponding to note 0, the center note of the MOS.
+The symmetric mode of the 9-note godzilla MOS has notes 0, 3, 4, 7, 8, 11, 12, 15, 16, 19 in [[19edo]], with 11-limit consonance set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. Its graph has 32 edges, and its automorphism group is the same as that of star and nova--the group of the 16-cell,  S2≀S4, the 8T44 transitive group of order 384. The graph can be drawn in four dimensions as the eight verticies of the 16-cell, plus another vertex in the center connecting with all of the rest, and corresponding to note 0, the center note of the MOS. The sixteen tetrads of star or nova correspond to sixteen pentads, which each add note 0 to the choice of notes 1 or 2, 3 or 4, 5 or 6, and 7 or 8. It has algebraic, edge, and vertex connectivities all 7. Godizlla[9] is a consonant class scale in multiple ways, skipping only class 1 and class 8.
 =Ten note scales=
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 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Nine note scales-Godzilla[9]"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Godzilla[9]&lt;/h2&gt;
-  The symmetric mode of the 9-note godzilla MOS has notes 0, 3, 4, 7, 8, 11, 12, 15, 16, 19 in &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, with 11-limit consonance set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. Its graph has 32 edges, and its automorphism group is the same as that of star and nova--the group of the 16-cell,  S2≀S4, the 8T44 transitive group. The graph can be drawn in four dimensions as the eight verticies of the 16-cell, plus another vertex in the center connecting with all of the rest, and corresponding to note 0, the center note of the MOS.&lt;br /&gt;
+  The symmetric mode of the 9-note godzilla MOS has notes 0, 3, 4, 7, 8, 11, 12, 15, 16, 19 in &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, with 11-limit consonance set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. Its graph has 32 edges, and its automorphism group is the same as that of star and nova--the group of the 16-cell,  S2≀S4, the 8T44 transitive group of order 384. The graph can be drawn in four dimensions as the eight verticies of the 16-cell, plus another vertex in the center connecting with all of the rest, and corresponding to note 0, the center note of the MOS. The sixteen tetrads of star or nova correspond to sixteen pentads, which each add note 0 to the choice of notes 1 or 2, 3 or 4, 5 or 6, and 7 or 8. It has algebraic, edge, and vertex connectivities all 7. Godizlla[9] is a consonant class scale in multiple ways, skipping only class 1 and class 8.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Ten note scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Ten note scales&lt;/h1&gt;