Graph-theoretic properties of scales: Difference between revisions

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<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 15:05:29 UTC</tt>.<br>

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

: The original revision id was <tt>~~445522248~~</tt>.<br>

: The original revision id was <tt>445590500</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>

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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 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.

=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. <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. 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 />

<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 15:05:29 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-08-19 22:19:08 UTC</tt>.<br>
-: The original revision id was <tt>445522248</tt>.<br>
+: The original revision id was <tt>445590500</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 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.
 =Ten note scales=
@@ Line 365: / Line 365: @@
 &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. &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. 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;
 &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;