Graph-theoretic properties of scales: Difference between revisions

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==Zeus7tri==

[[Zeus7tri]] is he tempering in zeus of 11/10, 5/4, 11/8, 3/2, 12/7, 15/8, 2. In 99et it has steps 0, 13, 32, 45, 58, 77, 90, 99, with an 11-limit consonance set {13, 13, 15, 17, 19, 22, 26, 28, 32, 35, 36, 41, 45, 48, 51, 54, 58, 63, 64, 67, 71, 73, 77, 80, 82, 84, 86, 86}. The scale contains two maximal hexads, consisting of the pentad of the notes 1 through 5 plus either 0 or 6. The automorphism group is of order 240, consisting of the direct product of the group of order two exchanging 0 and 6, and the symmetric group on the five other notes 1, 2, 3, 4, 5. It has vertex, edge and algebraic connectivities all 5.

[[Zeus7tri]] is the tempering in zeus of 11/10, 5/4, 11/8, 3/2, 12/7, 15/8, 2. In 99et it has steps 0, 13, 32, 45, 58, 77, 90, 99, with an 11-limit consonance set {13, 13, 15, 17, 19, 22, 26, 28, 32, 35, 36, 41, 45, 48, 51, 54, 58, 63, 64, 67, 71, 73, 77, 80, 82, 84, 86, 86}. The scale contains two maximal hexads, consisting of the pentad of the notes 1 through 5 plus either 0 or 6. The automorphism group is of order 240, consisting of the direct product of the group of order two exchanging 0 and 6, and the symmetric group on the five other notes 1, 2, 3, 4, 5. It has vertex, edge and algebraic connectivities all 5.

The scale is interesting in that it has the trivalent property, so that there are exactly three specific intervals for each generic interval save the octave multiples. Class 2 contains the three thirds, 7/6, 6/5 and 5/4.

==Archchro==

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<h2 id="toc10"><a name="Seven note scales-Zeus7tri"></a>Zeus7tri</h2>

<a class="wiki_link" href="/Zeus7tri">Zeus7tri</a> is he tempering in zeus of 11/10, 5/4, 11/8, 3/2, 12/7, 15/8, 2. In 99et it has steps 0, 13, 32, 45, 58, 77, 90, 99, with an 11-limit consonance set {13, 13, 15, 17, 19, 22, 26, 28, 32, 35, 36, 41, 45, 48, 51, 54, 58, 63, 64, 67, 71, 73, 77, 80, 82, 84, 86, 86}. The scale contains two maximal hexads, consisting of the pentad of the notes 1 through 5 plus either 0 or 6. The automorphism group is of order 240, consisting of the direct product of the group of order two exchanging 0 and 6, and the symmetric group on the five other notes 1, 2, 3, 4, 5. It has vertex, edge and algebraic connectivities all 5.<br />

<a class="wiki_link" href="/Zeus7tri">Zeus7tri</a> is the tempering in zeus of 11/10, 5/4, 11/8, 3/2, 12/7, 15/8, 2. In 99et it has steps 0, 13, 32, 45, 58, 77, 90, 99, with an 11-limit consonance set {13, 13, 15, 17, 19, 22, 26, 28, 32, 35, 36, 41, 45, 48, 51, 54, 58, 63, 64, 67, 71, 73, 77, 80, 82, 84, 86, 86}. The scale contains two maximal hexads, consisting of the pentad of the notes 1 through 5 plus either 0 or 6. The automorphism group is of order 240, consisting of the direct product of the group of order two exchanging 0 and 6, and the symmetric group on the five other notes 1, 2, 3, 4, 5. It has vertex, edge and algebraic connectivities all 5.<br />

<br />

The scale is interesting in that it has the trivalent property, so that there are exactly three specific intervals for each generic interval save the octave multiples. Class 2 contains the three thirds, 7/6, 6/5 and 5/4.<br />

<br />

<h2 id="toc11"><a name="Seven note scales-Archchro"></a>Archchro</h2>

@@ 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>2013-01-27 17:57:29 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-01-27 18:10:45 UTC</tt>.<br>
-: The original revision id was <tt>401839338</tt>.<br>
+: The original revision id was <tt>401841926</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 78: / Line 78: @@
 ==Zeus7tri==
-[[Zeus7tri]] is he tempering in zeus of 11/10, 5/4, 11/8, 3/2, 12/7, 15/8, 2. In 99et it has steps 0, 13, 32, 45, 58, 77, 90, 99, with an 11-limit consonance set {13, 13, 15, 17, 19, 22, 26, 28, 32, 35, 36, 41, 45, 48, 51, 54, 58, 63, 64, 67, 71, 73, 77, 80, 82, 84, 86, 86}. The scale contains two maximal hexads, consisting of the pentad of the notes 1 through 5 plus either 0 or 6. The automorphism group is of order 240, consisting of the direct product of the group of order two exchanging 0 and 6, and the symmetric group on the five other notes 1, 2, 3, 4, 5. It has vertex, edge and algebraic connectivities all 5.
+[[Zeus7tri]] is the tempering in zeus of 11/10, 5/4, 11/8, 3/2, 12/7, 15/8, 2. In 99et it has steps 0, 13, 32, 45, 58, 77, 90, 99, with an 11-limit consonance set {13, 13, 15, 17, 19, 22, 26, 28, 32, 35, 36, 41, 45, 48, 51, 54, 58, 63, 64, 67, 71, 73, 77, 80, 82, 84, 86, 86}. The scale contains two maximal hexads, consisting of the pentad of the notes 1 through 5 plus either 0 or 6. The automorphism group is of order 240, consisting of the direct product of the group of order two exchanging 0 and 6, and the symmetric group on the five other notes 1, 2, 3, 4, 5. It has vertex, edge and algebraic connectivities all 5.
+The scale is interesting in that it has the trivalent property, so that there are exactly three specific intervals for each generic interval save the octave multiples. Class 2 contains the three thirds, 7/6, 6/5 and 5/4.
 ==Archchro==
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 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Seven note scales-Zeus7tri"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Zeus7tri&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Zeus7tri"&gt;Zeus7tri&lt;/a&gt; is he tempering in zeus of 11/10, 5/4, 11/8, 3/2, 12/7, 15/8, 2. In 99et it has steps 0, 13, 32, 45, 58, 77, 90, 99, with an 11-limit consonance set {13, 13, 15, 17, 19, 22, 26, 28, 32, 35, 36, 41, 45, 48, 51, 54, 58, 63, 64, 67, 71, 73, 77, 80, 82, 84, 86, 86}. The scale contains two maximal hexads, consisting of the pentad of the notes 1 through 5 plus either 0 or 6. The automorphism group is of order 240, consisting of the direct product of the group of order two exchanging 0 and 6, and the symmetric group on the five other notes 1, 2, 3, 4, 5. It has vertex, edge and algebraic connectivities all 5.&lt;br /&gt;
+&lt;a class="wiki_link" href="/Zeus7tri"&gt;Zeus7tri&lt;/a&gt; is the tempering in zeus of 11/10, 5/4, 11/8, 3/2, 12/7, 15/8, 2. In 99et it has steps 0, 13, 32, 45, 58, 77, 90, 99, with an 11-limit consonance set {13, 13, 15, 17, 19, 22, 26, 28, 32, 35, 36, 41, 45, 48, 51, 54, 58, 63, 64, 67, 71, 73, 77, 80, 82, 84, 86, 86}. The scale contains two maximal hexads, consisting of the pentad of the notes 1 through 5 plus either 0 or 6. The automorphism group is of order 240, consisting of the direct product of the group of order two exchanging 0 and 6, and the symmetric group on the five other notes 1, 2, 3, 4, 5. It has vertex, edge and algebraic connectivities all 5.&lt;br /&gt;
+&lt;br /&gt;
+The scale is interesting in that it has the trivalent property, so that there are exactly three specific intervals for each generic interval save the octave multiples. Class 2 contains the three thirds, 7/6, 6/5 and 5/4.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Seven note scales-Archchro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Archchro&lt;/h2&gt;