Graph-theoretic properties of scales: Difference between revisions

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==Archchro==

[[Archchro]] is the tempering in hemif, a 2.3.7.11.13 subgroup scale, of [[Archytas' Chromatic]]. In the 58et tuning, it has steps of 0, 3, 10, 24, 34, 37, 44, 58, with a consonance set {6, 7, 10, 11, 13, 14, 17, 20, 21, 24, 27, 31, 34, 37, 38, 41, 44, 45, 47, 48, 51, 52}.

[[Archchro]] is the tempering in hemif, a 2.3.7.11.13 subgroup scale, of [[Archytas' Chromatic]]. In the 58et tuning, it has steps of 0, 3, 10, 24, 34, 37, 44, 58, with a consonance set {6, 7, 10, 11, 13, 14, 17, 20, 21, 24, 27, 31, 34, 37, 38, 41, 44, 45, 47, 48, 51, 52}. Archchro is intransitive, with one orbit consisting of notes 2, 3, and 6, and the other of notes 0, 1, 4 and 5. The three note orbit is permuted by the group of the triangle, which is to say, the symmetric group S3, and the four note orbit by the group of the square. Together these give an automorphism group of order 6 X 8 = 48. The eight permutations fixing 2, 3, and 7 are {0123456, 0123546, 1023456, 1023546, 4523016, 4523106, 5423016, 5423106}, and the six fixing 0, 1, 4 and 5 are {0123456, 0126453, 0132456, 0136452, 0162453, 0163452}.

=Eight note scales=

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<br />

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

<a class="wiki_link" href="/Archchro">Archchro</a> is the tempering in hemif, a 2.3.7.11.13 subgroup scale, of <a class="wiki_link" href="/Archytas%27%20Chromatic">Archytas' Chromatic</a>. In the 58et tuning, it has steps of 0, 3, 10, 24, 34, 37, 44, 58, with a consonance set {6, 7, 10, 11, 13, 14, 17, 20, 21, 24, 27, 31, 34, 37, 38, 41, 44, 45, 47, 48, 51, 52}.<br />

<a class="wiki_link" href="/Archchro">Archchro</a> is the tempering in hemif, a 2.3.7.11.13 subgroup scale, of <a class="wiki_link" href="/Archytas%27%20Chromatic">Archytas' Chromatic</a>. In the 58et tuning, it has steps of 0, 3, 10, 24, 34, 37, 44, 58, with a consonance set {6, 7, 10, 11, 13, 14, 17, 20, 21, 24, 27, 31, 34, 37, 38, 41, 44, 45, 47, 48, 51, 52}. Archchro is intransitive, with one orbit consisting of notes 2, 3, and 6, and the other of notes 0, 1, 4 and 5. The three note orbit is permuted by the group of the triangle, which is to say, the symmetric group S3, and the four note orbit by the group of the square. Together these give an automorphism group of order 6 X 8 = 48. The eight permutations fixing 2, 3, and 7 are {0123456, 0123546, 1023456, 1023546, 4523016, 4523106, 5423016, 5423106}, and the six fixing 0, 1, 4 and 5 are {0123456, 0126453, 0132456, 0136452, 0162453, 0163452}.<br />

<br />

<h1 id="toc11"><a name="Eight note scales"></a>Eight note scales</h1>

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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>2012-12-27 15:13:56 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-12-27 16:41:23 UTC</tt>.<br>
-: The original revision id was <tt>394767168</tt>.<br>
+: The original revision id was <tt>394774514</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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 ==Archchro==
-[[Archchro]] is the tempering in hemif, a 2.3.7.11.13 subgroup scale, of [[Archytas' Chromatic]]. In the 58et tuning, it has steps of 0, 3, 10, 24, 34, 37, 44, 58, with a consonance set {6, 7, 10, 11, 13, 14, 17, 20, 21, 24, 27, 31, 34, 37, 38, 41, 44, 45, 47, 48, 51, 52}.
+[[Archchro]] is the tempering in hemif, a 2.3.7.11.13 subgroup scale, of [[Archytas' Chromatic]]. In the 58et tuning, it has steps of 0, 3, 10, 24, 34, 37, 44, 58, with a consonance set {6, 7, 10, 11, 13, 14, 17, 20, 21, 24, 27, 31, 34, 37, 38, 41, 44, 45, 47, 48, 51, 52}. Archchro is intransitive, with one orbit consisting of notes 2, 3, and 6, and the other of notes 0, 1, 4 and 5. The three note orbit is permuted by the group of the triangle, which is to say, the symmetric group S3, and the four note orbit by the group of the square. Together these give an automorphism group of order 6 X 8 = 48. The eight permutations fixing 2, 3, and 7 are {0123456, 0123546, 1023456, 1023546, 4523016, 4523106, 5423016, 5423106}, and the six fixing 0, 1, 4 and 5 are {0123456, 0126453, 0132456, 0136452, 0162453, 0163452}.
 =Eight note scales=
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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-Archchro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Archchro&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Archchro"&gt;Archchro&lt;/a&gt; is the tempering in hemif, a 2.3.7.11.13 subgroup scale, of &lt;a class="wiki_link" href="/Archytas%27%20Chromatic"&gt;Archytas' Chromatic&lt;/a&gt;. In the 58et tuning, it has steps of 0, 3, 10, 24, 34, 37, 44, 58, with a consonance set {6, 7, 10, 11, 13, 14, 17, 20, 21, 24, 27, 31, 34, 37, 38, 41, 44, 45, 47, 48, 51, 52}.&lt;br /&gt;
+&lt;a class="wiki_link" href="/Archchro"&gt;Archchro&lt;/a&gt; is the tempering in hemif, a 2.3.7.11.13 subgroup scale, of &lt;a class="wiki_link" href="/Archytas%27%20Chromatic"&gt;Archytas' Chromatic&lt;/a&gt;. In the 58et tuning, it has steps of 0, 3, 10, 24, 34, 37, 44, 58, with a consonance set {6, 7, 10, 11, 13, 14, 17, 20, 21, 24, 27, 31, 34, 37, 38, 41, 44, 45, 47, 48, 51, 52}. Archchro is intransitive, with one orbit consisting of notes 2, 3, and 6, and the other of notes 0, 1, 4 and 5. The three note orbit is permuted by the group of the triangle, which is to say, the symmetric group S3, and the four note orbit by the group of the square. Together these give an automorphism group of order 6 X 8 = 48. The eight permutations fixing 2, 3, and 7 are {0123456, 0123546, 1023456, 1023546, 4523016, 4523106, 5423016, 5423106}, and the six fixing 0, 1, 4 and 5 are {0123456, 0126453, 0132456, 0136452, 0162453, 0163452}.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Eight note scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Eight note scales&lt;/h1&gt;