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>2012-12-~~27 16~~:54:28 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-12-30 10:51:52 UTC</tt>.<br>

: The original revision id was <tt>~~394775744~~</tt>.<br>

: The original revision id was <tt>395061678</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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==Gypsy==

[[Gypsy]] is the tempering in 7-limit marvel of the JI scale 16/15, 5/4, 4/3, 3/2, 8/5, 15/8, 2. This scale is mavchrome1, the first 25/24&135/128 Fokker block, and is also the 5-limit, 7-note JI hobbit, or "jobbit". It is also Helmholtz's Chromatic and the Slovakian gypsy major. Another mode is the Slovakian gypsy minor, noted by Tartini, and still another mode is the tempering of a 7-limit scale due to Dave Keenan, keenanjust. Last but hardly least, it is the tempering of the 7-limit scale listed in the Scala catalog as "al-farabi_chrom2" and ~~claimed to be~~ a permutation of Al-Farabi's ~~Chromatic~~.

[[Gypsy]] is the tempering in 7-limit marvel of the JI scale 16/15, 5/4, 4/3, 3/2, 8/5, 15/8, 2. This scale is mavchrome1, the first 25/24&135/128 Fokker block, and is also the 5-limit, 7-note JI hobbit, or "jobbit". It is also Helmholtz's Chromatic and the Slovakian gypsy major. Another mode is the Slovakian gypsy minor, noted by Tartini, and still another mode is the tempering of a 7-limit scale due to Dave Keenan, keenanjust. Last but hardly least, it is the tempering of the 7-limit scale listed in the Scala catalog as "al-farabi_chrom2", and is derived from a permutation of Al Farabi's chromatic tetrachord 7/6-15/14-16/15. This kind of tetrachordal permutation was a part of the medieval Islamic theory.

However arrived at, the scale in [[197edo|197et]] is 0, 19, 63, 82, 115, 134, 178, 197. It has two graphs of interest, since the graphs of 7-limit relations and of 9-limit relations are not isomorphic, but the automorphism groups (of order 16) of these graphs are. The 7-limit consonance set is {38, 44, 52, 63, 82, 96, 101, 115, 134, 145, 153, 159, 197} and the 9-limit set is {30, 33, 38, 44, 52, 63, 71, 82, 96, 101, 115, 126, 134, 145, 153, 159, 164, 167, 197}. The difference is {30, 33, 71, 126, 164, 167}. In Gypsy, the 9-limit intervals occur between 5/4 and 8/5, tempered to 9/7, and between 4/3 and 3/2.

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<br />

<h2 id="toc9"><a name="Seven note scales-Gypsy"></a>Gypsy</h2>

<a class="wiki_link" href="/Gypsy">Gypsy</a> is the tempering in 7-limit marvel of the JI scale 16/15, 5/4, 4/3, 3/2, 8/5, 15/8, 2. This scale is mavchrome1, the first 25/24&amp;135/128 Fokker block, and is also the 5-limit, 7-note JI hobbit, or &quot;jobbit&quot;. It is also Helmholtz's Chromatic and the Slovakian gypsy major. Another mode is the Slovakian gypsy minor, noted by Tartini, and still another mode is the tempering of a 7-limit scale due to Dave Keenan, keenanjust. Last but hardly least, it is the tempering of the 7-limit scale listed in the Scala catalog as &quot;al-farabi_chrom2&quot; and ~~claimed to be~~ a permutation of Al-Farabi's ~~Chromatic~~.<br />

<a class="wiki_link" href="/Gypsy">Gypsy</a> is the tempering in 7-limit marvel of the JI scale 16/15, 5/4, 4/3, 3/2, 8/5, 15/8, 2. This scale is mavchrome1, the first 25/24&amp;135/128 Fokker block, and is also the 5-limit, 7-note JI hobbit, or &quot;jobbit&quot;. It is also Helmholtz's Chromatic and the Slovakian gypsy major. Another mode is the Slovakian gypsy minor, noted by Tartini, and still another mode is the tempering of a 7-limit scale due to Dave Keenan, keenanjust. Last but hardly least, it is the tempering of the 7-limit scale listed in the Scala catalog as &quot;al-farabi_chrom2&quot;, and is derived from a permutation of Al Farabi's chromatic tetrachord 7/6-15/14-16/15. This kind of tetrachordal permutation was a part of the medieval Islamic theory.<br />

<br />

However arrived at, the scale in <a class="wiki_link" href="/197edo">197et</a> is 0, 19, 63, 82, 115, 134, 178, 197. It has two graphs of interest, since the graphs of 7-limit relations and of 9-limit relations are not isomorphic, but the automorphism groups (of order 16) of these graphs are. The 7-limit consonance set is {38, 44, 52, 63, 82, 96, 101, 115, 134, 145, 153, 159, 197} and the 9-limit set is {30, 33, 38, 44, 52, 63, 71, 82, 96, 101, 115, 126, 134, 145, 153, 159, 164, 167, 197}. The difference is {30, 33, 71, 126, 164, 167}. In Gypsy, the 9-limit intervals occur between 5/4 and 8/5, tempered to 9/7, and between 4/3 and 3/2.<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>2012-12-27 16:54:28 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-12-30 10:51:52 UTC</tt>.<br>
-: The original revision id was <tt>394775744</tt>.<br>
+: The original revision id was <tt>395061678</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 69: / Line 69: @@
 ==Gypsy==
-[[Gypsy]] is the tempering in 7-limit marvel of the JI scale 16/15, 5/4, 4/3, 3/2, 8/5, 15/8, 2. This scale is mavchrome1, the first 25/24&amp;135/128 Fokker block, and is also the 5-limit, 7-note JI hobbit, or "jobbit". It is also Helmholtz's Chromatic and the Slovakian gypsy major. Another mode is the Slovakian gypsy minor, noted by Tartini, and still another mode is the tempering of a 7-limit scale due to Dave Keenan, keenanjust. Last but hardly least, it is the tempering of the 7-limit scale listed in the Scala catalog as "al-farabi_chrom2" and claimed to be a permutation of Al-Farabi's Chromatic.
+[[Gypsy]] is the tempering in 7-limit marvel of the JI scale 16/15, 5/4, 4/3, 3/2, 8/5, 15/8, 2. This scale is mavchrome1, the first 25/24&amp;135/128 Fokker block, and is also the 5-limit, 7-note JI hobbit, or "jobbit". It is also Helmholtz's Chromatic and the Slovakian gypsy major. Another mode is the Slovakian gypsy minor, noted by Tartini, and still another mode is the tempering of a 7-limit scale due to Dave Keenan, keenanjust. Last but hardly least, it is the tempering of the 7-limit scale listed in the Scala catalog as "al-farabi_chrom2", and is derived from a permutation of Al Farabi's chromatic tetrachord 7/6-15/14-16/15. This kind of tetrachordal permutation was a part of the medieval Islamic theory.
 However arrived at, the scale in [[197edo|197et]] is 0, 19, 63, 82, 115, 134, 178, 197. It has two graphs of interest, since the graphs of 7-limit relations and of 9-limit relations are not isomorphic, but the automorphism groups (of order 16) of these graphs are. The 7-limit consonance set is {38, 44, 52, 63, 82, 96, 101, 115, 134, 145, 153, 159, 197} and the 9-limit set is {30, 33, 38, 44, 52, 63, 71, 82, 96, 101, 115, 126, 134, 145, 153, 159, 164, 167, 197}. The difference is {30, 33, 71, 126, 164, 167}. In Gypsy, the 9-limit intervals occur between 5/4 and 8/5, tempered to 9/7, and between 4/3 and 3/2.
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 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Seven note scales-Gypsy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Gypsy&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Gypsy"&gt;Gypsy&lt;/a&gt; is the tempering in 7-limit marvel of the JI scale 16/15, 5/4, 4/3, 3/2, 8/5, 15/8, 2. This scale is mavchrome1, the first 25/24&amp;amp;135/128 Fokker block, and is also the 5-limit, 7-note JI hobbit, or &amp;quot;jobbit&amp;quot;. It is also Helmholtz's Chromatic and the Slovakian gypsy major. Another mode is the Slovakian gypsy minor, noted by Tartini, and still another mode is the tempering of a 7-limit scale due to Dave Keenan, keenanjust. Last but hardly least, it is the tempering of the 7-limit scale listed in the Scala catalog as &amp;quot;al-farabi_chrom2&amp;quot; and claimed to be a permutation of Al-Farabi's Chromatic.&lt;br /&gt;
+&lt;a class="wiki_link" href="/Gypsy"&gt;Gypsy&lt;/a&gt; is the tempering in 7-limit marvel of the JI scale 16/15, 5/4, 4/3, 3/2, 8/5, 15/8, 2. This scale is mavchrome1, the first 25/24&amp;amp;135/128 Fokker block, and is also the 5-limit, 7-note JI hobbit, or &amp;quot;jobbit&amp;quot;. It is also Helmholtz's Chromatic and the Slovakian gypsy major. Another mode is the Slovakian gypsy minor, noted by Tartini, and still another mode is the tempering of a 7-limit scale due to Dave Keenan, keenanjust. Last but hardly least, it is the tempering of the 7-limit scale listed in the Scala catalog as &amp;quot;al-farabi_chrom2&amp;quot;, and is derived from a permutation of Al Farabi's chromatic tetrachord 7/6-15/14-16/15. This kind of tetrachordal permutation was a part of the medieval Islamic theory.&lt;br /&gt;
 &lt;br /&gt;
 However arrived at, the scale in &lt;a class="wiki_link" href="/197edo"&gt;197et&lt;/a&gt; is 0, 19, 63, 82, 115, 134, 178, 197. It has two graphs of interest, since the graphs of 7-limit relations and of 9-limit relations are not isomorphic, but the automorphism groups (of order 16) of these graphs are. The 7-limit consonance set is {38, 44, 52, 63, 82, 96, 101, 115, 134, 145, 153, 159, 197} and the 9-limit set is {30, 33, 38, 44, 52, 63, 71, 82, 96, 101, 115, 126, 134, 145, 153, 159, 164, 167, 197}. The difference is {30, 33, 71, 126, 164, 167}. In Gypsy, the 9-limit intervals occur between 5/4 and 8/5, tempered to 9/7, and between 4/3 and 3/2.&lt;br /&gt;