31edo: 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:~~Gedankenwelt~~|~~Gedankenwelt~~]] and made on <tt>~~2013~~-12~~-07 01~~:29:26 UTC</tt>.<br>

: This revision was by author [[User:csvargas31|csvargas31]] and made on <tt>2014-01-25 12:22:38 UTC</tt>.<br>

: The original revision id was <tt>~~475413966~~</tt>.<br>

: The original revision id was <tt>485217024</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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===12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth===

Exactly twice a supermajor second, thrice a neutral second, or four times a ~~major~~ second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates [[semisept]] temperament.

Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates [[semisept]] temperament.

====MOS Scales generated by 12\31:====

||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||

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<br />

<h3 id="toc23"><a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth"></a>12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth</h3>

Exactly twice a supermajor second, thrice a neutral second, or four times a ~~major~~ second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the <a class="wiki_link" href="/17-limit">17-limit</a> interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates <a class="wiki_link" href="/semisept">semisept</a> temperament.<br />

Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the <a class="wiki_link" href="/17-limit">17-limit</a> interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates <a class="wiki_link" href="/semisept">semisept</a> temperament.<br />

<h4 id="toc24"><a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"></a>MOS Scales generated by 12\31:</h4>

@@ 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:Gedankenwelt|Gedankenwelt]] and made on <tt>2013-12-07 01:29:26 UTC</tt>.<br>
+: This revision was by author [[User:csvargas31|csvargas31]] and made on <tt>2014-01-25 12:22:38 UTC</tt>.<br>
-: The original revision id was <tt>475413966</tt>.<br>
+: The original revision id was <tt>485217024</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 146: / Line 146: @@
 ===12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth===
-Exactly twice a supermajor second, thrice a neutral second, or four times a major second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates [[semisept]] temperament.
+Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the [[17-limit]] interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates [[semisept]] temperament.
 ====MOS Scales generated by 12\31:====
 ||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
@@ Line 4,893: / Line 4,893: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc23"&gt;&lt;a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth&lt;/h3&gt;
-  Exactly twice a supermajor second, thrice a neutral second, or four times a major second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates &lt;a class="wiki_link" href="/semisept"&gt;semisept&lt;/a&gt; temperament.&lt;br /&gt;
+  Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates &lt;a class="wiki_link" href="/semisept"&gt;semisept&lt;/a&gt; temperament.&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc24"&gt;&lt;a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;MOS Scales generated by 12\31:&lt;/h4&gt;

31edo: Difference between revisions

Wikispaces>csvargas31