20edo: Difference between revisions

Wikispaces>TallKite
**Imported revision 599949126 - Original comment: **
Wikispaces>TallKite
**Imported revision 599956060 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 04:52:49 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 06:23:59 UTC</tt>.<br>
: The original revision id was <tt>599949126</tt>.<br>
: The original revision id was <tt>599956060</tt>.<br>
: The revision comment was: <tt></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>
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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==Intervals==  
==Intervals==  
|| **Degree** || **Cents coarse/fine**
|| **Degree** || **Cents coarse/fine**
**DMS** |||| [[Ups and Downs Notation|up/down notation]] ||= **Approximate**
**DMS** ||||||= [[Ups and Downs Notation|up/down notation]] ||= **Approximate**
**Ratios** ||= **Nearest**
**Ratios** ||= **Nearest**
**Harmonic** ||
**Harmonic** ||
|| 0 || 0 || P1 || D ||= 1/1 ||= 1 ||
|| 0 || 0 || unison || P1 || D ||= 1/1 ||= 1 ||
|| 1 || 60, 72
|| 1 || 60, 72
18° || ^m2 || D^ ||= 29/28 ||= 33 ||
18° || upminor 2nd || ^m2 || D^ ||= 29/28 ||= 33 ||
|| 2 || 120, 144
|| 2 || 120, 144
36° || ~2 || D^^, Evv ||= 14/13, 15/14 ||= 69 ||
36° || mid 2nd || ~2 || D^^, Evv ||= 14/13, 15/14 ||= 69 ||
|| 3 || 180, 216
|| 3 || 180, 216
54° || vM2 || Ev ||= 10/9 ||= 71 ||
54° || downmajor 2nd || vM2 || Ev ||= 10/9 ||= 71 ||
|| 4 || 240, 288
|| 4 || 240, 288
72° || M2, m3 || E, F ||= 8/7, 15/13 ||= 37 ||
72° || major 2nd,
minor 3rd || M2, m3 || E, F ||= 8/7, 15/13 ||= 37 ||
|| 5 || 300, 360
|| 5 || 300, 360
90° || ^m3 || F^ ||= 13/11, 19/16 ||= 19 ||
90° || upminor 3rd || ^m3 || F^ ||= 13/11, 19/16 ||= 19 ||
|| 6 || 360, 432
|| 6 || 360, 432
108° || ~3 || F^^ ||= 16/13, 5/4 ||= 79 ||
108° || mid 3rd || ~3 || F^^ ||= 16/13, 5/4 ||= 79 ||
|| 7 || 420, 504
|| 7 || 420, 504
126° || vM3 || F#v ||= [[14_11|14/11]], [[51_40|51/40]] ||= 41 ||
126° || downmajor 3rd || vM3 || F#v ||= [[14_11|14/11]], [[51_40|51/40]] ||= 41 ||
|| 8 || 480, 576
|| 8 || 480, 576
144° || M3, P4 || F#, G ||= 25/19, 4/3 ||= 21 ||
144° || major 3rd,
perfect fourth || M3, P4 || F#, G ||= 25/19, 4/3 ||= 21 ||
|| 9 || 540, 648
|| 9 || 540, 648
162° || ^4 || G^ ||= 15/11, 11/8 ||= 11 ||
162° || up-fourth || ^4 || G^ ||= 15/11, 11/8 ||= 11 ||
|| 10 || 600, 720
|| 10 || 600, 720
180° || ^^4, vv5 || G^^, Avv ||= 7/5 ||= 91 ||
180° || double-up fourth,
double-down fifth || ^^4, vv5 || G^^, Avv ||= 7/5 ||= 91 ||
|| 11 || 660, 792
|| 11 || 660, 792
198° || v5 || Av ||= 22/15, 16/11 ||= 47 ||
198° || down-fifth || v5 || Av ||= 22/15, 16/11 ||= 47 ||
|| 12 || 720, 864
|| 12 || 720, 864
216° || P5, m6 || A ||= 38/25, 3/2 ||= 97 ||
216° || fifth || P5, m6 || A ||= 38/25, 3/2 ||= 97 ||
|| 13 || 780, 936
|| 13 || 780, 936
234° || ^m6 || A^ ||= 11/7, 25/16 ||= 25 ||
234° || upminor 6th || ^m6 || A^ ||= 11/7, 25/16 ||= 25 ||
|| 14 || 840, 1008
|| 14 || 840, 1008
252° || ~6 || A^^, Bvv ||= 13/8, 8/5 ||= 13 ||
252° || mid 6th || ~6 || A^^, Bvv ||= 13/8, 8/5 ||= 13 ||
|| 15 || 900, 1080
|| 15 || 900, 1080
270° || vM6 || Bv ||= 22/13, 32/19 ||= 27 ||
270° || downmajor 6th || vM6 || Bv ||= 22/13, 32/19 ||= 27 ||
|| 16 || 960, 1152
|| 16 || 960, 1152
288° || M6, m7 || B, C ||= 7/4, 26/15 ||= 7 ||
288° || major 6th,
minor 7th || M6, m7 || B, C ||= 7/4, 26/15 ||= 7 ||
|| 17 || 1020, 1224
|| 17 || 1020, 1224
306° || ^m7 || C^ ||= 9/5 ||= 115 ||
306° || upminor 7th || ^m7 || C^ ||= 9/5 ||= 115 ||
|| 18 || 1080, 1296
|| 18 || 1080, 1296
324° || ~7 || C^^, Dvv ||= 15/8, 13/7 ||= 15 ||
324° || mid 7th || ~7 || C^^, Dvv ||= 15/8, 13/7 ||= 15 ||
|| 19 || 1140, 1368
|| 19 || 1140, 1368
342° || vM7 || Dv ||= 56/29 ||= 31 ||
342° || downmajor 7th || vM7 || Dv ||= 56/29 ||= 31 ||
|| 20 || 1200, 1440
|| 20 || 1200, 1440
360° || 8ve || D ||= 2/1 ||= 2 ||
360° || octave || P8 || D ||= 2/1 ||= 2 ||
==Modes==  
==Modes==  
20 tone equal modes:
20 tone equal modes:
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&lt;strong&gt;DMS&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;DMS&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;up/down notation&lt;/a&gt;&lt;br /&gt;
         &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;up/down notation&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;0&lt;br /&gt;
         &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;unison&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;P1&lt;br /&gt;
         &lt;td&gt;P1&lt;br /&gt;
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         &lt;td&gt;60, 72&lt;br /&gt;
         &lt;td&gt;60, 72&lt;br /&gt;
18°&lt;br /&gt;
18°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;upminor 2nd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;^m2&lt;br /&gt;
         &lt;td&gt;^m2&lt;br /&gt;
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         &lt;td&gt;120, 144&lt;br /&gt;
         &lt;td&gt;120, 144&lt;br /&gt;
36°&lt;br /&gt;
36°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mid 2nd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;~2&lt;br /&gt;
         &lt;td&gt;~2&lt;br /&gt;
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         &lt;td&gt;180, 216&lt;br /&gt;
         &lt;td&gt;180, 216&lt;br /&gt;
54°&lt;br /&gt;
54°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;downmajor 2nd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;vM2&lt;br /&gt;
         &lt;td&gt;vM2&lt;br /&gt;
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         &lt;td&gt;240, 288&lt;br /&gt;
         &lt;td&gt;240, 288&lt;br /&gt;
72°&lt;br /&gt;
72°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;major 2nd, &lt;br /&gt;
minor 3rd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;M2, m3&lt;br /&gt;
         &lt;td&gt;M2, m3&lt;br /&gt;
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         &lt;td&gt;300, 360&lt;br /&gt;
         &lt;td&gt;300, 360&lt;br /&gt;
90°&lt;br /&gt;
90°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;upminor 3rd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;^m3&lt;br /&gt;
         &lt;td&gt;^m3&lt;br /&gt;
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         &lt;td&gt;360, 432&lt;br /&gt;
         &lt;td&gt;360, 432&lt;br /&gt;
108°&lt;br /&gt;
108°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mid 3rd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;~3&lt;br /&gt;
         &lt;td&gt;~3&lt;br /&gt;
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         &lt;td&gt;420, 504&lt;br /&gt;
         &lt;td&gt;420, 504&lt;br /&gt;
126°&lt;br /&gt;
126°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;downmajor 3rd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;vM3&lt;br /&gt;
         &lt;td&gt;vM3&lt;br /&gt;
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         &lt;td&gt;480, 576&lt;br /&gt;
         &lt;td&gt;480, 576&lt;br /&gt;
144°&lt;br /&gt;
144°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;major 3rd,&lt;br /&gt;
perfect fourth&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;M3, P4&lt;br /&gt;
         &lt;td&gt;M3, P4&lt;br /&gt;
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         &lt;td&gt;540, 648&lt;br /&gt;
         &lt;td&gt;540, 648&lt;br /&gt;
162°&lt;br /&gt;
162°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;up-fourth&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;^4&lt;br /&gt;
         &lt;td&gt;^4&lt;br /&gt;
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         &lt;td&gt;600, 720&lt;br /&gt;
         &lt;td&gt;600, 720&lt;br /&gt;
180°&lt;br /&gt;
180°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;double-up fourth,&lt;br /&gt;
double-down fifth&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;^^4, vv5&lt;br /&gt;
         &lt;td&gt;^^4, vv5&lt;br /&gt;
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         &lt;td&gt;660, 792&lt;br /&gt;
         &lt;td&gt;660, 792&lt;br /&gt;
198°&lt;br /&gt;
198°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;down-fifth&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;v5&lt;br /&gt;
         &lt;td&gt;v5&lt;br /&gt;
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         &lt;td&gt;720, 864&lt;br /&gt;
         &lt;td&gt;720, 864&lt;br /&gt;
216°&lt;br /&gt;
216°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;fifth&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;P5, m6&lt;br /&gt;
         &lt;td&gt;P5, m6&lt;br /&gt;
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         &lt;td&gt;780, 936&lt;br /&gt;
         &lt;td&gt;780, 936&lt;br /&gt;
234°&lt;br /&gt;
234°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;upminor 6th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;^m6&lt;br /&gt;
         &lt;td&gt;^m6&lt;br /&gt;
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         &lt;td&gt;840, 1008&lt;br /&gt;
         &lt;td&gt;840, 1008&lt;br /&gt;
252°&lt;br /&gt;
252°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mid 6th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;~6&lt;br /&gt;
         &lt;td&gt;~6&lt;br /&gt;
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         &lt;td&gt;900, 1080&lt;br /&gt;
         &lt;td&gt;900, 1080&lt;br /&gt;
270°&lt;br /&gt;
270°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;downmajor 6th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;vM6&lt;br /&gt;
         &lt;td&gt;vM6&lt;br /&gt;
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         &lt;td&gt;960, 1152&lt;br /&gt;
         &lt;td&gt;960, 1152&lt;br /&gt;
288°&lt;br /&gt;
288°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;major 6th,&lt;br /&gt;
minor 7th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;M6, m7&lt;br /&gt;
         &lt;td&gt;M6, m7&lt;br /&gt;
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         &lt;td&gt;1020, 1224&lt;br /&gt;
         &lt;td&gt;1020, 1224&lt;br /&gt;
306°&lt;br /&gt;
306°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;upminor 7th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;^m7&lt;br /&gt;
         &lt;td&gt;^m7&lt;br /&gt;
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         &lt;td&gt;1080, 1296&lt;br /&gt;
         &lt;td&gt;1080, 1296&lt;br /&gt;
324°&lt;br /&gt;
324°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mid 7th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;~7&lt;br /&gt;
         &lt;td&gt;~7&lt;br /&gt;
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         &lt;td&gt;1140, 1368&lt;br /&gt;
         &lt;td&gt;1140, 1368&lt;br /&gt;
342°&lt;br /&gt;
342°&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;downmajor 7th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;vM7&lt;br /&gt;
         &lt;td&gt;vM7&lt;br /&gt;
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360°&lt;br /&gt;
360°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;8ve&lt;br /&gt;
         &lt;td&gt;octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P8&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;D&lt;br /&gt;
         &lt;td&gt;D&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Books&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Books&lt;/h1&gt;
  &lt;!-- ws:start:WikiTextRemoteImageRule:737:&amp;lt;a href=&amp;quot;http://www.ronsword.com/&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/20_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 114px; width: 82px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/" target="_blank" rel="nofollow"&gt;&lt;img src="http://ronsword.com/images/20_tet_Coversm.jpg" alt="external image 20_tet_Coversm.jpg" title="external image 20_tet_Coversm.jpg" style="height: 114px; width: 82px;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:737 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank"&gt;&amp;quot;Icosaphonic Scales for Guitar&amp;quot; - Theory / Scale book with above modes and more&lt;/a&gt; by &lt;a class="wiki_link" href="/Ron%20Sword"&gt;Ron Sword&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
  &lt;!-- ws:start:WikiTextRemoteImageRule:779:&amp;lt;a href=&amp;quot;http://www.ronsword.com/&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/20_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 114px; width: 82px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/" target="_blank" rel="nofollow"&gt;&lt;img src="http://ronsword.com/images/20_tet_Coversm.jpg" alt="external image 20_tet_Coversm.jpg" title="external image 20_tet_Coversm.jpg" style="height: 114px; width: 82px;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:779 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank"&gt;&amp;quot;Icosaphonic Scales for Guitar&amp;quot; - Theory / Scale book with above modes and more&lt;/a&gt; by &lt;a class="wiki_link" href="/Ron%20Sword"&gt;Ron Sword&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>