25edo: Difference between revisions

Wikispaces>xenwolf
**Imported revision 576286773 - Original comment: link to file description (accessibility)**
Wikispaces>JosephRuhf
**Imported revision 597589954 - Original comment: **
Line 1: Line 1:
<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:xenwolf|xenwolf]] and made on <tt>2016-03-01 15:42:03 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-31 16:08:48 UTC</tt>.<br>
: The original revision id was <tt>576286773</tt>.<br>
: The original revision id was <tt>597589954</tt>.<br>
: The revision comment was: <tt>link to file description (accessibility)</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>
<h4>Original Wikitext content:</h4>
<h4>Original Wikitext content:</h4>
Line 28: Line 28:
Ratios* ||= Armodue
Ratios* ||= Armodue
Notation ||
Notation ||
|| 0 || 0 ||= 1/1 ||= 1 ||
|| 0 || 0
|| 1 || 48
||= 1/1 ||= 1 ||
|| 1 || 48, //57.6//
14°24' ||= 33/32, 39/38, 34/33 ||= 1# ||
14°24' ||= 33/32, 39/38, 34/33 ||= 1# ||
|| 2 || 96
|| 2 || 96, //115.2//
28°48' ||= 17/16, 20/19, 18/17 ||= 2b ||
28°48' ||= 17/16, 20/19, 18/17 ||= 2b ||
|| 3 || 144
|| 3 || 144, //172.8//
43°12' ||= 12/11, 38/35 ||= 2 ||
43°12' ||= 12/11, 38/35 ||= 2 ||
|| 4 || 192
|| 4 || 192, //230.4//
57°36' ||= 9/8, 10/9, 19/17 ||= 2# ||
57°36' ||= 9/8, 10/9, 19/17 ||= 2# ||
|| 5· || 240
|| 5· || 240, 288
72° ||= 8/7 ||= 3b ||
72° ||= 8/7 ||= 3b ||
|| 6 || 288
|| 6 || 288, //345.6//
86°24' ||= 19/16, 20/17 ||= 3 ||
86°24' ||= 19/16, 20/17 ||= 3 ||
|| 7 || 336 ||= 39/32, 17/14, 40/33 ||= 3# ||
|| 7 || 336, //403.2//
|| 8· || 384
100°48' ||= 39/32, 17/14, 40/33 ||= 3# ||
100°48' ||= 5/4 ||= 4b ||
|| 8· || 384, //460.8//
|| 9 || 432
115°12' ||= 5/4 ||= 4b ||
115°12' ||= 9/7, 32/25, 50/39 ||= 4 ||
|| 9 || 432, //518.4//
|| 10 || 480
129°36' ||= 9/7, 32/25, 50/39 ||= 4 ||
|| 10 || 480, 576
144° ||= 33/25, 25/19 ||= 4#/5b ||
144° ||= 33/25, 25/19 ||= 4#/5b ||
|| 11· || 528
|| 11· || 528, //633.6//
158°24' ||= 31/21, 34/25 ||= 5 ||
158°24' ||= 31/21, 34/25 ||= 5 ||
|| 12 || 576
|| 12 || 576, //691.2//
172°48' ||= 7/5, 39/28 ||= 5# ||
172°48' ||= 7/5, 39/28 ||= 5# ||
|| 13 || 624
|| 13 || 624, //748.8//
187°12' ||= 10/7, 56/39 ||= 6b ||
187°12' ||= 10/7, 56/39 ||= 6b ||
|| 14· || 672
|| 14· || 672, //806.4//
201°36' ||= 42/31, 25/17 ||= 6 ||
201°36' ||= 42/31, 25/17 ||= 6 ||
|| 15 || 720
|| 15 || 720, 864
216° ||= 50/33, 38/25 ||= 6# ||
216° ||= 50/33, 38/25 ||= 6# ||
|| 16 || 768
|| 16 || 768, //921.6//
230°24' ||= 14/9, 25/16, 39/25 ||= 7b ||
230°24' ||= 14/9, 25/16, 39/25 ||= 7b ||
|| 17· || 816
|| 17· || 816, //979.2//
244°48' ||= 8/5 ||= 7 ||
244°48' ||= 8/5 ||= 7 ||
|| 18 || 864
|| 18 || 864, //1036.8//
259°12' ||= 64/39, 28/17, 33/20 ||= 7# ||
259°12' ||= 64/39, 28/17, 33/20 ||= 7# ||
|| 19 || 912
|| 19 || 912, //1094.4//
273°36' ||= 32/19, 17/10 ||= 8b ||
273°36' ||= 32/19, 17/10 ||= 8b ||
|| 20· || 960
|| 20· || 960, 1152
288° ||= 7/4 ||= 8 ||
288° ||= 7/4 ||= 8 ||
|| 21 || 1008
|| 21 || 1008, //1209.6//
302°14' ||= 16/9, 9/5, 34/19 ||= 8# ||
302°14' ||= 16/9, 9/5, 34/19 ||= 8# ||
|| 22 || 1056
|| 22 || 1056, //1267.2//
316°48' ||= 11/6, 35/19 ||= 9b ||
316°48' ||= 11/6, 35/19 ||= 9b ||
|| 23 || 1104
|| 23 || 1104, //1324.8//
331°12' ||= 32/17, 17/9, 19/10 ||= 9 ||
331°12' ||= 32/17, 17/9, 19/10 ||= 9 ||
|| 24 || 1152
|| 24 || 1152, //1382.4//
345°36' ||= 33/17, 64/33, 76/39 ||= 9#/1b ||
345°36' ||= 33/17, 64/33, 76/39 ||= 9#/1b ||
|| 25 || 1200
|| 25 || 1200, 1440
360° ||= 2/1 ||= 1 ||
360° ||= 2/1 ||= 1 ||
*based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.
*based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.
Line 90: Line 92:


=Commas=  
=Commas=  
25 EDO tempers out the following commas. (Note: This assumes the val &lt; 25 40 58 70 86 93 |.)
25 EDO tempers out the following commas. (Note: This assumes the val &lt; [[tel/25 40 58 70 86 93|25 40 58 70 86 93]] |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 256/243 ||&lt; | 8 -5 &gt; ||&gt; 90.22 ||= Limma ||= Pythagorean Minor 2nd ||=  ||
||= 256/243 ||&lt; | 8 -5 &gt; ||&gt; 90.22 ||= Limma ||= Pythagorean Minor 2nd ||=  ||
||= 3125/3072 ||&lt; | -10 -1 5 &gt; ||&gt; 29.61 ||= Small Diesis ||= Magic Comma ||=  ||
||= 3125/3072 ||&lt; | -10 -1 5 &gt; ||&gt; 29.61 ||= Small Diesis ||= Magic Comma ||=  ||
||= 6719816/6714445 ||&lt; | 38 -2 -15 &gt; ||&gt; 1.38 ||= Hemithirds Comma ||=  ||=  ||
||= [[tel:6719816/6714445|6719816/6714445]] ||&lt; | 38 -2 -15 &gt; ||&gt; 1.38 ||= Hemithirds Comma ||=  ||=  ||
||= 16807/16384 || | -14 0 0 5 &gt; ||&gt; 44.13 ||  ||  ||  ||
||= 16807/16384 || | -14 0 0 5 &gt; ||&gt; 44.13 ||  ||  ||  ||
||= 49/48 ||&lt; | -4 -1 0 2 &gt; ||&gt; 35.70 ||= Slendro Diesis ||=  ||=  ||
||= 49/48 ||&lt; | -4 -1 0 2 &gt; ||&gt; 35.70 ||= Slendro Diesis ||=  ||=  ||
Line 150: Line 152:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;0&lt;br /&gt;
         &lt;td&gt;0&lt;br /&gt;
0°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
Line 159: Line 162:
         &lt;td&gt;1&lt;br /&gt;
         &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;48&lt;br /&gt;
         &lt;td&gt;48, &lt;em&gt;57.6&lt;/em&gt;&lt;br /&gt;
14°24'&lt;br /&gt;
14°24'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 170: Line 173:
         &lt;td&gt;2&lt;br /&gt;
         &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;96&lt;br /&gt;
         &lt;td&gt;96, &lt;em&gt;115.2&lt;/em&gt;&lt;br /&gt;
28°48'&lt;br /&gt;
28°48'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;3&lt;br /&gt;
         &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;144&lt;br /&gt;
         &lt;td&gt;144, &lt;em&gt;172.8&lt;/em&gt;&lt;br /&gt;
43°12'&lt;br /&gt;
43°12'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 192: Line 195:
         &lt;td&gt;4&lt;br /&gt;
         &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;192&lt;br /&gt;
         &lt;td&gt;192, &lt;em&gt;230.4&lt;/em&gt;&lt;br /&gt;
57°36'&lt;br /&gt;
57°36'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 203: Line 206:
         &lt;td&gt;5·&lt;br /&gt;
         &lt;td&gt;5·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;240&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;
Line 214: Line 217:
         &lt;td&gt;6&lt;br /&gt;
         &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;288&lt;br /&gt;
         &lt;td&gt;288, &lt;em&gt;345.6&lt;/em&gt;&lt;br /&gt;
86°24'&lt;br /&gt;
86°24'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;7&lt;br /&gt;
         &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;336&lt;br /&gt;
         &lt;td&gt;336, &lt;em&gt;403.2&lt;/em&gt;&lt;br /&gt;
100°48'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;39/32, 17/14, 40/33&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;39/32, 17/14, 40/33&lt;br /&gt;
Line 235: Line 239:
         &lt;td&gt;8·&lt;br /&gt;
         &lt;td&gt;8·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;384&lt;br /&gt;
         &lt;td&gt;384, &lt;em&gt;460.8&lt;/em&gt;&lt;br /&gt;
100°48'&lt;br /&gt;
115°12'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
Line 246: Line 250:
         &lt;td&gt;9&lt;br /&gt;
         &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;432&lt;br /&gt;
         &lt;td&gt;432, &lt;em&gt;518.4&lt;/em&gt;&lt;br /&gt;
115°12'&lt;br /&gt;
129°36'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;9/7, 32/25, 50/39&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;9/7, 32/25, 50/39&lt;br /&gt;
Line 257: Line 261:
         &lt;td&gt;10&lt;br /&gt;
         &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;480&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;
Line 268: Line 272:
         &lt;td&gt;11·&lt;br /&gt;
         &lt;td&gt;11·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;528&lt;br /&gt;
         &lt;td&gt;528, &lt;em&gt;633.6&lt;/em&gt;&lt;br /&gt;
158°24'&lt;br /&gt;
158°24'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;12&lt;br /&gt;
         &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;576&lt;br /&gt;
         &lt;td&gt;576, &lt;em&gt;691.2&lt;/em&gt;&lt;br /&gt;
172°48'&lt;br /&gt;
172°48'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;13&lt;br /&gt;
         &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;624&lt;br /&gt;
         &lt;td&gt;624, &lt;em&gt;748.8&lt;/em&gt;&lt;br /&gt;
187°12'&lt;br /&gt;
187°12'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;14·&lt;br /&gt;
         &lt;td&gt;14·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;672&lt;br /&gt;
         &lt;td&gt;672, &lt;em&gt;806.4&lt;/em&gt;&lt;br /&gt;
201°36'&lt;br /&gt;
201°36'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;720&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;
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         &lt;td&gt;16&lt;br /&gt;
         &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;768&lt;br /&gt;
         &lt;td&gt;768, &lt;em&gt;921.6&lt;/em&gt;&lt;br /&gt;
230°24'&lt;br /&gt;
230°24'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;17·&lt;br /&gt;
         &lt;td&gt;17·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;816&lt;br /&gt;
         &lt;td&gt;816, &lt;em&gt;979.2&lt;/em&gt;&lt;br /&gt;
244°48'&lt;br /&gt;
244°48'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;18&lt;br /&gt;
         &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;864&lt;br /&gt;
         &lt;td&gt;864, &lt;em&gt;1036.8&lt;/em&gt;&lt;br /&gt;
259°12'&lt;br /&gt;
259°12'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;19&lt;br /&gt;
         &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;912&lt;br /&gt;
         &lt;td&gt;912, &lt;em&gt;1094.4&lt;/em&gt;&lt;br /&gt;
273°36'&lt;br /&gt;
273°36'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;20·&lt;br /&gt;
         &lt;td&gt;20·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;960&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;
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         &lt;td&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1008&lt;br /&gt;
         &lt;td&gt;1008, &lt;em&gt;1209.6&lt;/em&gt;&lt;br /&gt;
302°14'&lt;br /&gt;
302°14'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;22&lt;br /&gt;
         &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1056&lt;br /&gt;
         &lt;td&gt;1056, &lt;em&gt;1267.2&lt;/em&gt;&lt;br /&gt;
316°48'&lt;br /&gt;
316°48'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;23&lt;br /&gt;
         &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1104&lt;br /&gt;
         &lt;td&gt;1104, &lt;em&gt;1324.8&lt;/em&gt;&lt;br /&gt;
331°12'&lt;br /&gt;
331°12'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 411: Line 415:
         &lt;td&gt;24&lt;br /&gt;
         &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1152&lt;br /&gt;
         &lt;td&gt;1152, &lt;em&gt;1382.4&lt;/em&gt;&lt;br /&gt;
345°36'&lt;br /&gt;
345°36'&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 422: Line 426:
         &lt;td&gt;25&lt;br /&gt;
         &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1200&lt;br /&gt;
         &lt;td&gt;1200, 1440&lt;br /&gt;
360°&lt;br /&gt;
360°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 444: Line 448:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Commas&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Commas&lt;/h1&gt;
  25 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 25 40 58 70 86 93 |.)&lt;br /&gt;
  25 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/25%2040%2058%2070%2086%2093"&gt;25 40 58 70 86 93&lt;/a&gt; |.)&lt;br /&gt;




Line 491: Line 495:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;6719816/6714445&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;[[tel:6719816/6714445|6719816/6714445]]&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: left;"&gt;| 38 -2 -15 &amp;gt;&lt;br /&gt;
         &lt;td style="text-align: left;"&gt;| 38 -2 -15 &amp;gt;&lt;br /&gt;