5edo: Difference between revisions

Wikispaces>PiotrGrochowski
**Imported revision 592319366 - Original comment: **
Wikispaces>JosephRuhf
**Imported revision 597456972 - 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:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-16 03:42:22 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-29 16:37:21 UTC</tt>.<br>
: The original revision id was <tt>592319366</tt>.<br>
: The original revision id was <tt>597456972</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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**in fifths of**
**in fifths of**
**an octave** || **Interval**
**an octave** || **Interval**
**in ¢, DMS** || **Closest**
**in ¢ (coarse, fine), DMS** || **Closest**
**diatonic**
**diatonic**
**interval name** || **The "neighborhood" of just intervals** ||
**interval name** || **The "neighborhood" of just intervals** ||
|| 0 || 0.0, 0° || unison / prime || exactly 1/1 ||
|| 0 || 0.0, 0° || unison / prime || exactly 1/1 ||
|| 1 || 240.0.
|| 1 || 240.0, 288.0, 72° || second / third || +8.826 c (coarse), +10.591 c (fine), +2°38'52" from septimal second 8/7
72° || second / third || +8.826 c, +2°38'52" from septimal second 8/7
-4.969 c (coarse), -5.963 c (fine), -1°29'26" from diminished third 144/125
-4.969 c, -1°29'26" from diminished third 144/125
-13.076 c (coarse), -15.961 c (fine), -3&lt;span style="line-height: 1.5;"&gt;°55'22"&lt;/span&gt; from augmented second 125/108
-13.076 c, -3&lt;span style="line-height: 1.5;"&gt;°55'22"&lt;/span&gt; from augmented second 125/108
-26.871 c (coarse), -32.245 c (fine), -8&lt;span style="line-height: 1.5;"&gt;°3'41"&lt;/span&gt; from septimal minor third 7/6 ||
-26.871 c, -8&lt;span style="line-height: 1.5;"&gt;°3'41"&lt;/span&gt; from septimal minor third 7/6 ||
|| 2 || 480.0, 576.0, 144° || fourth || +9.219 c (coarse), +11.063 c (fine), +2°45'57" from narrow fourth 21/16
|| 2 || 480.0,
-0.686 c (coarse), -0.775 c (fine), -11'37" from smaller fourth 33/25
144° || fourth || +9.219 c, +2°45'57" from narrow fourth 21/16
-18.045 c (coarse), -21.654 c (fine), -5°24'49" from just fourth 4/3 ||
-0.686 c, -11'37" from smaller fourth 33/25
|| 3 || 720.0, 864.0, 216° || fifth || +18.045 c (coarse), +21.654 c (fine), +5°24'49" from just fifth 3/2
-18.045 c, -5°24'49" from just fourth 4/3 ||
+0.686 c (coarse), +0.775 c (fine), +11'37" from bigger fifth 50/33
|| 3 || 720.0,
-9.219 c (coarse), -11.063 c (fine), -2°45'57" from wide fifth 21/16 ||
216° || fifth || +18.045 c, +5°24'49" from just fifth 3/2
|| 4 || 960.0, 1152.0, 288° || sixth, seventh || 26.871 c (coarse), 32.245 c (fine), 8°3'41" from septimal major sixth 12/7
+0.686 c&lt;span style="line-height: 1.5;"&gt;, +11'37" &lt;/span&gt;from bigger fifth 50/33
13.076 c (coarse), 15.961 c (fine), 3°55'22" from diminished seventh 216/125
-9.219 c&lt;span style="line-height: 1.5;"&gt;, +2°45'57" &lt;/span&gt;from wide fifth 32/21 ||
4.969 c (coarse)&lt;span style="line-height: 1.5;"&gt;, 5.963 c (fine), 1°29'26" &lt;/span&gt;from augmented sixth 125/72
|| 4 || 960.0,
-8.826 c (coarse), -10.591 c (fine), -2°38'52" from septimal seventh 7/4 ||
288° || sixth, seventh || 26.871 c, 8°3'41" from septimal major sixth 12/7
|| 5 || 1200.0, 1440.0, 360° || eighth || exactly 2/1 ||
13.076 c, 3°55'22" from diminished seventh 216/125
4.969 c&lt;span style="line-height: 1.5;"&gt;, 1°29'26" &lt;/span&gt;from augmented sixth 125/72
-8.826 c, -2°38'52" from septimal seventh 7/4 ||
|| 5 || 1200.0,
360° || eighth || exactly 2/1 ||


[[media type="custom" key="24802268"]]
[[media type="custom" key="24802268"]]
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==Commas Tempered==  
==Commas Tempered==  
5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 8 12 14 17 19 |.)
5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 [[tel:8 12 14 17 19|8 12 14 17 19]] |.)


||~ Comma ||~ Value (cents) ||~ Name ||~ Second Name ||~ Third Name ||~ Val ||
||~ Comma ||~ Value (cents) ||~ Name ||~ Second Name ||~ Third Name ||~ Val ||
||= 256/243 ||&gt; 90.225 || Limma || Pythagorean Minor 2nd ||  || | 8 -5 &gt; ||
||= 256/243 ||&gt; 90.225 || Limma || Pythagorean Minor 2nd ||  || | 8 -5 &gt; ||
||= 81/80 ||&gt; 21.506 || Syntonic Comma || Didymos Comma || Meantone Comma || | -4 4 -1 &gt; ||
||= 81/80 ||&gt; 21.506 || Syntonic Comma || Didymos Comma || Meantone Comma || | -4 4 -1 &gt; ||
||= 2889416/2882415 ||&gt; 4.200 || Vulture ||  ||  || | 24 -21 4 &gt; ||
||= [[tel:2889416/2882415|2889416/2882415]] ||&gt; 4.200 || Vulture ||  ||  || | 24 -21 4 &gt; ||
||= 36/35 ||&gt; 48.770 || Septimal Quarter Tone ||  ||  || | 2 2 -1 -1 &gt; ||
||= 36/35 ||&gt; 48.770 || Septimal Quarter Tone ||  ||  || | 2 2 -1 -1 &gt; ||
||= 49/48 ||&gt; 35.697 || Slendro Diesis ||  ||  || | -4 -1 0 2 &gt; ||
||= 49/48 ||&gt; 35.697 || Slendro Diesis ||  ||  || | -4 -1 0 2 &gt; ||
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||= 19683/19600 ||&gt; 7.316 || Cataharry ||  ||  || | -4 9 -2 -2 &gt; ||
||= 19683/19600 ||&gt; 7.316 || Cataharry ||  ||  || | -4 9 -2 -2 &gt; ||
||= 5120/5103 ||&gt; 5.758 || Hemifamity ||  ||  || | 10 -6 1 -1 &gt; ||
||= 5120/5103 ||&gt; 5.758 || Hemifamity ||  ||  || | 10 -6 1 -1 &gt; ||
||= 1065875/1063543 ||&gt; 3.792 || Wadisma ||  ||  || | -26 -1 1 9 &gt; ||
||= [[tel:1065875/1063543|1065875/1063543]] ||&gt; 3.792 || Wadisma ||  ||  || | -26 -1 1 9 &gt; ||
||= 420175/419904 ||&gt; 1.117 || Wizma ||  ||  || | -6 -8 2 5 &gt; ||
||= [[tel:420175/419904|420175/419904]] ||&gt; 1.117 || Wizma ||  ||  || | -6 -8 2 5 &gt; ||
||= 99/98 ||&gt; 17.576 || Mothwellsma ||  ||  || | -1 2 0 -2 1 &gt; ||
||= 99/98 ||&gt; 17.576 || Mothwellsma ||  ||  || | -1 2 0 -2 1 &gt; ||
||= 896/891 ||&gt; 9.688 || Pentacircle ||  ||  || | 7 -4 0 1 -1 &gt; ||
||= 896/891 ||&gt; 9.688 || Pentacircle ||  ||  || | 7 -4 0 1 -1 &gt; ||
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;Interval&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Interval&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;in ¢, DMS&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;in ¢ (coarse, fine), DMS&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;Closest&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Closest&lt;/strong&gt;&lt;br /&gt;
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         &lt;td&gt;1&lt;br /&gt;
         &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;240.0.&lt;br /&gt;
         &lt;td&gt;240.0, 288.0, 72°&lt;br /&gt;
72°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;second / third&lt;br /&gt;
         &lt;td&gt;second / third&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;+8.826 c, +2°38'52&amp;quot; from septimal second 8/7&lt;br /&gt;
         &lt;td&gt;+8.826 c (coarse), +10.591 c (fine), +2°38'52&amp;quot; from septimal second 8/7&lt;br /&gt;
-4.969 c, -1°29'26&amp;quot; from diminished third 144/125&lt;br /&gt;
-4.969 c (coarse), -5.963 c (fine), -1°29'26&amp;quot; from diminished third 144/125&lt;br /&gt;
-13.076 c, -3&lt;span style="line-height: 1.5;"&gt;°55'22&amp;quot;&lt;/span&gt; from augmented second 125/108&lt;br /&gt;
-13.076 c (coarse), -15.961 c (fine), -3&lt;span style="line-height: 1.5;"&gt;°55'22&amp;quot;&lt;/span&gt; from augmented second 125/108&lt;br /&gt;
-26.871 c, -8&lt;span style="line-height: 1.5;"&gt;°3'41&amp;quot;&lt;/span&gt; from septimal minor third 7/6&lt;br /&gt;
-26.871 c (coarse), -32.245 c (fine), -8&lt;span style="line-height: 1.5;"&gt;°3'41&amp;quot;&lt;/span&gt; from septimal minor third 7/6&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;2&lt;br /&gt;
         &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;480.0,&lt;br /&gt;
         &lt;td&gt;480.0, 576.0, 144°&lt;br /&gt;
144°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;fourth&lt;br /&gt;
         &lt;td&gt;fourth&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;+9.219 c, +2°45'57&amp;quot; from narrow fourth 21/16&lt;br /&gt;
         &lt;td&gt;+9.219 c (coarse), +11.063 c (fine), +2°45'57&amp;quot; from narrow fourth 21/16&lt;br /&gt;
-0.686 c, -11'37&amp;quot; from smaller fourth 33/25&lt;br /&gt;
-0.686 c (coarse), -0.775 c (fine), -11'37&amp;quot; from smaller fourth 33/25&lt;br /&gt;
-18.045 c, -5°24'49&amp;quot; from just fourth 4/3&lt;br /&gt;
-18.045 c (coarse), -21.654 c (fine), -5°24'49&amp;quot; from just fourth 4/3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&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;720.0,&lt;br /&gt;
         &lt;td&gt;720.0, 864.0, 216°&lt;br /&gt;
216°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;fifth&lt;br /&gt;
         &lt;td&gt;fifth&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;+18.045 c, +5°24'49&amp;quot; from just fifth 3/2&lt;br /&gt;
         &lt;td&gt;+18.045 c (coarse), +21.654 c (fine), +5°24'49&amp;quot; from just fifth 3/2&lt;br /&gt;
+0.686 c&lt;span style="line-height: 1.5;"&gt;, +11'37&amp;quot; &lt;/span&gt;from bigger fifth 50/33&lt;br /&gt;
+0.686 c (coarse), +0.775 c (fine), +11'37&amp;quot; from bigger fifth 50/33&lt;br /&gt;
-9.219 c&lt;span style="line-height: 1.5;"&gt;, +2°45'57&amp;quot; &lt;/span&gt;from wide fifth 32/21&lt;br /&gt;
-9.219 c (coarse), -11.063 c (fine), -2°45'57&amp;quot; from wide fifth 21/16&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;4&lt;br /&gt;
         &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;960.0,&lt;br /&gt;
         &lt;td&gt;960.0, 1152.0, 288°&lt;br /&gt;
288°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;sixth, seventh&lt;br /&gt;
         &lt;td&gt;sixth, seventh&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;26.871 c, 8°3'41&amp;quot; from septimal major sixth 12/7&lt;br /&gt;
         &lt;td&gt;26.871 c (coarse), 32.245 c (fine), 8°3'41&amp;quot; from septimal major sixth 12/7&lt;br /&gt;
13.076 c, 3°55'22&amp;quot; from diminished seventh 216/125&lt;br /&gt;
13.076 c (coarse), 15.961 c (fine), 3°55'22&amp;quot; from diminished seventh 216/125&lt;br /&gt;
4.969 c&lt;span style="line-height: 1.5;"&gt;, 1°29'26&amp;quot; &lt;/span&gt;from augmented sixth 125/72&lt;br /&gt;
4.969 c (coarse)&lt;span style="line-height: 1.5;"&gt;, 5.963 c (fine), 1°29'26&amp;quot; &lt;/span&gt;from augmented sixth 125/72&lt;br /&gt;
-8.826 c, -2°38'52&amp;quot; from septimal seventh 7/4&lt;br /&gt;
-8.826 c (coarse), -10.591 c (fine), -2°38'52&amp;quot; from septimal seventh 7/4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;5&lt;br /&gt;
         &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1200.0,&lt;br /&gt;
         &lt;td&gt;1200.0, 1440.0, 360°&lt;br /&gt;
360°&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;eighth&lt;br /&gt;
         &lt;td&gt;eighth&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:29:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="x5-edo in Musicmaking-Commas Tempered"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:29 --&gt;Commas Tempered&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:29:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="x5-edo in Musicmaking-Commas Tempered"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:29 --&gt;Commas Tempered&lt;/h2&gt;
  5-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 5 8 12 14 17 19 |.)&lt;br /&gt;
  5-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 5 &lt;a class="wiki_link" href="http://tel.wikispaces.com/8%2012%2014%2017%2019"&gt;8 12 14 17 19&lt;/a&gt; |.)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;


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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;2889416/2882415&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;[[tel:2889416/2882415|2889416/2882415]]&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: right;"&gt;4.200&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;4.200&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;1065875/1063543&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;[[tel:1065875/1063543|1065875/1063543]]&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: right;"&gt;3.792&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;3.792&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;420175/419904&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;[[tel:420175/419904|420175/419904]]&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: right;"&gt;1.117&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1.117&lt;br /&gt;