10edo: 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:

: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-13 10:12:49 UTC</tt>.

: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-21 13:30:42 UTC</tt>.

: The original revision id was <tt>~~589279364~~</tt>.

: The original revision id was <tt>589879786</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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=[[media type="custom" key="10886138"]]=

=Intervals=

|| Degree || ~~Cent~~

|| Degree || Cents

~~Values~~ || Approximate

DMS || Approximate

Ratios* || Additional Ratios of 3, 5 and 9 || Name ||

|| 0 || 0 || 1/1 || || unison ||

|| 0 || 0

|| 1 || 120 || 15/14, 16/15, 13/14 || 10/9, 13/12 || small neutral second/large minor second ||

0° || 1/1 || 256/243, 50/49 || unison ||

|| 2 || 240 || 15/13, 8/7 || 9/8, 7/6 || second/third ||

|| 1 || 120

|| 3 || 360 || 16/13 || 5/4 || large neutral third ||

36° || 15/14, 16/15, 13/14 || 10/9, 13/12, 81/80 || small neutral second/large minor second ||

|| 4 || 480 || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth ||

|| 2 || 240

|| 5 || 600 || 91/64, 169/120 || 7/5, 10/7, 13/9, 18/13 || tritone ||

72° || 15/13, 8/7 || 9/8, 7/6 || second/third ||

|| 6 || 720 || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth ||

|| 3 || 360

|| 7 || 840 || 13/8 || 8/5 || neutral sixth ||

108° || 16/13 || 5/4 || large neutral third ||

|| 8 || 960 || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh ||

|| 4 || 480

|| 9 || 1080 || 15/8, 28/15, 13/7 || 9/5, 24/13 || small major 7th ||

144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth ||

|| 10 || 1200 || 2/1 || || octave ||

|| 5 || 600

180° || 91/64, 169/120 || 7/5, 10/7, 13/9, 18/13 || tritone ||

|| 6 || 720

216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth ||

|| 7 || 840

252° || 13/8 || 8/5 || neutral sixth ||

|| 8 || 960

288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh ||

|| 9 || 1080

324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th ||

|| 10 || 1200

360° || 2/1 || 243/128, 49/25 || octave ||

*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.

adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals.

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<td>Degree

</td>

<td>~~Cent~~

<td>Cents

~~Values~~

DMS

</td>

<td>Approximate

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</td>

<td>0

0°

</td>

<td>1/1

</td>

<td>

<td>256/243, 50/49

</td>

<td>unison

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</td>

<td>120

36°

</td>

<td>15/14, 16/15, 13/14

</td>

<td>10/9, 13/12

<td>10/9, 13/12, 81/80

</td>

<td>small neutral second/large minor second

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</td>

<td>240

72°

</td>

<td>15/13, 8/7

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</td>

<td>360

108°

</td>

<td>16/13

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</td>

<td>480

144°

</td>

<td>64/49, 169/128

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</td>

<td>600

180°

</td>

<td>91/64, 169/120

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</td>

<td>720

216°

</td>

<td>49/32, 256/169

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</td>

<td>840

252°

</td>

<td>13/8

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</td>

<td>960

288°

</td>

<td>7/4, 26/15, 125/72

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</td>

<td>1080

324°

</td>

<td>15/8, 28/15, 13/7

</td>

<td>9/5, 24/13

<td>9/5, 24/13, 160/81

</td>

<td>small major 7th

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</td>

<td>1200

360°

</td>

<td>2/1

</td>

<td>

<td>243/128, 49/25

</td>

<td>octave

@@ 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:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-13 10:12:49 UTC</tt>.<br>
+: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-21 13:30:42 UTC</tt>.<br>
-: The original revision id was <tt>589279364</tt>.<br>
+: The original revision id was <tt>589879786</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 15: / Line 15: @@
 =[[media type="custom" key="10886138"]]=
 =Intervals=
-|| Degree || Cent
+|| Degree || Cents
-Values || Approximate
+DMS || Approximate
 Ratios* || Additional Ratios of 3, 5 and 9 || Name ||
-|| 0 || 0 || 1/1 ||   || unison ||
+|| 0 || 0
-|| 1 || 120 || 15/14, 16/15, 13/14 || 10/9, 13/12 || small neutral second/large minor second ||
+° || 1/1 || 256/243, 50/49 || unison ||
-|| 2 || 240 || 15/13, 8/7 || 9/8, 7/6 || second/third ||
+|| 1 || 120
-|| 3 || 360 || 16/13 || 5/4 || large neutral third ||
+° || 15/14, 16/15, 13/14 || 10/9, 13/12, 81/80 || small neutral second/large minor second ||
-|| 4 || 480 || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth ||
+|| 2 || 240
-|| 5 || 600 || 91/64, 169/120 || 7/5, 10/7, 13/9, 18/13 || tritone ||
+° || 15/13, 8/7 || 9/8, 7/6 || second/third ||
-|| 6 || 720 || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth ||
+|| 3 || 360
-|| 7 || 840 || 13/8 || 8/5 || neutral sixth ||
+° || 16/13 || 5/4 || large neutral third ||
-|| 8 || 960 || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh ||
+|| 4 || 480
-|| 9 || 1080 || 15/8, 28/15, 13/7 || 9/5, 24/13 || small major 7th ||
+° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth ||
-|| 10 || 1200 || 2/1 ||   || octave ||
+|| 5 || 600
+° || 91/64, 169/120 || 7/5, 10/7, 13/9, 18/13 || tritone ||
+|| 6 || 720
+° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth ||
+|| 7 || 840
+° || 13/8 || 8/5 || neutral sixth ||
+|| 8 || 960
+° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh ||
+|| 9 || 1080
+° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th ||
+|| 10 || 1200
+° || 2/1 || 243/128, 49/25 || octave ||
 *based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
 adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals.
@@ Line 121: / Line 132: @@
          &lt;td&gt;Degree&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cent&lt;br /&gt;
+         &lt;td&gt;Cents&lt;br /&gt;
-Values&lt;br /&gt;
+DMS&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Approximate&lt;br /&gt;
@@ Line 136: / Line 147: @@
 &lt;/td&gt;
          &lt;td&gt;0&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;256/243, 50/49&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;unison&lt;br /&gt;
@@ Line 148: / Line 160: @@
 &lt;/td&gt;
          &lt;td&gt;120&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;15/14, 16/15, 13/14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;10/9, 13/12&lt;br /&gt;
+         &lt;td&gt;10/9, 13/12, 81/80&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;small neutral second/large minor second&lt;br /&gt;
@@ Line 160: / Line 173: @@
 &lt;/td&gt;
          &lt;td&gt;240&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;15/13, 8/7&lt;br /&gt;
@@ Line 172: / Line 186: @@
 &lt;/td&gt;
          &lt;td&gt;360&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;16/13&lt;br /&gt;
@@ Line 184: / Line 199: @@
 &lt;/td&gt;
          &lt;td&gt;480&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;64/49, 169/128&lt;br /&gt;
@@ Line 196: / Line 212: @@
 &lt;/td&gt;
          &lt;td&gt;600&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;91/64, 169/120&lt;br /&gt;
@@ Line 208: / Line 225: @@
 &lt;/td&gt;
          &lt;td&gt;720&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;49/32, 256/169&lt;br /&gt;
@@ Line 220: / Line 238: @@
 &lt;/td&gt;
          &lt;td&gt;840&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;13/8&lt;br /&gt;
@@ Line 232: / Line 251: @@
 &lt;/td&gt;
          &lt;td&gt;960&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/4, 26/15, 125/72&lt;br /&gt;
@@ Line 244: / Line 264: @@
 &lt;/td&gt;
          &lt;td&gt;1080&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;15/8, 28/15, 13/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9/5, 24/13&lt;br /&gt;
+         &lt;td&gt;9/5, 24/13, 160/81&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;small major 7th&lt;br /&gt;
@@ Line 256: / Line 277: @@
 &lt;/td&gt;
          &lt;td&gt;1200&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;2/1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;243/128, 49/25&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;octave&lt;br /&gt;