16edo: 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:~~Nickname2~~|~~Nickname2~~]] and made on <tt>2016-06-~~15 09~~:56:56 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-30 17:21:24 UTC</tt>.

: The original revision id was <tt>~~585437115~~</tt>.

: The original revision id was <tt>597503264</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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=Intervals=

|| Degree || Cents

|| Degree || Cents (coarse, fine)

DMS ||= Approximate

Ratios* || Interval Name ||

|| 0 || 0 ||= 1/1 || Unison ||

|| 1 || 75

|| 1 || 75, 90

22º30' ||= 28/27, 27/26 || Subminor 2nd ||

|| 2 || 150

|| 2 || 150, 180

45° ||= 12/11, 35/32 || Neutral 2nd ||

|| 3 || 225

|| 3 || 225, 270

67°30' ||= 8/7 || Supermajor 2nd,

Septimal Whole-Tone ||

|| 4 || 300

|| 4 || 300, 360

90° ||= 19/16, 32/27 || Minor 3rd ||

|| 5 || 375

|| 5 || 375, 450

112°30' ||= 5/4, 26/21 || Major 3rd ||

|| 6 || 450

|| 6 || 450, 540

135° ||= 13/10, 35/27 || Sub-4th,

Supermajor 3rd ||

|| 7 || 525

|| 7 || 525, 630

157°30' ||= 27/20, 52/35, 256/189 || Wide 4th ||

|| 8 || 600

|| 8 || 600, 720

180° ||= 7/5, 10/7 || Tritone ||

|| 9 || 675

|| 9 || 675, 810

202°30' ||= 40/27, 35/26, 189/128 || Narrow 5th ||

|| 10 || 750

|| 10 || 750, 900

225° ||= 20/13, 54/35 || Super-5th,

Subminor 6th ||

|| 11 || 825

|| 11 || 825, 990

247°30' ||= 8/5, 21/13 || Minor 6th ||

|| 12 || 900

|| 12 || 900, 1080

270° ||= 27/16, 32/19 || Major 6th ||

|| 13 || 975

|| 13 || 975, 1170

292°30' ||= 7/4 || Subminor 7th,

Septimal Minor 7th ||

|| 14 || 1050

|| 14 || 1050, 1260

315° ||= 11/6, 64/35 || Neutral 7th ||

|| 15 || 1125

|| 15 || 1125, 1350

337°30' ||= 27/14, 52/27 || Supermajor 7th ||

|| 16 || 1200

|| 16 || 1200, 1440

360° ||= 2/1 || Octave ||

*based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.

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=Commas=

16 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] < 16 25 37 45 55 59 |.)

16 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] < [[tel:16 25 37 45 55 59|16 25 37 45 55 59]] |.)

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||

||= 135/128 ||< | -7 3 1 > ||> 92.18 ||= Major Chroma ||= Major Limma ||= Pelogic Comma ||

||= 648/625 ||< | 3 4 -4 > ||> 62.57 ||= Major Diesis ||= Diminished Comma ||= ||

||= 3125/3072 ||< | -10 -1 5 > ||> 29.61 ||= Small Diesis ||= Magic Comma ||= ||

||= 1212717/1210381 ||< | 23 6 -14 > ||> 3.34 ||= Vishnuzma ||= Semisuper ||= ||

||= [[tel:1212717/1210381|1212717/1210381]] ||< | 23 6 -14 > ||> 3.34 ||= Vishnuzma ||= Semisuper ||= ||

||= 36/35 ||< | 2 2 -1 -1 > ||> 48.77 ||= Septimal Quarter Tone ||= ||= ||

||= 525/512 ||< | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||= ||

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<td>Degree

</td>

<td>Cents

<td>Cents (coarse, fine)

DMS

</td>

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<td>1

</td>

<td>75

<td>75, 90

22º30'

</td>

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<td>2

</td>

<td>150

<td>150, 180

45°

</td>

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<td>3

</td>

<td>225

<td>225, 270

67°30'

</td>

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<td>4

</td>

<td>300

<td>300, 360

90°

</td>

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<td>5

</td>

<td>375

<td>375, 450

112°30'

</td>

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<td>6

</td>

<td>450

<td>450, 540

135°

</td>

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<td>7

</td>

<td>525

<td>525, 630

157°30'

</td>

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<td>8

</td>

<td>600

<td>600, 720

180°

</td>

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<td>9

</td>

<td>675

<td>675, 810

202°30'

</td>

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<td>10

</td>

<td>750

<td>750, 900

225°

</td>

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<td>11

</td>

<td>825

<td>825, 990

247°30'

</td>

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<td>12

</td>

<td>900

<td>900, 1080

270°

</td>

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<td>13

</td>

<td>975

<td>975, 1170

292°30'

</td>

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<td>14

</td>

<td>1050

<td>1050, 1260

315°

</td>

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<td>15

</td>

<td>1125

<td>1125, 1350

337°30'

</td>

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<td>16

</td>

<td>1200

<td>1200, 1440

360°

</td>

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<h1 id="toc8"><a name="Commas"></a>Commas</h1>

16 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes <a class="wiki_link" href="/val">val</a> &lt; 16 25 37 45 55 59 |.)

16 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes <a class="wiki_link" href="/val">val</a> &lt; <a class="wiki_link" href="http://tel.wikispaces.com/16%2025%2037%2045%2055%2059">16 25 37 45 55 59</a> |.)

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</tr>

<tr>

<td style="text-align: center;">1212717/1210381

<td style="text-align: center;">[[tel:1212717/1210381|1212717/1210381]]

</td>

<td style="text-align: left;">| 23 6 -14 &gt;

@@ 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:Nickname2|Nickname2]] and made on <tt>2016-06-15 09:56:56 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-30 17:21:24 UTC</tt>.<br>
-: The original revision id was <tt>585437115</tt>.<br>
+: The original revision id was <tt>597503264</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 17: / Line 17: @@
 =Intervals=
-|| Degree || Cents
+|| Degree || Cents (coarse, fine)
 DMS ||= Approximate
 Ratios* || Interval Name ||
 || 0 || 0 ||= 1/1 || Unison ||
-|| 1 || 75
+|| 1 || 75, 90
 º30' ||= 28/27, 27/26 || Subminor 2nd ||
-|| 2 || 150
+|| 2 || 150, 180
 ° ||= 12/11, 35/32 || Neutral 2nd ||
-|| 3 || 225
+|| 3 || 225, 270
 °30' ||= 8/7 || Supermajor 2nd,
 Septimal Whole-Tone ||
-|| 4 || 300
+|| 4 || 300, 360
 ° ||= 19/16, 32/27 || Minor 3rd ||
-|| 5 || 375
+|| 5 || 375, 450
 °30' ||= 5/4, 26/21 || Major 3rd ||
-|| 6 || 450
+|| 6 || 450, 540
 ° ||= 13/10, 35/27 || Sub-4th,
 Supermajor 3rd ||
-|| 7 || 525
+|| 7 || 525, 630
 °30' ||= 27/20, 52/35, 256/189 || Wide 4th ||
-|| 8 || 600
+|| 8 || 600, 720
 ° ||= 7/5, 10/7 || Tritone ||
-|| 9 || 675
+|| 9 || 675, 810
 °30' ||= 40/27, 35/26, 189/128 || Narrow 5th ||
-|| 10 || 750
+|| 10 || 750, 900
 ° ||= 20/13, 54/35 || Super-5th,
 Subminor 6th ||
-|| 11 || 825
+|| 11 || 825, 990
 °30' ||= 8/5, 21/13 || Minor 6th ||
-|| 12 || 900
+|| 12 || 900, 1080
 ° ||= 27/16, 32/19 || Major 6th ||
-|| 13 || 975
+|| 13 || 975, 1170
 °30' ||= 7/4 || Subminor 7th,
 Septimal Minor 7th ||
-|| 14 || 1050
+|| 14 || 1050, 1260
 ° ||= 11/6, 64/35 || Neutral 7th ||
-|| 15 || 1125
+|| 15 || 1125, 1350
 °30' ||= 27/14, 52/27 || Supermajor 7th ||
-|| 16 || 1200
+|| 16 || 1200, 1440
 ° ||= 2/1 || Octave ||
 *based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.
@@ Line 172: / Line 172: @@
 =Commas=
-EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] &lt; 16 25 37 45 55 59 |.)
+EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] &lt; [[tel:16 25 37 45 55 59|16 25 37 45 55 59]] |.)
 ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
 ||= 135/128 ||&lt; | -7 3 1 &gt; ||&gt; 92.18 ||= Major Chroma ||= Major Limma ||= Pelogic Comma ||
 ||= 648/625 ||&lt; | 3 4 -4 &gt; ||&gt; 62.57 ||= Major Diesis ||= Diminished Comma ||=   ||
 ||= 3125/3072 ||&lt; | -10 -1 5 &gt; ||&gt; 29.61 ||= Small Diesis ||= Magic Comma ||=   ||
-||= 1212717/1210381 ||&lt; | 23 6 -14 &gt; ||&gt; 3.34 ||= Vishnuzma ||= Semisuper ||=   ||
+||= [[tel:1212717/1210381|1212717/1210381]] ||&lt; | 23 6 -14 &gt; ||&gt; 3.34 ||= Vishnuzma ||= Semisuper ||=   ||
 ||= 36/35 ||&lt; | 2 2 -1 -1 &gt; ||&gt; 48.77 ||= Septimal Quarter Tone ||=   ||=   ||
 ||= 525/512 ||&lt; | -9 1 2 1 &gt; ||&gt; 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||=   ||
@@ Line 246: / Line 246: @@
          &lt;td&gt;Degree&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cents&lt;br /&gt;
+         &lt;td&gt;Cents (coarse, fine)&lt;br /&gt;
 DMS&lt;br /&gt;
 &lt;/td&gt;
@@ Line 268: / Line 268: @@
          &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;75&lt;br /&gt;
+         &lt;td&gt;75, 90&lt;br /&gt;
 º30'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 279: / Line 279: @@
          &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;150&lt;br /&gt;
+         &lt;td&gt;150, 180&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 290: / Line 290: @@
          &lt;td&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;225&lt;br /&gt;
+         &lt;td&gt;225, 270&lt;br /&gt;
 °30'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 302: / Line 302: @@
          &lt;td&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;300&lt;br /&gt;
+         &lt;td&gt;300, 360&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 313: / Line 313: @@
          &lt;td&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;375&lt;br /&gt;
+         &lt;td&gt;375, 450&lt;br /&gt;
 °30'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 324: / Line 324: @@
          &lt;td&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;450&lt;br /&gt;
+         &lt;td&gt;450, 540&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 336: / Line 336: @@
          &lt;td&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;525&lt;br /&gt;
+         &lt;td&gt;525, 630&lt;br /&gt;
 °30'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 347: / Line 347: @@
          &lt;td&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;600&lt;br /&gt;
+         &lt;td&gt;600, 720&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 358: / Line 358: @@
          &lt;td&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;675&lt;br /&gt;
+         &lt;td&gt;675, 810&lt;br /&gt;
 °30'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 369: / Line 369: @@
          &lt;td&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;750&lt;br /&gt;
+         &lt;td&gt;750, 900&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 381: / Line 381: @@
          &lt;td&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;825&lt;br /&gt;
+         &lt;td&gt;825, 990&lt;br /&gt;
 °30'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 392: / Line 392: @@
          &lt;td&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;900&lt;br /&gt;
+         &lt;td&gt;900, 1080&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 403: / Line 403: @@
          &lt;td&gt;13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;975&lt;br /&gt;
+         &lt;td&gt;975, 1170&lt;br /&gt;
 °30'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 415: / Line 415: @@
          &lt;td&gt;14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1050&lt;br /&gt;
+         &lt;td&gt;1050, 1260&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 426: / Line 426: @@
          &lt;td&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1125&lt;br /&gt;
+         &lt;td&gt;1125, 1350&lt;br /&gt;
 °30'&lt;br /&gt;
 &lt;/td&gt;
@@ Line 437: / Line 437: @@
          &lt;td&gt;16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200&lt;br /&gt;
+         &lt;td&gt;1200, 1440&lt;br /&gt;
 °&lt;br /&gt;
 &lt;/td&gt;
@@ Line 786: / Line 786: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Commas&lt;/h1&gt;
-EDO &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes &lt;a class="wiki_link" href="/val"&gt;val&lt;/a&gt; &amp;lt; 16 25 37 45 55 59 |.)&lt;br /&gt;
+EDO &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes &lt;a class="wiki_link" href="/val"&gt;val&lt;/a&gt; &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/16%2025%2037%2045%2055%2059"&gt;16 25 37 45 55 59&lt;/a&gt; |.)&lt;br /&gt;
@@ Line 847: / Line 847: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;1212717/1210381&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;[[tel:1212717/1210381|1212717/1210381]]&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;| 23 6 -14 &amp;gt;&lt;br /&gt;