23edo: 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:JosephRuhf|JosephRuhf]] and made on <tt>~~2014~~-11-27 18:57:12 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-27 11:24:51 UTC</tt>.

: The original revision id was <tt>~~532961576~~</tt>.

: The original revision id was <tt>545564324</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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[[image:Ciclo Icositrifonía.png width="491" height="490" link="Harmony of 23edo"]]

|| [[Degree]] || [[Cent]]s value ||= Approximate

|| [[Degree]] || [[Cent]]s value

DMS value ||= Approximate

Ratios* ||= Armodue

Notation ||

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

|| 1 || 52.1739 ||= 33/32, 34/33 ||= 2b ||

|| 1 || 52.1739

|| 2 || 104.3478 ||= 17/16, 16/15, 18/17 ||= 1# ||

15°39'8" ||= 33/32, 34/33 ||= 2b ||

|| 3 || 156.5217 ||= 11/10, 12/11, 35/32 ||= 2 ||

|| 2 || 104.3478

|| 4· || 208.6957 ||= 9/8, 44/39 ||= 3b ||

31°18'16" ||= 17/16, 16/15, 18/17 ||= 1# ||

|| 5 || 260.8696 ||= 7/6, 15/13, 29/25 ||= 2# ||

|| 3 || 156.5217

|| 6 || 313.0435 ||= 6/5 ||= 3 ||

47°57'23" ||= 11/10, 12/11, 35/32 ||= 2 ||

|| 7· || 365.2174 ||= 16/13, 21/17, 26/21 ||= 4b ||

|| 4· || 208.6957

|| 8 || 417.3913 ||= 14/11, 33/26 ||= 3# ||

62°36'31" ||= 9/8, 44/39 ||= 3b ||

|| 9 || 469.5652 ||= 21/16, 17/13 ||= 4 ||

|| 5 || 260.8696

|| 10· || 521.7391 ||= 23/17, 88/65, 256/189 ||= 5 ||

78°15'39" ||= 7/6, 15/13, 29/25 ||= 2# ||

|| 11 || 573.913 ||= 7/5, 32/23, 46/33 ||= 6b ||

|| 6 || 313.0435

|| 12 || 626.087 ||= 10/7, 23/16, 33/23 ||= 5# ||

93°54'47" ||= 6/5 ||= 3 ||

|| 13· || 678.2609 ||= 34/23, 65/44, 189/128 ||= 6 ||

|| 7· || 365.2174

|| 14 || 730.4348 ||= 32/21, 26/17 ||= 7b ||

109°33'55" ||= 16/13, 21/17, 26/21 ||= 4b ||

|| 15 || 782.6087 ||= 11/7, 52/33 ||= 6# ||

|| 8 || 417.3913

|| 16· || 834.7826 ||= 13/8, 34/21, 21/13 ||= 7 ||

125°13'3* ||= 14/11, 33/26 ||= 3# ||

|| 17 || 886.9565 ||= 5/3 ||= 8b ||

|| 9 || 469.5652

|| 18 || 939.1304 ||= 12/7, 26/15, 50/29 ||= 7# ||

140°52'10" ||= 21/16, 17/13 ||= 4 ||

|| 19· || 991.3043 ||= 16/9, 39/22 ||= 8 ||

|| 10· || 521.7391

|| 20 || 1043.4783 ||= 11/6, 20/11, 64/35 ||= 9b ||

156°31'18" ||= 23/17, 88/65, 256/189 ||= 5 ||

|| 21 || 1095.6522 ||= 15/8, 17/9, 32/17 ||= 8# ||

|| 11 || 573.913

|| 22 || 1147.8261 ||= 33/17, 64/33 ||= 9 ||

172°10'26" ||= 7/5, 32/23, 46/33 ||= 6b ||

|| 23·· || 1200 ||= 2/1 ||= 1 ||

|| 12 || 626.087

187°49'34" ||= 10/7, 23/16, 33/23 ||= 5# ||

|| 13· || 678.2609

204°28'42" ||= 34/23, 65/44, 189/128 ||= 6 ||

|| 14 || 730.4348

219°7'50" ||= 32/21, 26/17 ||= 7b ||

|| 15 || 782.6087

234°46'57" ||= 11/7, 52/33 ||= 6# ||

|| 16· || 834.7826

251°26'5" ||= 13/8, 34/21, 21/13 ||= 7 ||

|| 17 || 886.9565

266°5'13" ||= 5/3 ||= 8b ||

|| 18 || 939.1304

282°44'21" ||= 12/7, 26/15, 50/29 ||= 7# ||

|| 19· || 991.3043

297°23'29" ||= 16/9, 39/22 ||= 8 ||

|| 20 || 1043.4783

313°2'37" ||= 11/6, 20/11, 64/35 ||= 9b ||

|| 21 || 1095.6522

328°41'44" ||= 15/8, 17/9, 32/17 ||= 8# ||

|| 22 || 1147.8261

344°40'52" ||= 33/17, 64/33 ||= 9 ||

|| 23·· || 1200

360° ||= 2/1 ||= 1 ||

*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.

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</td>

<td><a class="wiki_link" href="/Cent">Cent</a>s value

DMS value

</td>

<td style="text-align: center;">Approximate

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</td>

<td>52.1739

15°39'8&quot;

</td>

<td style="text-align: center;">33/32, 34/33

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</td>

<td>104.3478

31°18'16&quot;

</td>

<td style="text-align: center;">17/16, 16/15, 18/17

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</td>

<td>156.5217

47°57'23&quot;

</td>

<td style="text-align: center;">11/10, 12/11, 35/32

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</td>

<td>208.6957

62°36'31&quot;

</td>

<td style="text-align: center;">9/8, 44/39

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</td>

<td>260.8696

78°15'39&quot;

</td>

<td style="text-align: center;">7/6, 15/13, 29/25

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</td>

<td>313.0435

93°54'47&quot;

</td>

<td style="text-align: center;">6/5

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</td>

<td>365.2174

109°33'55&quot;

</td>

<td style="text-align: center;">16/13, 21/17, 26/21

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</td>

<td>417.3913

125°13'3*

</td>

<td style="text-align: center;">14/11, 33/26

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</td>

<td>469.5652

140°52'10&quot;

</td>

<td style="text-align: center;">21/16, 17/13

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</td>

<td>521.7391

156°31'18&quot;

</td>

<td style="text-align: center;">23/17, 88/65, 256/189

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</td>

<td>573.913

172°10'26&quot;

</td>

<td style="text-align: center;">7/5, 32/23, 46/33

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</td>

<td>626.087

187°49'34&quot;

</td>

<td style="text-align: center;">10/7, 23/16, 33/23

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</td>

<td>678.2609

204°28'42&quot;

</td>

<td style="text-align: center;">34/23, 65/44, 189/128

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</td>

<td>730.4348

219°7'50&quot;

</td>

<td style="text-align: center;">32/21, 26/17

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</td>

<td>782.6087

234°46'57&quot;

</td>

<td style="text-align: center;">11/7, 52/33

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</td>

<td>834.7826

251°26'5&quot;

</td>

<td style="text-align: center;">13/8, 34/21, 21/13

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</td>

<td>886.9565

266°5'13&quot;

</td>

<td style="text-align: center;">5/3

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</td>

<td>939.1304

282°44'21&quot;

</td>

<td style="text-align: center;">12/7, 26/15, 50/29

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</td>

<td>991.3043

297°23'29&quot;

</td>

<td style="text-align: center;">16/9, 39/22

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</td>

<td>1043.4783

313°2'37&quot;

</td>

<td style="text-align: center;">11/6, 20/11, 64/35

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</td>

<td>1095.6522

328°41'44&quot;

</td>

<td style="text-align: center;">15/8, 17/9, 32/17

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</td>

<td>1147.8261

344°40'52&quot;

</td>

<td style="text-align: center;">33/17, 64/33

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</td>

<td>1200

360°

</td>

<td style="text-align: center;">2/1

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2014-11-27 18:57:12 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-27 11:24:51 UTC</tt>.<br>
-: The original revision id was <tt>532961576</tt>.<br>
+: The original revision id was <tt>545564324</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 20: / Line 20: @@
 [[image:Ciclo Icositrifonía.png width="491" height="490" link="Harmony of 23edo"]]
-|| &lt;span style="color: #660000;"&gt;[[Degree]]&lt;/span&gt; || [[Cent]]s value ||= Approximate
+|| &lt;span style="color: #660000;"&gt;[[Degree]]&lt;/span&gt; || [[Cent]]s value
+DMS value ||= Approximate
 Ratios* ||= Armodue
 Notation ||
 || 0 || 0 ||= 1/1 ||= 1 ||
-|| 1 || 52.1739 ||= 33/32, 34/33 ||= 2b ||
+|| 1 || 52.1739
-|| 2 || 104.3478 ||= 17/16, 16/15, 18/17 ||= 1# ||
+°39'8" ||= 33/32, 34/33 ||= 2b ||
-|| 3 || 156.5217 ||= 11/10, 12/11, 35/32 ||= 2 ||
+|| 2 || 104.3478
-|| 4· || 208.6957 ||= 9/8, 44/39 ||= 3b ||
+°18'16" ||= 17/16, 16/15, 18/17 ||= 1# ||
-|| 5 || 260.8696 ||= 7/6, 15/13, 29/25 ||= 2# ||
+|| 3 || 156.5217
-|| 6 || 313.0435 ||= 6/5 ||= 3 ||
+°57'23" ||= 11/10, 12/11, 35/32 ||= 2 ||
-|| 7· || 365.2174 ||= 16/13, 21/17, 26/21 ||= 4b ||
+|| 4· || 208.6957
-|| 8 || 417.3913 ||= 14/11, 33/26 ||= 3# ||
+°36'31" ||= 9/8, 44/39 ||= 3b ||
-|| 9 || 469.5652 ||= 21/16, 17/13 ||= 4 ||
+|| 5 || 260.8696
-|| 10· || 521.7391 ||= 23/17, 88/65, 256/189 ||= 5 ||
+°15'39" ||= 7/6, 15/13, 29/25 ||= 2# ||
-|| 11 || 573.913 ||= 7/5, 32/23, 46/33 ||= 6b ||
+|| 6 || 313.0435
-|| 12 || 626.087 ||= 10/7, 23/16, 33/23 ||= 5# ||
+°54'47" ||= 6/5 ||= 3 ||
-|| 13· || 678.2609 ||= 34/23, 65/44, 189/128 ||= 6 ||
+|| 7· || 365.2174
-|| 14 || 730.4348 ||= 32/21, 26/17 ||= 7b ||
+°33'55" ||= 16/13, 21/17, 26/21 ||= 4b ||
-|| 15 || 782.6087 ||= 11/7, 52/33 ||= 6# ||
+|| 8 || 417.3913
-|| 16· || 834.7826 ||= 13/8, 34/21, 21/13 ||= 7 ||
+°13'3* ||= 14/11, 33/26 ||= 3# ||
-|| 17 || 886.9565 ||= 5/3 ||= 8b ||
+|| 9 || 469.5652
-|| 18 || 939.1304 ||= 12/7, 26/15, 50/29 ||= 7# ||
+°52'10" ||= 21/16, 17/13 ||= 4 ||
-|| 19· || 991.3043 ||= 16/9, 39/22 ||= 8 ||
+|| 10· || 521.7391
-|| 20 || 1043.4783 ||= 11/6, 20/11, 64/35 ||= 9b ||
+°31'18" ||= 23/17, 88/65, 256/189 ||= 5 ||
-|| 21 || 1095.6522 ||= 15/8, 17/9, 32/17 ||= 8# ||
+|| 11 || 573.913
-|| 22 || 1147.8261 ||= 33/17, 64/33 ||= 9 ||
+°10'26" ||= 7/5, 32/23, 46/33 ||= 6b ||
-|| 23·· || 1200 ||= 2/1 ||= 1 ||
+|| 12 || 626.087
+°49'34" ||= 10/7, 23/16, 33/23 ||= 5# ||
+|| 13· || 678.2609
+°28'42" ||= 34/23, 65/44, 189/128 ||= 6 ||
+|| 14 || 730.4348
+°7'50" ||= 32/21, 26/17 ||= 7b ||
+|| 15 || 782.6087
+°46'57" ||= 11/7, 52/33 ||= 6# ||
+|| 16· || 834.7826
+°26'5" ||= 13/8, 34/21, 21/13 ||= 7 ||
+|| 17 || 886.9565
+°5'13" ||= 5/3 ||= 8b ||
+|| 18 || 939.1304
+°44'21" ||= 12/7, 26/15, 50/29 ||= 7# ||
+|| 19· || 991.3043
+°23'29" ||= 16/9, 39/22 ||= 8 ||
+|| 20 || 1043.4783
+°2'37" ||= 11/6, 20/11, 64/35 ||= 9b ||
+|| 21 || 1095.6522
+°41'44" ||= 15/8, 17/9, 32/17 ||= 8# ||
+|| 22 || 1147.8261
+°40'52" ||= 33/17, 64/33 ||= 9 ||
+|| 23·· || 1200
+° ||= 2/1 ||= 1 ||
 *based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.
@@ Line 221: / Line 245: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;a class="wiki_link" href="/Cent"&gt;Cent&lt;/a&gt;s value&lt;br /&gt;
+DMS value&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Approximate&lt;br /&gt;
@@ Line 243: / Line 268: @@
 &lt;/td&gt;
          &lt;td&gt;52.1739&lt;br /&gt;
+°39'8&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/32, 34/33&lt;br /&gt;
@@ Line 253: / Line 279: @@
 &lt;/td&gt;
          &lt;td&gt;104.3478&lt;br /&gt;
+°18'16&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/16, 16/15, 18/17&lt;br /&gt;
@@ Line 263: / Line 290: @@
 &lt;/td&gt;
          &lt;td&gt;156.5217&lt;br /&gt;
+°57'23&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/10, 12/11, 35/32&lt;br /&gt;
@@ Line 273: / Line 301: @@
 &lt;/td&gt;
          &lt;td&gt;208.6957&lt;br /&gt;
+°36'31&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/8, 44/39&lt;br /&gt;
@@ Line 283: / Line 312: @@
 &lt;/td&gt;
          &lt;td&gt;260.8696&lt;br /&gt;
+°15'39&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/6, 15/13, 29/25&lt;br /&gt;
@@ Line 293: / Line 323: @@
 &lt;/td&gt;
          &lt;td&gt;313.0435&lt;br /&gt;
+°54'47&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
@@ Line 303: / Line 334: @@
 &lt;/td&gt;
          &lt;td&gt;365.2174&lt;br /&gt;
+°33'55&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/13, 21/17, 26/21&lt;br /&gt;
@@ Line 313: / Line 345: @@
 &lt;/td&gt;
          &lt;td&gt;417.3913&lt;br /&gt;
+°13'3*&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;14/11, 33/26&lt;br /&gt;
@@ Line 323: / Line 356: @@
 &lt;/td&gt;
          &lt;td&gt;469.5652&lt;br /&gt;
+°52'10&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;21/16, 17/13&lt;br /&gt;
@@ Line 333: / Line 367: @@
 &lt;/td&gt;
          &lt;td&gt;521.7391&lt;br /&gt;
+°31'18&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;23/17, 88/65, 256/189&lt;br /&gt;
@@ Line 343: / Line 378: @@
 &lt;/td&gt;
          &lt;td&gt;573.913&lt;br /&gt;
+°10'26&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/5, 32/23, 46/33&lt;br /&gt;
@@ Line 353: / Line 389: @@
 &lt;/td&gt;
          &lt;td&gt;626.087&lt;br /&gt;
+°49'34&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;10/7, 23/16, 33/23&lt;br /&gt;
@@ Line 363: / Line 400: @@
 &lt;/td&gt;
          &lt;td&gt;678.2609&lt;br /&gt;
+°28'42&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;34/23, 65/44, 189/128&lt;br /&gt;
@@ Line 373: / Line 411: @@
 &lt;/td&gt;
          &lt;td&gt;730.4348&lt;br /&gt;
+°7'50&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;32/21, 26/17&lt;br /&gt;
@@ Line 383: / Line 422: @@
 &lt;/td&gt;
          &lt;td&gt;782.6087&lt;br /&gt;
+°46'57&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/7, 52/33&lt;br /&gt;
@@ Line 393: / Line 433: @@
 &lt;/td&gt;
          &lt;td&gt;834.7826&lt;br /&gt;
+°26'5&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;13/8, 34/21, 21/13&lt;br /&gt;
@@ Line 403: / Line 444: @@
 &lt;/td&gt;
          &lt;td&gt;886.9565&lt;br /&gt;
+°5'13&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5/3&lt;br /&gt;
@@ Line 413: / Line 455: @@
 &lt;/td&gt;
          &lt;td&gt;939.1304&lt;br /&gt;
+°44'21&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;12/7, 26/15, 50/29&lt;br /&gt;
@@ Line 423: / Line 466: @@
 &lt;/td&gt;
          &lt;td&gt;991.3043&lt;br /&gt;
+°23'29&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/9, 39/22&lt;br /&gt;
@@ Line 433: / Line 477: @@
 &lt;/td&gt;
          &lt;td&gt;1043.4783&lt;br /&gt;
+°2'37&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/6, 20/11, 64/35&lt;br /&gt;
@@ Line 443: / Line 488: @@
 &lt;/td&gt;
          &lt;td&gt;1095.6522&lt;br /&gt;
+°41'44&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;15/8, 17/9, 32/17&lt;br /&gt;
@@ Line 453: / Line 499: @@
 &lt;/td&gt;
          &lt;td&gt;1147.8261&lt;br /&gt;
+°40'52&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/17, 64/33&lt;br /&gt;
@@ Line 463: / Line 510: @@
 &lt;/td&gt;
          &lt;td&gt;1200&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;