23edo: Difference between revisions

Wikispaces>Nickname2
**Imported revision 583021901 - Original comment: **
Wikispaces>JosephRuhf
**Imported revision 597549152 - 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:Nickname2|Nickname2]] and made on <tt>2016-05-13 08:21:16 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-31 09:19:52 UTC</tt>.<br>
: The original revision id was <tt>583021901</tt>.<br>
: The original revision id was <tt>597549152</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>
Line 20: Line 20:
[[image:Ciclo Icositrifonía.png width="491" height="490" link="Harmony of 23edo"]]
[[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
|| &lt;span style="color: #660000;"&gt;[[Degree]]&lt;/span&gt; || [[Cent]]s value coarse, fine
DMS value ||= Approximate
DMS value ||= Approximate
Ratios* ||= Armodue
Ratios* ||= Armodue
Notation || Notes ||
Notation || Notes ||
|| 0 || 0 ||= 1/1 ||= 1 ||  ||
|| 0 || 0 ||= 1/1 ||= 1 ||  ||
|| 1 || 52.1739
|| 1 || 52.1739, 62.6087
15°39'8" ||= 33/32, 34/33 ||= 2b ||  ||
15°39'8" ||= 33/32, 34/33 ||= 2b ||  ||
|| 2 || 104.3478
|| 2 || [[tel/104.3478|104.3478]], 125.2174
31°18'16" ||= 17/16, 16/15, 18/17 ||= 1# || Less than 1-cent off 17/16 ||
31°18'16" ||= 17/16, 16/15, 18/17 ||= 1# || Less than 1-cent off 17/16 ||
|| 3 || 156.5217
|| 3 || [[tel/156.5217|156.5217]], 187.8261
47°57'23" ||= 11/10, 12/11, 35/32 ||= 2 ||  ||
47°57'23" ||= 11/10, 12/11, 35/32 ||= 2 ||  ||
|| 4· || 208.6957
|| 4· || 208.69565, 250.4348
62°36'31" ||= 9/8, 44/39 ||= 3b ||  ||
62°36'31" ||= 9/8, 44/39 ||= 3b ||  ||
|| 5 || 260.8696
|| 5 || [[tel/260.8696|260.8696]], 313.0435
78°15'39" ||= 7/6, 15/13, 29/25 ||= 2# ||  ||
78°15'39" ||= 7/6, 15/13, 29/25 ||= 2# ||  ||
|| 6 || 313.0435
|| 6 || [[tel/313.0435|313.0435]], 375.6522
93°54'47" ||= 6/5 ||= 3 || Much better at approximating 6/5 than 12-EDO ||
93°54'47" ||= 6/5 ||= 3 || Much better at approximating 6/5 than 12-EDO ||
|| 7· || 365.2174
|| 7· || [[tel/365.2174|365.2174]], 438.2681
109°33'55" ||= 16/13, 21/17, 26/21 ||= 4b ||  ||
109°33'55" ||= 16/13, 21/17, 26/21 ||= 4b ||  ||
|| 8 || 417.3913
|| 8 || [[tel/417.3913|417.3913]], 500.8696
125°13'3* ||= 14/11, 33/26 ||= 3# || Practically just approximation of 14/11 ||
125°13'3* ||= 14/11, 33/26 ||= 3# || Practically just approximation of 14/11 ||
|| 9 || 469.5652
|| 9 || [[tel/469.5652|469.5652]], 563.4783
140°52'10" ||= 21/16, 17/13 ||= 4 ||  ||
140°52'10" ||= 21/16, 17/13 ||= 4 ||  ||
|| 10· || 521.7391
|| 10· || 578.7391. 626.087
156°31'18" ||= 23/17, 88/65, 256/189 ||= 5 ||  ||
156°31'18" ||= 23/17, 88/65, 256/189 ||= 5 ||  ||
|| 11 || 573.913
|| 11 || 573.913, 688.69565
172°10'26" ||= 7/5, 32/23, 46/33 ||= 6b ||  ||
172°10'26" ||= 7/5, 32/23, 46/33 ||= 6b ||  ||
|| 12 || 626.087
|| 12 || 626.087, 751.30435
187°49'34" ||= 10/7, 23/16, 33/23 ||= 5# ||  ||
187°49'34" ||= 10/7, 23/16, 33/23 ||= 5# ||  ||
|| 13· || 678.2609
|| 13· || [[tel/678.2609|678.2609]], 813.913
204°28'42" ||= 34/23, 65/44, 189/128 ||= 6 || Great generator for Hornbostel temperament. ||
204°28'42" ||= 34/23, 65/44, 189/128 ||= 6 || Great generator for Hornbostel temperament. ||
|| 14 || 730.4348
|| 14 || [[tel/730.4348|730.4348]], 876.5217
219°7'50" ||= 32/21, 26/17 ||= 7b ||  ||
219°7'50" ||= 32/21, 26/17 ||= 7b ||  ||
|| 15 || 782.6087
|| 15 || [[tel/782.6087|782.6087]], 939.1304
234°46'57" ||= 11/7, 52/33 ||= 6# ||  ||
234°46'57" ||= 11/7, 52/33 ||= 6# ||  ||
|| 16· || 834.7826
|| 16· || [[tel/834.7826|834.7826]], 1001.7391
251°26'5" ||= 13/8, 34/21, 21/13 ||= 7 ||  ||
251°26'5" ||= 13/8, 34/21, 21/13 ||= 7 ||  ||
|| 17 || 886.9565
|| 17 || [[tel/886.9565|886.9565]], 1064.3478
266°5'13" ||= 5/3 ||= 8b ||  ||
266°5'13" ||= 5/3 ||= 8b ||  ||
|| 18 || 939.1304
|| 18 || [[tel/939.1304|939.1304]], 1126.9565
282°44'21" ||= 12/7, 26/15, 50/29 ||= 7# ||  ||
282°44'21" ||= 12/7, 26/15, 50/29 ||= 7# ||  ||
|| 19· || 991.3043
|| 19· || 991.30435, 1189.5652
297°23'29" ||= 16/9, 39/22 ||= 8 ||  ||
297°23'29" ||= 16/9, 39/22 ||= 8 ||  ||
|| 20 || 1043.4783
|| 20 || 1043.4783, 1252.1739
313°2'37" ||= 11/6, 20/11, 64/35 ||= 9b ||  ||
313°2'37" ||= 11/6, 20/11, 64/35 ||= 9b ||  ||
|| 21 || 1095.6522
|| 21 || 1095.6522, 1314.7926
328°41'44" ||= 15/8, 17/9, 32/17 ||= 8# ||  ||
328°41'44" ||= 15/8, 17/9, 32/17 ||= 8# ||  ||
|| 22 || 1147.8261
|| 22 || 1147.8261, 1377.3913
344°40'52" ||= 33/17, 64/33 ||= 9 ||  ||
344°40'52" ||= 33/17, 64/33 ||= 9 ||  ||
|| 23·· || 1200
|| 23·· || 1200, 1440
360° ||= 2/1 ||= 1 ||  ||
360° ||= 2/1 ||= 1 ||  ||


Line 127: Line 127:


=Commas=  
=Commas=  
23 EDO tempers out the following commas. (Note: This assumes the val &lt; 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).
23 EDO tempers out the following commas. (Note: This assumes the val &lt; [[tel/23 36 53 65 80 85|23 36 53 65 80 85]] |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||~ 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 ||
||= 135/128 ||&lt; | -7 3 1 &gt; ||&gt; 92.18 ||= Major Chroma ||= Major Limma ||= Pelogic Comma ||
Line 246: Line 246:
         &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/Degree"&gt;Degree&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/Degree"&gt;Degree&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/Cent"&gt;Cent&lt;/a&gt;s value&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/Cent"&gt;Cent&lt;/a&gt;s value coarse, fine&lt;br /&gt;
DMS value&lt;br /&gt;
DMS value&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 273: Line 273:
         &lt;td&gt;1&lt;br /&gt;
         &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;52.1739&lt;br /&gt;
         &lt;td&gt;52.1739, 62.6087&lt;br /&gt;
15°39'8&amp;quot;&lt;br /&gt;
15°39'8&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 286: Line 286:
         &lt;td&gt;2&lt;br /&gt;
         &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;104.3478&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/104.3478"&gt;104.3478&lt;/a&gt;, 125.2174&lt;br /&gt;
31°18'16&amp;quot;&lt;br /&gt;
31°18'16&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 299: Line 299:
         &lt;td&gt;3&lt;br /&gt;
         &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;156.5217&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/156.5217"&gt;156.5217&lt;/a&gt;, 187.8261&lt;br /&gt;
47°57'23&amp;quot;&lt;br /&gt;
47°57'23&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 312: Line 312:
         &lt;td&gt;4·&lt;br /&gt;
         &lt;td&gt;4·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;208.6957&lt;br /&gt;
         &lt;td&gt;208.69565, 250.4348&lt;br /&gt;
62°36'31&amp;quot;&lt;br /&gt;
62°36'31&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 325: Line 325:
         &lt;td&gt;5&lt;br /&gt;
         &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;260.8696&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/260.8696"&gt;260.8696&lt;/a&gt;, 313.0435&lt;br /&gt;
78°15'39&amp;quot;&lt;br /&gt;
78°15'39&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 338: Line 338:
         &lt;td&gt;6&lt;br /&gt;
         &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;313.0435&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/313.0435"&gt;313.0435&lt;/a&gt;, 375.6522&lt;br /&gt;
93°54'47&amp;quot;&lt;br /&gt;
93°54'47&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 351: Line 351:
         &lt;td&gt;7·&lt;br /&gt;
         &lt;td&gt;7·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;365.2174&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/365.2174"&gt;365.2174&lt;/a&gt;, 438.2681&lt;br /&gt;
109°33'55&amp;quot;&lt;br /&gt;
109°33'55&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 364: Line 364:
         &lt;td&gt;8&lt;br /&gt;
         &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;417.3913&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/417.3913"&gt;417.3913&lt;/a&gt;, 500.8696&lt;br /&gt;
125°13'3*&lt;br /&gt;
125°13'3*&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 377: Line 377:
         &lt;td&gt;9&lt;br /&gt;
         &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;469.5652&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/469.5652"&gt;469.5652&lt;/a&gt;, 563.4783&lt;br /&gt;
140°52'10&amp;quot;&lt;br /&gt;
140°52'10&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 390: Line 390:
         &lt;td&gt;10·&lt;br /&gt;
         &lt;td&gt;10·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;521.7391&lt;br /&gt;
         &lt;td&gt;578.7391. 626.087&lt;br /&gt;
156°31'18&amp;quot;&lt;br /&gt;
156°31'18&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 403: Line 403:
         &lt;td&gt;11&lt;br /&gt;
         &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;573.913&lt;br /&gt;
         &lt;td&gt;573.913, 688.69565&lt;br /&gt;
172°10'26&amp;quot;&lt;br /&gt;
172°10'26&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 416: Line 416:
         &lt;td&gt;12&lt;br /&gt;
         &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;626.087&lt;br /&gt;
         &lt;td&gt;626.087, 751.30435&lt;br /&gt;
187°49'34&amp;quot;&lt;br /&gt;
187°49'34&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 429: Line 429:
         &lt;td&gt;13·&lt;br /&gt;
         &lt;td&gt;13·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;678.2609&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/678.2609"&gt;678.2609&lt;/a&gt;, 813.913&lt;br /&gt;
204°28'42&amp;quot;&lt;br /&gt;
204°28'42&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 442: Line 442:
         &lt;td&gt;14&lt;br /&gt;
         &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;730.4348&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/730.4348"&gt;730.4348&lt;/a&gt;, 876.5217&lt;br /&gt;
219°7'50&amp;quot;&lt;br /&gt;
219°7'50&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 455: Line 455:
         &lt;td&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;782.6087&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/782.6087"&gt;782.6087&lt;/a&gt;, 939.1304&lt;br /&gt;
234°46'57&amp;quot;&lt;br /&gt;
234°46'57&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 468: Line 468:
         &lt;td&gt;16·&lt;br /&gt;
         &lt;td&gt;16·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;834.7826&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/834.7826"&gt;834.7826&lt;/a&gt;, 1001.7391&lt;br /&gt;
251°26'5&amp;quot;&lt;br /&gt;
251°26'5&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 481: Line 481:
         &lt;td&gt;17&lt;br /&gt;
         &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;886.9565&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/886.9565"&gt;886.9565&lt;/a&gt;, 1064.3478&lt;br /&gt;
266°5'13&amp;quot;&lt;br /&gt;
266°5'13&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 494: Line 494:
         &lt;td&gt;18&lt;br /&gt;
         &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;939.1304&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/939.1304"&gt;939.1304&lt;/a&gt;, 1126.9565&lt;br /&gt;
282°44'21&amp;quot;&lt;br /&gt;
282°44'21&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 507: Line 507:
         &lt;td&gt;19·&lt;br /&gt;
         &lt;td&gt;19·&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;991.3043&lt;br /&gt;
         &lt;td&gt;991.30435, 1189.5652&lt;br /&gt;
297°23'29&amp;quot;&lt;br /&gt;
297°23'29&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 520: Line 520:
         &lt;td&gt;20&lt;br /&gt;
         &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1043.4783&lt;br /&gt;
         &lt;td&gt;1043.4783, 1252.1739&lt;br /&gt;
313°2'37&amp;quot;&lt;br /&gt;
313°2'37&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 533: Line 533:
         &lt;td&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1095.6522&lt;br /&gt;
         &lt;td&gt;1095.6522, 1314.7926&lt;br /&gt;
328°41'44&amp;quot;&lt;br /&gt;
328°41'44&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 546: Line 546:
         &lt;td&gt;22&lt;br /&gt;
         &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1147.8261&lt;br /&gt;
         &lt;td&gt;1147.8261, 1377.3913&lt;br /&gt;
344°40'52&amp;quot;&lt;br /&gt;
344°40'52&amp;quot;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 559: Line 559:
         &lt;td&gt;23··&lt;br /&gt;
         &lt;td&gt;23··&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 627: Line 627:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Commas&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Commas&lt;/h1&gt;
  23 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).&lt;br /&gt;
  23 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/23%2036%2053%2065%2080%2085"&gt;23 36 53 65 80 85&lt;/a&gt; |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).&lt;br /&gt;