23edo: Difference between revisions

Wikispaces>igliashon
**Imported revision 242753327 - Original comment: **
Wikispaces>igliashon
**Imported revision 242821659 - 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:igliashon|igliashon]] and made on <tt>2011-07-25 12:52:10 UTC</tt>.<br>
: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-25 21:10:59 UTC</tt>.<br>
: The original revision id was <tt>242753327</tt>.<br>
: The original revision id was <tt>242821659</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 16: Line 16:


=&lt;span style="font-size: 1.4em;"&gt;Intervals&lt;/span&gt;=  
=&lt;span style="font-size: 1.4em;"&gt;Intervals&lt;/span&gt;=  
|| &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 ||= Approximate
Ratios* ||
Ratios* ||
|| 0 || 0 || 1/1 ||
|| 0 || 0 ||= 1/1 ||
|| 1 || 52.1739 || 33/32, 34/33 ||
|| 1 || 52.1739 ||= 33/32, 34/33 ||
|| 2 || 104.3478 || 17/16, 15/16, 18/17 ||
|| 2 || 104.3478 ||= 17/16, 15/16, 18/17 ||
|| 3 || 156.5217 || 11/10, 12/11 ||
|| 3 || 156.5217 ||= 11/10, 12/11 ||
|| 4 || 208.6957 || 9/8 ||
|| 4 || 208.6957 ||= 9/8 ||
|| 5 || 260.8696 || 7/6, 15/13 ||
|| 5 || 260.8696 ||= 7/6, 15/13 ||
|| 6 || 313.0435 || 6/5 ||
|| 6 || 313.0435 ||= 6/5 ||
|| 7 || 365.2174 || 21/17, 26/21 ||
|| 7 || 365.2174 ||= 21/17, 26/21 ||
|| 8 || 417.3913 || 14/11, 33/26 ||
|| 8 || 417.3913 ||= 14/11, 33/26 ||
|| 9 || 469.5652 || 21/16, 17/13 ||
|| 9 || 469.5652 ||= 21/16, 17/13 ||
|| 10 || 521.7391 || 65/48, 256/189 ||
|| 10 || 521.7391 ||= 65/48, 256/189 ||
|| 11 || 573.913 || 7/5 ||
|| 11 || 573.913 ||= 7/5 ||
|| 12 || 626.087 || 10/7 ||
|| 12 || 626.087 ||= 10/7 ||
|| 13 || 678.2609 || 96/65, 189/128 ||
|| 13 || 678.2609 ||= 96/65, 189/128 ||
|| 14 || 730.4348 || 32/21, 26/17 ||
|| 14 || 730.4348 ||= 32/21, 26/17 ||
|| 15 || 782.6087 || 11/7, 52/33 ||
|| 15 || 782.6087 ||= 11/7, 52/33 ||
|| 16 || 834.7826 || 13/8, 21/13 ||
|| 16 || 834.7826 ||= 13/8, 21/13 ||
|| 17 || 886.9565 || 5/3 ||
|| 17 || 886.9565 ||= 5/3 ||
|| 18 || 939.1304 || 12/7, 26/15 ||
|| 18 || 939.1304 ||= 12/7, 26/15 ||
|| 19 || 991.3043 || 16/9 ||
|| 19 || 991.3043 ||= 16/9 ||
|| 20 || 1043.4783 || 11/6, 20/11 ||
|| 20 || 1043.4783 ||= 11/6, 20/11 ||
|| 21 || 1095.6522 || 15/8, 17/9, 32/17 ||
|| 21 || 1095.6522 ||= 15/8, 17/9, 32/17 ||
|| 22 || 1147.8261 || 33/17, 64/33 ||
|| 22 || 1147.8261 ||= 33/17, 64/33 ||
|| 23 || 1200 || 2/1 ||
|| 23 || 1200 ||= 2/1 ||


*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.
*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.
Line 192: Line 192:
         &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&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Approximate&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;Approximate&lt;br /&gt;
Ratios*&lt;br /&gt;
Ratios*&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 201: Line 201:
         &lt;td&gt;0&lt;br /&gt;
         &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1/1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 209: Line 209:
         &lt;td&gt;52.1739&lt;br /&gt;
         &lt;td&gt;52.1739&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;33/32, 34/33&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;33/32, 34/33&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 217: Line 217:
         &lt;td&gt;104.3478&lt;br /&gt;
         &lt;td&gt;104.3478&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17/16, 15/16, 18/17&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;17/16, 15/16, 18/17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 225: Line 225:
         &lt;td&gt;156.5217&lt;br /&gt;
         &lt;td&gt;156.5217&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11/10, 12/11&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;11/10, 12/11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 233: Line 233:
         &lt;td&gt;208.6957&lt;br /&gt;
         &lt;td&gt;208.6957&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;9/8&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;9/8&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 241: Line 241:
         &lt;td&gt;260.8696&lt;br /&gt;
         &lt;td&gt;260.8696&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7/6, 15/13&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;7/6, 15/13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 249: Line 249:
         &lt;td&gt;313.0435&lt;br /&gt;
         &lt;td&gt;313.0435&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;6/5&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 257: Line 257:
         &lt;td&gt;365.2174&lt;br /&gt;
         &lt;td&gt;365.2174&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;21/17, 26/21&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;21/17, 26/21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 265: Line 265:
         &lt;td&gt;417.3913&lt;br /&gt;
         &lt;td&gt;417.3913&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;14/11, 33/26&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;14/11, 33/26&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 273: Line 273:
         &lt;td&gt;469.5652&lt;br /&gt;
         &lt;td&gt;469.5652&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;21/16, 17/13&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;21/16, 17/13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 281: Line 281:
         &lt;td&gt;521.7391&lt;br /&gt;
         &lt;td&gt;521.7391&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;65/48, 256/189&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;65/48, 256/189&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 289: Line 289:
         &lt;td&gt;573.913&lt;br /&gt;
         &lt;td&gt;573.913&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7/5&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;7/5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 297: Line 297:
         &lt;td&gt;626.087&lt;br /&gt;
         &lt;td&gt;626.087&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;10/7&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;10/7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 305: Line 305:
         &lt;td&gt;678.2609&lt;br /&gt;
         &lt;td&gt;678.2609&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;96/65, 189/128&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;96/65, 189/128&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 313: Line 313:
         &lt;td&gt;730.4348&lt;br /&gt;
         &lt;td&gt;730.4348&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;32/21, 26/17&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;32/21, 26/17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 321: Line 321:
         &lt;td&gt;782.6087&lt;br /&gt;
         &lt;td&gt;782.6087&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11/7, 52/33&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;11/7, 52/33&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 329: Line 329:
         &lt;td&gt;834.7826&lt;br /&gt;
         &lt;td&gt;834.7826&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13/8, 21/13&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;13/8, 21/13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 337: Line 337:
         &lt;td&gt;886.9565&lt;br /&gt;
         &lt;td&gt;886.9565&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5/3&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;5/3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 345: Line 345:
         &lt;td&gt;939.1304&lt;br /&gt;
         &lt;td&gt;939.1304&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;12/7, 26/15&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;12/7, 26/15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 353: Line 353:
         &lt;td&gt;991.3043&lt;br /&gt;
         &lt;td&gt;991.3043&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;16/9&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;16/9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 361: Line 361:
         &lt;td&gt;1043.4783&lt;br /&gt;
         &lt;td&gt;1043.4783&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11/6, 20/11&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;11/6, 20/11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 369: Line 369:
         &lt;td&gt;1095.6522&lt;br /&gt;
         &lt;td&gt;1095.6522&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15/8, 17/9, 32/17&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;15/8, 17/9, 32/17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 377: Line 377:
         &lt;td&gt;1147.8261&lt;br /&gt;
         &lt;td&gt;1147.8261&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;33/17, 64/33&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;33/17, 64/33&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 385: Line 385:
         &lt;td&gt;1200&lt;br /&gt;
         &lt;td&gt;1200&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2/1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;