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206edo: Difference between revisions

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**Imported revision 238145405 - Original comment: **
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-06-22 07:34:11 UTC</tt>.<br>
 
: The original revision id was <tt>238145405</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
206edo is closely related to [[103edo]], but the [[patent val]]s differ on the mapping for 3, 11, and 19.  
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
It is in[[consistent]] to the [[5-odd-limit]] and higher limits, with four mappings possible for the 19-limit:
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Scales=
* {{val| 206 327 478 578 713 762 842 875 }} ([[patent val]])
[[skwares8]]
* {{val| 206 '''326''' 478 578 713 762 842 875 }} (206b)
[[skwares11]]
* {{val| 206 '''326''' 478 578 '''712''' 762 842 875 }} (206be)
[[skwares14]]</pre></div>
* {{val| 206 327 '''479''' '''579''' 713 '''763''' 842 875 }} (206cdf)
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;206edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Scales&lt;/h1&gt;
Using the patent val, it [[tempering out|tempers out]] 48828125/47775744 ([[sycamore comma]]) and 32768000000/31381059609 in the 5-limit; 4000/3969, 84035/82944, and 458752/455625 in the 7-limit; [[385/384]], 2401/2376, 6875/6804, and 9375/9317 in the 11-limit; [[352/351]], [[1575/1573]], 1625/1617, 2197/2178, and [[4096/4095]] in the 13-limit; [[289/288]], [[375/374]], [[442/441]], [[715/714]], and 2000/1989 in the 17-limit; 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit.  
&lt;a class="wiki_link" href="/skwares8"&gt;skwares8&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/skwares11"&gt;skwares11&lt;/a&gt;&lt;br /&gt;
Using the 206b val, it tempers out 78732/78125 ([[sensipent comma]]) and 34171875/33554432 ([[ampersand comma]]) in the 5-limit; [[225/224]], [[1029/1024]], and 177147/175000 in the 7-limit; 4375/4356, [[9801/9800]], 15309/15125, and 73728/73205 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1701/1690, and 31213/30976 in the 13-limit; [[273/272]], [[833/832]], 850/847, [[1089/1088]], [[1225/1224]], and 1458/1445 in the 17-limit; 210/209, 495/494, 729/722, 1235/1232, and [[1445/1444]] in the 19-limit.
&lt;a class="wiki_link" href="/skwares14"&gt;skwares14&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
 
Using the 206be val, it tempers out [[243/242]], 385/384, 441/440, and 43923/43750 in the 11-limit; 351/350, 625/624, [[847/845]], [[1001/1000]], and [[1573/1568]] in the 13-limit; 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit; 363/361 and 729/722 in the 19-limit.
 
Using the 206cdf val, it tempers out 2048/2025 ([[diaschisma]]), and {{monzo| 4 -45 29 }} in the 5-limit; [[4375/4374]], 110592/109375, and 235298/234375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit; 640/637, 847/845, 1001/1000, and [[2197/2187]] in the 13-limit; [[136/135]], [[256/255]], 561/560, and 1275/1274 in the 17-limit; 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit.
 
=== Odd harmonics ===
{{Harmonics in equal|206}}
 
=== Subsets and supersets ===
206edo contains 2edo and 103edo as subsets. 412edo, which doubles it, provides an excellent correction to the approximation of harmonic 3.
 
== Scales ==
* [[skwares8]]
* [[skwares11]]
* [[skwares14]]
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