20203edo: Difference between revisions

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**Imported revision 557206925 - Original comment: **
 
Expand and simplify the comma basis
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET|Consistency=45|Distinct consistency=45}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-23 12:26:26 UTC</tt>.<br>
 
: The original revision id was <tt>557206925</tt>.<br>
20203edo is a very strong high-limit system, and specializes in the [[17-limit|17-]] and [[19-limit]], with lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any smaller edo until [[102557edo|102557]] and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower [[43-limit]] relative error than any smaller edo except for [[7361edo|7361]], [[14348edo|14348]] and [[17461edo|17461]].  
: 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>
A 43-limit [[comma basis]] for this temperament is {29792/29791, 32799/32798, 43264/43263, 45696/45695, 47151/47150, 52326/52325, 53361/53360, 69875/69874, 81796/81795, 83521/83520, 87465/87464, 96876/96875, 111112/111111}. In the [[13-limit]] it tempers out [[123201/123200]] and [[1990656/1990625]]; in the [[17-limit]] [[194481/194480]] and [[336141/336140]]; in the [[19-limit]] 89376/89375,  104976/104975, and 165376/165375; in the [[23-limit]] 43264/43263 and 52326/52325 among others.
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">The 20203 division divides the octave into 20203 equal parts of  cents each. It is a very strong higher limit edo, with a lower 19-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any edo until 128125. It is also distinctly consistent through the 45 limit, and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461.</pre></div>
=== Prime harmonics ===
<h4>Original HTML content:</h4>
{{Harmonics in equal|20203|columns=11}}
<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;20203edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 20203 division divides the octave into 20203 equal parts of  cents each. It is a very strong higher limit edo, with a lower 19-limit &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness"&gt;relative error&lt;/a&gt; than any edo until 128125. It is also distinctly consistent through the 45 limit, and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461.&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Harmonics in equal|20203|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 20203edo (continued)}}