1783edo: Difference between revisions

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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:genewardsmith|genewardsmith]] and made on <tt>2015-08-16 14:11:49 UTC</tt>.<br>
 
: The original revision id was <tt>556763043</tt>.<br>
1783edo is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than anything until [[2513edo|2513]]. It is [[consistent]] to the [[9-odd-limit]], but there is a large relative delta for the [[harmonic]] [[7/1|7]]. Together with decent approximations to [[11/1|11]], [[13/1|13]], [[17/1|17]], and [[19/1|19]], it makes for a good no-7 19-limit tuning.
: 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>
In the 5-limit the equal temperament [[tempering out|tempers out]] the [[monzisma]], {{monzo| 54 -37 2}}; egads, {{monzo| -36 -52 51 }}; gross, {{monzo| 144 -22 -47 }}; and pirate, {{monzo| -90 -15 49 }}.  
<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 1783 equal division divides the octave into 1783 equal parts of 0.673 cents each. It is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than anything until [[2513edo|2513]]. It tempers out the monzisma, | 54 -37 2 &gt;; egads, | -36 -52 51 &gt;; gross, | 144 -22 -47 &gt;; and pirate, | -90 -15 49 &gt;.</pre></div>
Using the [[patent val]], it tempers out 2460375/2458624 in the 7-limit; [[3025/3024]] and 180224/180075 in the 11-limit; [[1716/1715]] and [[4096/4095]] in the 13-limit. The alternative 1783d [[val]] tempers out [[4375/4374]] in the 7-limit; 41503/41472 and 160083/160000 in the 11-limit; [[10648/10647]] in the 13-limit.
<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;1783edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 1783 equal division divides the octave into 1783 equal parts of 0.673 cents each. It is a very strong 5-limit system, with a lower 5-limit &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness"&gt;relative error&lt;/a&gt; than anything until &lt;a class="wiki_link" href="/2513edo"&gt;2513&lt;/a&gt;. It tempers out the monzisma, | 54 -37 2 &amp;gt;; egads, | -36 -52 51 &amp;gt;; gross, | 144 -22 -47 &amp;gt;; and pirate, | -90 -15 49 &amp;gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Prime harmonics ===
{{Harmonics in equal|1783|prec=4}}
 
=== Subsets and supersets ===
1783edo is the 276th [[prime edo]]. [[3566edo]], which doubles it, provides a good correction to the approximation of [[7/1|harmonic 7]].