940edo: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

~~This is an imported revision from Wikispaces. The revision metadata~~ is ~~included below for reference:<br>~~

~~: This revision was by author~~ [[~~User:genewardsmith~~|~~genewardsmith~~]] ~~and made on <tt>2011~~-11-~~12 03:27:54 UTC</tt>.<br>~~

~~: The original revision id was <tt>274576932</tt>~~.~~<br>~~

940edo is [[consistency|distinctly consistent]] through the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675.

~~: 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 non-patent val {{val| 940 1491 2184 2638 3254 3481 }} gives a tuning almost identical to the [[POTE tuning]] for the 13-limit [[pele]] temperament, tempering out 196/195, 352/351 and 364/363.

~~<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 //940 equal ~~division// divides the octave into 940 equal parts of 1.277 cents each. It is uniquely~~ [[~~consistent~~]] ~~through the 11-limit, tempering out~~ 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it ~~supports~~ [[~~Breedsmic temperaments#Decoid|~~decoid ~~temperament~~]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[~~The Archipelago#Rank tree temperaments|~~greenland]] and [[~~The Archipelago#Rank tree temperaments|~~baffin]] temperaments, and for the rank ~~five temperament~~ temperament tempering out 676/675. The non-patent val ~~<~~940 1491 2184 2638 3254 3481| gives a tuning almost identical to the POTE tuning for the 13-limit [[~~Hemifamity family#Pele|~~pele ~~temperament~~]] tempering out 196/195, 352/351 and 364/363.~~</pre></div>~~

In higher limits, it is a satisfactory no-13's 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to it where it has good 3/2 and 5/4, but 15/8 is one step off from the closest location.

~~<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"><html><head><title>940edo</title></head><body>The <em>940 equal division</em> divides the octave into 940 equal parts of 1.~~277 cents each. It~~ is ~~uniquely <a class="wiki_link" href="/consistent">consistent</a> through~~ the ~~11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625~~ and ~~9801/9800 in the 11-limit~~, which ~~means it supports <~~a ~~class="wiki_link" href="/Breedsmic%20temperaments#Decoid">decoid temperament</a> and in fact gives an excellent tuning for~~ it~~. In the 13-limit,~~ it ~~tempers out 676~~/~~675, 1001~~/~~1000~~, ~~1716~~/~~1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives~~ the ~~<a class~~=~~"wiki_link" href~~=~~"/optimal%20patent%20val">optimal patent val</a> for 13-limit decoid. It also gives the optimal patent val for <a class~~=~~"wiki_link" href~~=~~"/The%20Archipelago#Rank tree temperaments">greenland</a>~~ and ~~<a class~~=~~"wiki_link" href~~=~~"/The%20Archipelago#Rank tree temperaments">baffin</a> temperaments~~, and ~~for~~ the ~~rank five temperament temperament tempering out 676/675. The non-patent val &lt;940 1491 2184 2638 3254 3481| gives a tuning almost identical~~ to the ~~POTE tuning for~~ the 13-limit ~~<a class="wiki_link" href="/Hemifamity%20family#Pele">pele temperament</a> tempering out 196/195, 352/351 and 364/363~~.~~</body></html></pre></div>~~

=== Odd harmonics ===

=== Subsets and supersets ===

Since 940 factors into {{factorization|940}}, 940edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 47, 94, 188, 235, 470 }}, of which 94edo is notable.

[[1880edo]], which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit.

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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>2011-11-12 03:27:54 UTC</tt>.<br>
-: The original revision id was <tt>274576932</tt>.<br>
+edo is [[consistency|distinctly consistent]] through the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675.
-: 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 non-patent val {{val| 940 1491 2184 2638 3254 3481 }} gives a tuning almost identical to the [[POTE tuning]] for the 13-limit [[pele]] temperament, tempering out 196/195, 352/351 and 364/363.
-<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 //940 equal division// divides the octave into 940 equal parts of 1.277 cents each. It is uniquely [[consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it supports [[Breedsmic temperaments#Decoid|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The Archipelago#Rank tree temperaments|greenland]] and [[The Archipelago#Rank tree temperaments|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675. The non-patent val &lt;940 1491 2184 2638 3254 3481| gives a tuning almost identical to the POTE tuning for the 13-limit [[Hemifamity family#Pele|pele temperament]] tempering out 196/195, 352/351 and 364/363.</pre></div>
+In higher limits, it is a satisfactory no-13's 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to it where it has good 3/2 and 5/4, but 15/8 is one step off from the closest location.
-<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;940edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;940 equal division&lt;/em&gt; divides the octave into 940 equal parts of 1.277 cents each. It is uniquely &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt; through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it supports &lt;a class="wiki_link" href="/Breedsmic%20temperaments#Decoid"&gt;decoid temperament&lt;/a&gt; and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 13-limit decoid. It also gives the optimal patent val for &lt;a class="wiki_link" href="/The%20Archipelago#Rank tree temperaments"&gt;greenland&lt;/a&gt; and &lt;a class="wiki_link" href="/The%20Archipelago#Rank tree temperaments"&gt;baffin&lt;/a&gt; temperaments, and for the rank five temperament temperament tempering out 676/675. The non-patent val &amp;lt;940 1491 2184 2638 3254 3481| gives a tuning almost identical to the POTE tuning for the 13-limit &lt;a class="wiki_link" href="/Hemifamity%20family#Pele"&gt;pele temperament&lt;/a&gt; tempering out 196/195, 352/351 and 364/363.&lt;/body&gt;&lt;/html&gt;</pre></div>
+=== Odd harmonics ===
+{{Harmonics in equal|940}}
+=== Subsets and supersets ===
+Since 940 factors into {{factorization|940}}, 940edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 47, 94, 188, 235, 470 }}, of which 94edo is notable.
+[[1880edo]], which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit.