76edo: Difference between revisions

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**Imported revision 596770372 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The ''76 equal division'' 5-limit patent val is [[contorted|contorted]] in the 5-limit, reflecting the fact that 76 = 4 * 19. In the 7-limit it tempers out 2401/2400 as well as 81/80, and so supports [[Meantone_family#Squares|squares temperament]]. In the 11-limit, it tempers out 245/242 and 385/384, and supports the 24&amp;26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[Pelogic_family|hornbostel temperament]] POTE fifth, whereas its sharp fifth, 45\76, makes for an excellent [[Archytas_clan#Superpyth|superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-10-24 22:07:12 UTC</tt>.<br>
: The original revision id was <tt>596770372</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>
<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 //76 equal division// 5-limit patent val is [[contorted]] in the 5-limit, reflecting the fact that 76 = 4 * 19. In the 7-limit it tempers out 2401/2400 as well as 81/80, and so supports [[Meantone family#Squares|squares temperament]]. In the 11-limit, it tempers out 245/242 and 385/384, and supports the 24&amp;26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the [[Pelogic family|hornbostel temperament]] POTE fifth, whereas its sharp fifth, 45\76, makes for an excellent [[Archytas clan#Superpyth|superpyth]] fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.


Using non-patent vals, 76edo provides an excellent tuning for [[teff]] temperament, a low complexity, medium accuracy, and high limit (17 or 19) temperament.</pre></div>
Using non-patent vals, 76edo provides an excellent tuning for [[Teff|teff]] temperament, a low complexity, medium accuracy, and high limit (17 or 19) temperament.
<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;76edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;76 equal division&lt;/em&gt; 5-limit patent val is &lt;a class="wiki_link" href="/contorted"&gt;contorted&lt;/a&gt; in the 5-limit, reflecting the fact that 76 = 4 * 19. In the 7-limit it tempers out 2401/2400 as well as 81/80, and so supports &lt;a class="wiki_link" href="/Meantone%20family#Squares"&gt;squares temperament&lt;/a&gt;. In the 11-limit, it tempers out 245/242 and 385/384, and supports the 24&amp;amp;26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the &lt;a class="wiki_link" href="/Pelogic%20family"&gt;hornbostel temperament&lt;/a&gt; POTE fifth, whereas its sharp fifth, 45\76, makes for an excellent &lt;a class="wiki_link" href="/Archytas%20clan#Superpyth"&gt;superpyth&lt;/a&gt; fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.&lt;br /&gt;
&lt;br /&gt;
Using non-patent vals, 76edo provides an excellent tuning for &lt;a class="wiki_link" href="/teff"&gt;teff&lt;/a&gt; temperament, a low complexity, medium accuracy, and high limit (17 or 19) temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>