36edo: 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:

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-23 08:40:11 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-23 09:09:17 UTC</tt>.

: The original revision id was <tt>~~213150844~~</tt>.

: The original revision id was <tt>213160270</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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36 tempers out, like 12, 81/80, 128/125 and 648/625 in the 5-limit. It departs from 12 in the 7-limit, tempering out 686/675, and as a no-fives temperament, 1029/1024 and 118098/117649. In the 11-limit, it tempers out 56/55, 245/242 and 540/539, and is the [[optimal patent val]] for the rank four temperament tempering out 56/55, as well as the rank three temperament [[Didymus rank three family|melpomene]] tempering out 81/80 and 56/55. In the 13-limit, it tempers out 78/77, in the 17-limit 51/50, and in the 19-limit 76/75, 91/90 and 96/95.

As a 5-limit temperament, the patent val for 36edo is [[Wedgies and Multivals|contorted]], meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals.

A curious alternative val for the 5-limit is <36 65 116| which is not contorted. It is also a meantone val, in the sense that 81/80 is tempered out. However, the "comma" |29 0 -9> is also tempered out, and the "fifth", 29\36, is actually approximately 7/4, whereas the "major third", 44\36, is actually approximately 7/3. Any 5-limit musical piece or scale which is a [[transversal]] for a meantone piece or scale will be converted to a no-fives piece tempering out 1029/1024 in place of 81/80.

Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale.

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36 tempers out, like 12, 81/80, 128/125 and 648/625 in the 5-limit. It departs from 12 in the 7-limit, tempering out 686/675, and as a no-fives temperament, 1029/1024 and 118098/117649. In the 11-limit, it tempers out 56/55, 245/242 and 540/539, and is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank four temperament tempering out 56/55, as well as the rank three temperament <a class="wiki_link" href="/Didymus%20rank%20three%20family">melpomene</a> tempering out 81/80 and 56/55. In the 13-limit, it tempers out 78/77, in the 17-limit 51/50, and in the 19-limit 76/75, 91/90 and 96/95.

As a 5-limit temperament, the patent val for 36edo is <a class="wiki_link" href="/Wedgies%20and%20Multivals">contorted</a>, meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals.

A curious alternative val for the 5-limit is &lt;36 65 116| which is not contorted. It is also a meantone val, in the sense that 81/80 is tempered out. However, the &quot;comma&quot; |29 0 -9&gt; is also tempered out, and the &quot;fifth&quot;, 29\36, is actually approximately 7/4, whereas the &quot;major third&quot;, 44\36, is actually approximately 7/3. Any 5-limit musical piece or scale which is a <a class="wiki_link" href="/transversal">transversal</a> for a meantone piece or scale will be converted to a no-fives piece tempering out 1029/1024 in place of 81/80.

Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale.

@@ Line 1: / Line 1: @@
 <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>2011-03-23 08:40:11 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-23 09:09:17 UTC</tt>.<br>
-: The original revision id was <tt>213150844</tt>.<br>
+: The original revision id was <tt>213160270</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>
@@ Line 17: / Line 17: @@
 tempers out, like 12, 81/80, 128/125 and 648/625 in the 5-limit. It departs from 12 in the 7-limit, tempering out 686/675, and as a no-fives temperament, 1029/1024 and 118098/117649. In the 11-limit, it tempers out 56/55, 245/242 and 540/539, and is the [[optimal patent val]] for the rank four temperament tempering out 56/55, as well as the rank three temperament [[Didymus rank three family|melpomene]] tempering out 81/80 and 56/55. In the 13-limit, it tempers out 78/77, in the 17-limit 51/50, and in the 19-limit 76/75, 91/90 and 96/95.
+As a 5-limit temperament, the patent val for 36edo is [[Wedgies and Multivals|contorted]], meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals.
+A curious alternative val for the 5-limit is &lt;36 65 116| which is not contorted. It is also a meantone val, in the sense that 81/80 is tempered out. However, the "comma" |29 0 -9&gt; is also tempered out, and the "fifth", 29\36, is actually approximately 7/4, whereas the "major third", 44\36, is actually approximately 7/3. Any 5-limit musical piece or scale which is a [[transversal]] for a meantone piece or scale will be converted to a no-fives piece tempering out 1029/1024 in place of 81/80.
 Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale.
@@ Line 67: / Line 70: @@
 &lt;br /&gt;
 tempers out, like 12, 81/80, 128/125 and 648/625 in the 5-limit. It departs from 12 in the 7-limit, tempering out 686/675, and as a no-fives temperament, 1029/1024 and 118098/117649. In the 11-limit, it tempers out 56/55, 245/242 and 540/539, and is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the rank four temperament tempering out 56/55, as well as the rank three temperament &lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;melpomene&lt;/a&gt; tempering out 81/80 and 56/55. In the 13-limit, it tempers out 78/77, in the 17-limit 51/50, and in the 19-limit 76/75, 91/90 and 96/95.&lt;br /&gt;
+&lt;br /&gt;
+As a 5-limit temperament, the patent val for 36edo is &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;contorted&lt;/a&gt;, meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals.&lt;br /&gt;
+A curious alternative val for the 5-limit is &amp;lt;36 65 116| which is not contorted. It is also a meantone val, in the sense that 81/80 is tempered out. However, the &amp;quot;comma&amp;quot; |29 0 -9&amp;gt; is also tempered out, and the &amp;quot;fifth&amp;quot;, 29\36, is actually approximately 7/4, whereas the &amp;quot;major third&amp;quot;, 44\36, is actually approximately 7/3. Any 5-limit musical piece or scale which is a &lt;a class="wiki_link" href="/transversal"&gt;transversal&lt;/a&gt; for a meantone piece or scale will be converted to a no-fives piece tempering out 1029/1024 in place of 81/80. &lt;br /&gt;
 &lt;br /&gt;
 Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale.&lt;br /&gt;