84edo: Difference between revisions

Line 1:

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

''84edo'' divides the [[Octave|octave]] into 84 equal parts of size 14.286 [[cent|cent]]s each and it is the highest edo where the size of 3 has a common factor with its cardinality. It makes for an excellent orwell tuning and also a good one for compton, and the 84e val, <84 133 195 236 290|, is almost identical to the 11-limit POTE tuning for orwell. In the [[13-limit|13-limit]] it is the [[Optimal_patent_val|optimal patent val]] for the rank five temperament tempering out 144/143.

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

~~: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-11-01 18:13:58 UTC</tt>. ~~

~~: The original revision id was <tt>597691574</tt>. ~~

~~: The revision comment was: <tt>removed tel links</tt> ~~

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

~~<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">//84edo// divides the [[octave]] into 84 equal parts of size 14.286 [[cent]]s each and it is the highest edo where the size of 3 has a common factor with its cardinality. It makes for an excellent orwell tuning and also a good one for compton, and the 84e val, <84 133 195 236 290|, is almost identical to the 11-limit POTE tuning for orwell. In the [[13-limit]] it is the [[optimal patent val]] for the rank five temperament tempering out 144/143.

[[5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152

[[5-limit|5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152

[[7-limit]] commas: 225/224, 1728/1715, 2430/2401, 6144/6125

[[7-limit|7-limit]] commas: 225/224, 1728/1715, 2430/2401, 6144/6125

[[11-limit|11-limit]] commas: 441/440, 1344/1331, 1375/1372

~~[[11-limit]] commas: 441/440, 1344/1331, 1375/1372~~

84e: 99/98, 121/120, 176/175, 385/384, 540/539, 5632/5625

[[13-limit]] commas: 144/143, 351/350, 364/363, 625/625

[[13-limit|13-limit]] commas: 144/143, 351/350, 364/363, 625/625

84e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000

==Music==

'''''Ten''''' by John Cage, 1991, for chamber ensemble. [http://youtu.be/PE_2Ds_6qGk Ives Ensemble] recording (YouTube).

'''''Two4''''' by John Cage, 1991, for violin and piano or shō. [http://youtu.be/sLOrpd5onCs Harr & Miyata] recording (YouTube).

'''''Two5''''' by John Cage, 1991, for tenor trombone and piano. [http://youtu.be/YOtQZIqfY1w Fulkerson & Denyer] recording (YouTube).

~~//<~~span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"~~>**Ten**<~~/span~~>//<~~span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"~~>~~ by John Cage, ~~1991~~, for ~~chamber ensemble~~. [[@http://youtu.be/~~PE_2Ds_6qGk|Ives Ensemble]]~~ &~~lt;/span&gt~~;recording (YouTube).

'''''Two6''''' by John Cage, 1992, for violin and piano. [http://youtu.be/XkX37zH6AbU Haar & Snijders] recording (YouTube).

//**Two4**// by John Cage, 1991, for violin and piano or shō. [[~~@http~~:~~//youtu.be/sLOrpd5onCs|Harr & Miyata~~]] ~~recording (YouTube).~~

[[Category:compton]]

//**Two5**// by John Cage, 1991, for tenor trombone and piano. [[~~@http~~:~~//youtu.be/YOtQZIqfY1w|Fulkerson & Denyer~~]] ~~recording (YouTube).~~

[[Category:edo]]

//**Two6**// by John Cage, 1992, for violin and piano. [[~~@http~~:~~//youtu.be/XkX37zH6AbU|Haar & Snijders~~]] ~~recording (YouTube).</pre></div>~~

[[Category:john_cage]]

~~<h4>Original HTML content~~:~~</h4>~~

[[Category:listen]]

~~<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>84edo</title></head><body>84edo divides the <a class="wiki_link" href="/octave">octave</a> into 84 equal parts of size 14.286 <a class="wiki_link" href="/cent">cent</a>s each and it is the highest edo where the size of 3 has a common factor with its cardinality. It makes for an excellent orwell tuning and also a good one for compton, and the 84e val, &lt;84 133 195 236 290|, is almost identical to the 11-limit POTE tuning for orwell. In the <a class="wiki_link" href="/13-limit">13-limit</a> it is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank five temperament tempering out 144/143.

[[Category:orwell]]

~~ ~~

~~<a class="wiki_link" href="/5-limit">5-limit</a> commas: 78732/78125, 531441/524288, 2109375/2097152 ~~

~~ ~~

~~<a class="wiki_link" href="/7-limit">7-limit</a> commas: 225/224, 1728/1715, 2430/2401, 6144/6125 ~~

~~ ~~

~~<a class="wiki_link" href="/11-limit">11-limit</a> commas: 441/440, 1344/1331, 1375/1372 ~~

~~84e: 99/98, 121/120, 176/175, 385/384, 540/539, 5632/5625 ~~

~~ ~~

~~<a class="wiki_link" href="/13-limit">13-limit</a> commas: 144/143, 351/350, 364/363, 625/625 ~~

~~84e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000 ~~

~~ ~~

~~<h2 id="toc0"><a name="x-Music"></a>Music</h2>~~

~~ ~~

Ten by John Cage, 1991, for chamber ensemble. <a class="wiki_link_ext" href="http://youtu.be/PE_2Ds_6qGk" rel="nofollow" target="_blank">Ives Ensemble</a> recording (YouTube).

Two4 by John Cage, 1991, for violin and piano or shō. <a class="wiki_link_ext" href="http://youtu.be/sLOrpd5onCs" rel="nofollow" target="_blank">Harr &amp; Miyata</a> recording (YouTube).

Two5 by John Cage, 1991, for tenor trombone and piano. <a class="wiki_link_ext" href="http://youtu.be/YOtQZIqfY1w" rel="nofollow" target="_blank">Fulkerson &amp; Denyer</a> recording (YouTube).

Two6 by John Cage, 1992, for violin and piano. <a class="wiki_link_ext" href="http://youtu.be/XkX37zH6AbU" rel="nofollow" target="_blank">Haar &amp; Snijders</a> recording (YouTube).</body></html></pre></div>

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+''84edo'' divides the [[Octave|octave]] into 84 equal parts of size 14.286 [[cent|cent]]s each and it is the highest edo where the size of 3 has a common factor with its cardinality. It makes for an excellent orwell tuning and also a good one for compton, and the 84e val, &lt;84 133 195 236 290|, is almost identical to the 11-limit POTE tuning for orwell. In the [[13-limit|13-limit]] it is the [[Optimal_patent_val|optimal patent val]] for the rank five temperament tempering out 144/143.
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-11-01 18:13:58 UTC</tt>.<br>
-: The original revision id was <tt>597691574</tt>.<br>
-: The revision comment was: <tt>removed tel links</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">//84edo// divides the [[octave]] into 84 equal parts of size 14.286 [[cent]]s each and it is the highest edo where the size of 3 has a common factor with its cardinality. It makes for an excellent orwell tuning and also a good one for compton, and the 84e val, &lt;84 133 195 236 290|, is almost identical to the 11-limit POTE tuning for orwell. In the [[13-limit]] it is the [[optimal patent val]] for the rank five temperament tempering out 144/143.
-[[5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152
+[[5-limit|5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152
-[[7-limit]] commas: 225/224, 1728/1715, 2430/2401, 6144/6125
+[[7-limit|7-limit]] commas: 225/224, 1728/1715, 2430/2401, 6144/6125
+[[11-limit|11-limit]] commas: 441/440, 1344/1331, 1375/1372
-[[11-limit]] commas: 441/440, 1344/1331, 1375/1372
 e: 99/98, 121/120, 176/175, 385/384, 540/539, 5632/5625
-[[13-limit]] commas: 144/143, 351/350, 364/363, 625/625
+[[13-limit|13-limit]] commas: 144/143, 351/350, 364/363, 625/625
 e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000
 ==Music==
+''<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;">'''Ten'''</span>''<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"> by John Cage, 1991, for chamber ensemble. [http://youtu.be/PE_2Ds_6qGk Ives Ensemble] </span>recording (YouTube).
+''<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;">'''Two4'''</span>''<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"> by John Cage, 1991, for violin and piano or shō. [http://youtu.be/sLOrpd5onCs Harr &amp; Miyata] recording (YouTube).</span>
+''<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;">'''Two5'''</span>''<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"> by John Cage, 1991, for tenor trombone and piano. [http://youtu.be/YOtQZIqfY1w Fulkerson &amp; Denyer] recording (YouTube).</span>
-//&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt;**Ten**&lt;/span&gt;//&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt; by John Cage, 1991, for chamber ensemble. [[@http://youtu.be/PE_2Ds_6qGk|Ives Ensemble]] &lt;/span&gt;recording (YouTube).
+''<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;">'''Two6'''</span>''<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"> by John Cage, 1992, for violin and piano. </span>[http://youtu.be/XkX37zH6AbU Haar &amp; Snijders] recording (YouTube).
-//&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt;**Two4**&lt;/span&gt;//&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt; by John Cage, 1991, for violin and piano or shō. [[@http://youtu.be/sLOrpd5onCs|Harr &amp; Miyata]] recording (YouTube).&lt;/span&gt;
+[[Category:compton]]
-//&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt;**Two5**&lt;/span&gt;//&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt; by John Cage, 1991, for tenor trombone and piano. [[@http://youtu.be/YOtQZIqfY1w|Fulkerson &amp; Denyer]] recording (YouTube).&lt;/span&gt;
+[[Category:edo]]
-//&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt;**Two6**&lt;/span&gt;//&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt; by John Cage, 1992, for violin and piano. &lt;/span&gt;[[@http://youtu.be/XkX37zH6AbU|Haar &amp; Snijders]] recording (YouTube).</pre></div>
+[[Category:john_cage]]
-<h4>Original HTML content:</h4>
+[[Category:listen]]
-<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;84edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;84edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 84 equal parts of size 14.286 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each and it is the highest edo where the size of 3 has a common factor with its cardinality. It makes for an excellent orwell tuning and also a good one for compton, and the 84e val, &amp;lt;84 133 195 236 290|, is almost identical to the 11-limit POTE tuning for orwell. In the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; it is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the rank five temperament tempering out 144/143.&lt;br /&gt;
+[[Category:orwell]]
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; commas: 78732/78125, 531441/524288, 2109375/2097152&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; commas: 225/224, 1728/1715, 2430/2401, 6144/6125&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; commas: 441/440, 1344/1331, 1375/1372&lt;br /&gt;
-e: 99/98, 121/120, 176/175, 385/384, 540/539, 5632/5625&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; commas: 144/143, 351/350, 364/363, 625/625&lt;br /&gt;
-e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h2&gt;
- &lt;br /&gt;
-&lt;em&gt;&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt;&lt;strong&gt;Ten&lt;/strong&gt;&lt;/span&gt;&lt;/em&gt;&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt; by John Cage, 1991, for chamber ensemble. &lt;a class="wiki_link_ext" href="http://youtu.be/PE_2Ds_6qGk" rel="nofollow" target="_blank"&gt;Ives Ensemble&lt;/a&gt; &lt;/span&gt;recording (YouTube).&lt;br /&gt;
-&lt;em&gt;&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt;&lt;strong&gt;Two4&lt;/strong&gt;&lt;/span&gt;&lt;/em&gt;&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt; by John Cage, 1991, for violin and piano or shō. &lt;a class="wiki_link_ext" href="http://youtu.be/sLOrpd5onCs" rel="nofollow" target="_blank"&gt;Harr &amp;amp; Miyata&lt;/a&gt; recording (YouTube).&lt;/span&gt;&lt;br /&gt;
-&lt;em&gt;&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt;&lt;strong&gt;Two5&lt;/strong&gt;&lt;/span&gt;&lt;/em&gt;&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt; by John Cage, 1991, for tenor trombone and piano. &lt;a class="wiki_link_ext" href="http://youtu.be/YOtQZIqfY1w" rel="nofollow" target="_blank"&gt;Fulkerson &amp;amp; Denyer&lt;/a&gt; recording (YouTube).&lt;/span&gt;&lt;br /&gt;
-&lt;em&gt;&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt;&lt;strong&gt;Two6&lt;/strong&gt;&lt;/span&gt;&lt;/em&gt;&lt;span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"&gt; by John Cage, 1992, for violin and piano. &lt;/span&gt;&lt;a class="wiki_link_ext" href="http://youtu.be/XkX37zH6AbU" rel="nofollow" target="_blank"&gt;Haar &amp;amp; Snijders&lt;/a&gt; recording (YouTube).&lt;/body&gt;&lt;/html&gt;</pre></div>