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| <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:<br>
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| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-11-01 18:13:58 UTC</tt>.<br>
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| : The original revision id was <tt>597691574</tt>.<br>
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| : The revision comment was: <tt>removed tel links</tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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.
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| [[5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152 | | [[5-limit|5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152 |
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| [[7-limit]] commas: 225/224, 1728/1715, 2430/2401, 6144/6125 | | [[7-limit|7-limit]] commas: 225/224, 1728/1715, 2430/2401, 6144/6125 |
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| | [[11-limit|11-limit]] commas: 441/440, 1344/1331, 1375/1372 |
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| [[11-limit]] commas: 441/440, 1344/1331, 1375/1372
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| 84e: 99/98, 121/120, 176/175, 385/384, 540/539, 5632/5625 | | 84e: 99/98, 121/120, 176/175, 385/384, 540/539, 5632/5625 |
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| [[13-limit]] commas: 144/143, 351/350, 364/363, 625/625 | | [[13-limit|13-limit]] commas: 144/143, 351/350, 364/363, 625/625 |
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| 84e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000 | | 84e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000 |
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| ==Music== | | ==Music== |
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| | ''<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). |
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| | ''<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 & Miyata] recording (YouTube).</span> |
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| | ''<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 & Denyer] recording (YouTube).</span> |
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| //<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;">'''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 & Snijders] 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 & Miyata]] recording (YouTube).</span>
| | [[Category:compton]] |
| //<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 & Denyer]] recording (YouTube).</span>
| | [[Category:edo]] |
| //<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 & 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><em>84edo</em> 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.<br />
| | [[Category:orwell]] |
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| <a class="wiki_link" href="/5-limit">5-limit</a> commas: 78732/78125, 531441/524288, 2109375/2097152<br />
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| <a class="wiki_link" href="/7-limit">7-limit</a> commas: 225/224, 1728/1715, 2430/2401, 6144/6125<br />
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| <a class="wiki_link" href="/11-limit">11-limit</a> commas: 441/440, 1344/1331, 1375/1372<br />
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| 84e: 99/98, 121/120, 176/175, 385/384, 540/539, 5632/5625<br />
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| <br />
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| <a class="wiki_link" href="/13-limit">13-limit</a> commas: 144/143, 351/350, 364/363, 625/625<br />
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| 84e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Music"></a><!-- ws:end:WikiTextHeadingRule:0 -->Music</h2>
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| <br />
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| <em><span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"><strong>Ten</strong></span></em><span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"> 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> </span>recording (YouTube).<br />
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| <em><span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"><strong>Two4</strong></span></em><span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"> 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).</span><br />
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| <em><span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"><strong>Two5</strong></span></em><span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"> 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).</span><br />
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| <em><span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"><strong>Two6</strong></span></em><span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 14px;"> by John Cage, 1992, for violin and piano. </span><a class="wiki_link_ext" href="http://youtu.be/XkX37zH6AbU" rel="nofollow" target="_blank">Haar &amp; Snijders</a> recording (YouTube).</body></html></pre></div>
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84edo divides the octave into 84 equal parts of size 14.286 cents 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
7-limit commas: 225/224, 1728/1715, 2430/2401, 6144/6125
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
84e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000
Music
Ten by John Cage, 1991, for chamber ensemble. Ives Ensemble recording (YouTube).
Two4 by John Cage, 1991, for violin and piano or shō. Harr & Miyata recording (YouTube).
Two5 by John Cage, 1991, for tenor trombone and piano. Fulkerson & Denyer recording (YouTube).
Two6 by John Cage, 1992, for violin and piano. Haar & Snijders recording (YouTube).