Orwell: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 302258912 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 302293460 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-16 03:21:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>302293460</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> | 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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[[Semicomma family#Seven%20limit%20children-Orwell|Orwell]] — so named because 19 steps of [[84edo]], or 19\84, is a possible generator — is an excellent 7-limit temperament and an amazing (because of the low complexity of 11) 11-limit temperament. The "perfect twelfth" 3/1 is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. It's a member of the [[Semicomma family]]. Alternately, the "fifth harmonic" 5/1 divided into 3 equal steps also makes a good orwell generator, being ~12/7. | [[Semicomma family#Seven%20limit%20children-Orwell|Orwell]] — so named because 19 steps of [[84edo]], or 19\84, is a possible generator — is an excellent 7-limit temperament and an amazing (because of the low complexity of 11) 11-limit temperament. The "perfect twelfth" 3/1 is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. It's a member of the [[Semicomma family]]. Alternately, the "fifth harmonic" 5/1 divided into 3 equal steps also makes a good orwell generator, being ~12/7. | ||
In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the [[orwell tetrad]] 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the [[keenanismic tetrads]] and the [[swetismic chords]]. | In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the [[orwell tetrad]] 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the [[keenanismic chords|keenanismic tetrads]] and the [[swetismic chords]]. | ||
Compatible equal temperaments include [[22edo]], [[31edo]], [[53edo]], and [[84edo]]. Orwell is in better tune in lower limits than higher ones; the [[optimal patent val]] is [[296edo]] in the 5-limit, [[137edo]] in the 7-limit, and [[53edo]] in the 11-limit. It tempers out the semicomma in the 5-limit, and so belongs to the [[semicomma family]]. In the 7-limit it tempers out 225/224, 1728/1715, 2430/2401 and 6144/6125 in the 7-limit, and 99/98, 121/120, 176/175, 385/384 and 540/539 in the 11-limit. By adding 275/273 to the list of commas it can be extended to the 13-limit as [[Semicomma family#Julia|julia temperament]], and by adding instead 66/65, [[Semicomma family#Winston|winston temperament]]. | Compatible equal temperaments include [[22edo]], [[31edo]], [[53edo]], and [[84edo]]. Orwell is in better tune in lower limits than higher ones; the [[optimal patent val]] is [[296edo]] in the 5-limit, [[137edo]] in the 7-limit, and [[53edo]] in the 11-limit. It tempers out the semicomma in the 5-limit, and so belongs to the [[semicomma family]]. In the 7-limit it tempers out 225/224, 1728/1715, 2430/2401 and 6144/6125 in the 7-limit, and 99/98, 121/120, 176/175, 385/384 and 540/539 in the 11-limit. By adding 275/273 to the list of commas it can be extended to the 13-limit as [[Semicomma family#Julia|julia temperament]], and by adding instead 66/65, [[Semicomma family#Winston|winston temperament]]. | ||
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<a class="wiki_link" href="/Semicomma%20family#Seven%20limit%20children-Orwell">Orwell</a> — so named because 19 steps of <a class="wiki_link" href="/84edo">84edo</a>, or 19\84, is a possible generator — is an excellent 7-limit temperament and an amazing (because of the low complexity of 11) 11-limit temperament. The &quot;perfect twelfth&quot; 3/1 is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. It's a member of the <a class="wiki_link" href="/Semicomma%20family">Semicomma family</a>. Alternately, the &quot;fifth harmonic&quot; 5/1 divided into 3 equal steps also makes a good orwell generator, being ~12/7.<br /> | <a class="wiki_link" href="/Semicomma%20family#Seven%20limit%20children-Orwell">Orwell</a> — so named because 19 steps of <a class="wiki_link" href="/84edo">84edo</a>, or 19\84, is a possible generator — is an excellent 7-limit temperament and an amazing (because of the low complexity of 11) 11-limit temperament. The &quot;perfect twelfth&quot; 3/1 is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. It's a member of the <a class="wiki_link" href="/Semicomma%20family">Semicomma family</a>. Alternately, the &quot;fifth harmonic&quot; 5/1 divided into 3 equal steps also makes a good orwell generator, being ~12/7.<br /> | ||
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In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the <a class="wiki_link" href="/orwell%20tetrad">orwell tetrad</a> 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the <a class="wiki_link" href="/keenanismic% | In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the <a class="wiki_link" href="/orwell%20tetrad">orwell tetrad</a> 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the <a class="wiki_link" href="/keenanismic%20chords">keenanismic tetrads</a> and the <a class="wiki_link" href="/swetismic%20chords">swetismic chords</a>.<br /> | ||
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Compatible equal temperaments include <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/53edo">53edo</a>, and <a class="wiki_link" href="/84edo">84edo</a>. Orwell is in better tune in lower limits than higher ones; the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> is <a class="wiki_link" href="/296edo">296edo</a> in the 5-limit, <a class="wiki_link" href="/137edo">137edo</a> in the 7-limit, and <a class="wiki_link" href="/53edo">53edo</a> in the 11-limit. It tempers out the semicomma in the 5-limit, and so belongs to the <a class="wiki_link" href="/semicomma%20family">semicomma family</a>. In the 7-limit it tempers out 225/224, 1728/1715, 2430/2401 and 6144/6125 in the 7-limit, and 99/98, 121/120, 176/175, 385/384 and 540/539 in the 11-limit. By adding 275/273 to the list of commas it can be extended to the 13-limit as <a class="wiki_link" href="/Semicomma%20family#Julia">julia temperament</a>, and by adding instead 66/65, <a class="wiki_link" href="/Semicomma%20family#Winston">winston temperament</a>.<br /> | Compatible equal temperaments include <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/53edo">53edo</a>, and <a class="wiki_link" href="/84edo">84edo</a>. Orwell is in better tune in lower limits than higher ones; the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> is <a class="wiki_link" href="/296edo">296edo</a> in the 5-limit, <a class="wiki_link" href="/137edo">137edo</a> in the 7-limit, and <a class="wiki_link" href="/53edo">53edo</a> in the 11-limit. It tempers out the semicomma in the 5-limit, and so belongs to the <a class="wiki_link" href="/semicomma%20family">semicomma family</a>. In the 7-limit it tempers out 225/224, 1728/1715, 2430/2401 and 6144/6125 in the 7-limit, and 99/98, 121/120, 176/175, 385/384 and 540/539 in the 11-limit. By adding 275/273 to the list of commas it can be extended to the 13-limit as <a class="wiki_link" href="/Semicomma%20family#Julia">julia temperament</a>, and by adding instead 66/65, <a class="wiki_link" href="/Semicomma%20family#Winston">winston temperament</a>.<br /> | ||