Orwell: 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:<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-~~16 03~~:21:51 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-20 11:40:46 UTC</tt>.<br>

: The original revision id was <tt>~~302293460~~</tt>.<br>

: The original revision id was <tt>303362416</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>

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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 [[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#Orwell-13-limit|tridecimal orwell]], and by adding instead 66/65, [[Semicomma family#Winston|winston temperament]].

==Interval chain==

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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%20chords">keenanismic tetrads</a> and the <a class="wiki_link" href="/swetismic%20chords">swetismic chords</a>.<br />

<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 />

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#Orwell-13-limit">tridecimal orwell</a>, and by adding instead 66/65, <a class="wiki_link" href="/Semicomma%20family#Winston">winston temperament</a>.<br />

<br />

<h2 id="toc1"><a name="Properties-Interval chain"></a>Interval chain</h2>

@@ 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>2012-02-16 03:21:51 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-20 11:40:46 UTC</tt>.<br>
-: The original revision id was <tt>302293460</tt>.<br>
+: The original revision id was <tt>303362416</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 12: / Line 12: @@
 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#Orwell-13-limit|tridecimal orwell]], and by adding instead 66/65, [[Semicomma family#Winston|winston temperament]].
 ==Interval chain==
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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 &lt;a class="wiki_link" href="/orwell%20tetrad"&gt;orwell tetrad&lt;/a&gt; 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 &lt;a class="wiki_link" href="/keenanismic%20chords"&gt;keenanismic tetrads&lt;/a&gt; and the &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-Compatible equal temperaments include &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, and &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;. Orwell is in better tune in lower limits than higher ones; the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; is &lt;a class="wiki_link" href="/296edo"&gt;296edo&lt;/a&gt; in the 5-limit, &lt;a class="wiki_link" href="/137edo"&gt;137edo&lt;/a&gt; in the 7-limit, and &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; in the 11-limit. It tempers out the semicomma in the 5-limit, and so belongs to the &lt;a class="wiki_link" href="/semicomma%20family"&gt;semicomma family&lt;/a&gt;. 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 &lt;a class="wiki_link" href="/Semicomma%20family#Julia"&gt;julia temperament&lt;/a&gt;, and by adding instead 66/65, &lt;a class="wiki_link" href="/Semicomma%20family#Winston"&gt;winston temperament&lt;/a&gt;.&lt;br /&gt;
+Compatible equal temperaments include &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, and &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;. Orwell is in better tune in lower limits than higher ones; the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; is &lt;a class="wiki_link" href="/296edo"&gt;296edo&lt;/a&gt; in the 5-limit, &lt;a class="wiki_link" href="/137edo"&gt;137edo&lt;/a&gt; in the 7-limit, and &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; in the 11-limit. It tempers out the semicomma in the 5-limit, and so belongs to the &lt;a class="wiki_link" href="/semicomma%20family"&gt;semicomma family&lt;/a&gt;. 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 &lt;a class="wiki_link" href="/Semicomma%20family#Orwell-13-limit"&gt;tridecimal orwell&lt;/a&gt;, and by adding instead 66/65, &lt;a class="wiki_link" href="/Semicomma%20family#Winston"&gt;winston temperament&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Properties-Interval chain"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Interval chain&lt;/h2&gt;