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:~~Kosmorsky~~|~~Kosmorsky~~]] and made on <tt>~~2011~~-12-~~22 16~~:27:47 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-13 04:03:16 UTC</tt>.<br>

: The original revision id was <tt>~~288211894~~</tt>.<br>

: The original revision id was <tt>291900617</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>

<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">[[toc|flat]]

=Properties=

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 limit children-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]].

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, 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]].

==Interval chain==

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<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Orwell</title></head><body><a href="#Properties">Properties</a> | <a href="#MOSes">MOSes</a> | <a href="#Chords of orwell">Chords of orwell</a> | <a href="#MOS transversals">MOS transversals</a> | <a href="#Music">Music</a> | <a href="#Keyboards">Keyboards</a> | <a href="#toc9"></a>

<h1 id="toc0"><a name="Properties"></a>Properties</h1>

<br />

Orwell — 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 />

<h1 id="toc0"><a name="Properties"></a>Properties</h1>

<a class="wiki_link" href="/Semicomma%20family#Seven limit children-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 />

<br />

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%20tetrads">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, 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 />

<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:Kosmorsky|Kosmorsky]] and made on <tt>2011-12-22 16:27:47 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-13 04:03:16 UTC</tt>.<br>
-: The original revision id was <tt>288211894</tt>.<br>
+: The original revision id was <tt>291900617</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>
 <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">[[toc|flat]]
 =Properties=
-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 limit children-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]].
-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, 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]].
 ==Interval chain==
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 <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Orwell&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:20:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;a href="#Properties"&gt;Properties&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt; | &lt;a href="#MOSes"&gt;MOSes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Chords of orwell"&gt;Chords of orwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#MOS transversals"&gt;MOS transversals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Keyboards"&gt;Keyboards&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#toc9"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Properties&lt;/h1&gt;
+&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;br /&gt;
-  Orwell — so named because 19 steps of &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;, 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 &amp;quot;perfect twelfth&amp;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 &lt;a class="wiki_link" href="/Semicomma%20family"&gt;Semicomma family&lt;/a&gt;. Alternately, the &amp;quot;fifth harmonic&amp;quot; 5/1 divided into 3 equal steps also makes a good orwell generator, being ~12/7.&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Properties&lt;/h1&gt;
+  &lt;a class="wiki_link" href="/Semicomma%20family#Seven limit children-Orwell"&gt;Orwell&lt;/a&gt; — so named because 19 steps of &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;, 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 &amp;quot;perfect twelfth&amp;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 &lt;a class="wiki_link" href="/Semicomma%20family"&gt;Semicomma family&lt;/a&gt;. Alternately, the &amp;quot;fifth harmonic&amp;quot; 5/1 divided into 3 equal steps also makes a good orwell generator, being ~12/7.&lt;br /&gt;
 &lt;br /&gt;
 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%20tetrads"&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, 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#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;
 &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;