Orwell tetrad: Difference between revisions

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: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2015-03-23 02:38:07 UTC</tt>.<br>

<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">The **orwell tetrad** is a four-note chord which in close position (reduced to the octave) consists of a chain of three subminor thirds, thirds of approximately [[7_6|7/6]] in size, and a major third, of approximately [[5_4|5/4]] in size, which closes at the octave since the [[orwell comma]], 1728/1715, is tempered out; in other words, a 7/6-7/6-7/6-5/4 chord. Equal temperaments tempering out 1728/1715 and hence containing orwell tetrads include 22, 26, 27, 31, 53, 58, 80, 84, 111 and 137.

The orwell tetrad can in a natural way be extended to the [[11-limit]] as 1-7/6-11/8-8/5 by tempering out 99/98, a comma of 11-limit [[orwell]]. With a bit more accuracy, tempering out 176/175 and so also 540/539 allows it to be seen as the [[Orwellismic family#Guanyin|guanyin]] tetrad, a tempered version of 1-7/6-15/11-8/5. Equal temperaments with guanyin tetrads include 22, 31, 53, 58, 80 and 111. In orwell temperament, where 121/120 is tempered out, the guanyin and orwell tetrads are the same.

The tetrad can be extended to a 15-limit nonad, the orwell-tempered version of 1-11/10-7/6-9/7-11/8-3/2-8/5-7/4-15/8, with steps of size 11/10-15/14-11/10-15/14-11/10-15/14-11/10-15/14-15/14. The orwell nonad is the same as the Orwell[9] MOS, considered as a chord. Since it can be considered to be a chord, it is possible to retune music from 12edo to Orwell[9] by using [[orwell9-12|this scale]]. Examples of music retuned in this way are given below:

==sound examples ==

[[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/k404-orwell9.mp3|Scarlatti K404]]

[[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/swing-orwell9.mp3|Swing, Swing, Swing]]

* [[Chords of orwell]]</pre></div>

<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 tetrad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;orwell tetrad&lt;/strong&gt; is a four-note chord which in close position (reduced to the octave) consists of a chain of three subminor thirds, thirds of approximately &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; in size, and a major third, of approximately &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt; in size, which closes at the octave since the &lt;a class="wiki_link" href="/orwell%20comma"&gt;orwell comma&lt;/a&gt;, 1728/1715, is tempered out; in other words, a 7/6-7/6-7/6-5/4 chord. Equal temperaments tempering out 1728/1715 and hence containing orwell tetrads include 22, 26, 27, 31, 53, 58, 80, 84, 111 and 137.&lt;br /&gt;

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The orwell tetrad can in a natural way be extended to the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; as 1-7/6-11/8-8/5 by tempering out 99/98, a comma of 11-limit &lt;a class="wiki_link" href="/orwell"&gt;orwell&lt;/a&gt;. With a bit more accuracy, tempering out 176/175 and so also 540/539 allows it to be seen as the &lt;a class="wiki_link" href="/Orwellismic%20family#Guanyin"&gt;guanyin&lt;/a&gt; tetrad, a tempered version of 1-7/6-15/11-8/5. Equal temperaments with guanyin tetrads include 22, 31, 53, 58, 80 and 111. In orwell temperament, where 121/120 is tempered out, the guanyin and orwell tetrads are the same.&lt;br /&gt;

The tetrad can be extended to a 15-limit nonad, the orwell-tempered version of 1-11/10-7/6-9/7-11/8-3/2-8/5-7/4-15/8, with steps of size 11/10-15/14-11/10-15/14-11/10-15/14-11/10-15/14-15/14. The orwell nonad is the same as the Orwell[9] MOS, considered as a chord. Since it can be considered to be a chord, it is possible to retune music from 12edo to Orwell[9] by using &lt;a class="wiki_link" href="/orwell9-12"&gt;this scale&lt;/a&gt;. Examples of music retuned in this way are given below:&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-sound examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;sound examples &lt;/h2&gt;

&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/k404-orwell9.mp3" rel="nofollow"&gt;Scarlatti K404&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/reger135b-fantasie-orwell9.mp3" rel="nofollow"&gt;Reger Fantasie op135b&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/swing-orwell9.mp3" rel="nofollow"&gt;Swing, Swing, Swing&lt;/a&gt;&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-see also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt; see also &lt;/h2&gt;