Orwell tetrad: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The '''orwell tetrad''' is a [[tetrad|four-note chord]] which in close position (reduced to the octave) consists of a chain of three [[subminor]] thirds, thirds of approximately [[7/6]] in size, and a major third, of approximately [[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. This chord contains two fifths that are flattened by [[36/35]], which is about a [[quartertone]]. Equal temperaments tempering out 1728/1715 and hence containing orwell tetrads include {{EDOs| 22, 26, 27, 31, 53, 58, 80, 84, 111 and 137 }}.
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>2011-08-23 13:52:32 UTC</tt>.<br>
: The original revision id was <tt>247965029</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">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 in size, and a major third, of approximately 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 and 111.  


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 [[orwell temperament]]. 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.</pre></div>
[[File:OrwellTetrad22edo.mp3]]
<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;em&gt;orwell tetrad&lt;/em&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 7/6 in size, and a major third, of approximately 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 and 111. &lt;br /&gt;
Orwell tetrad, in [[22edo]] tuning
&lt;br /&gt;
 
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 &lt;a class="wiki_link" href="/orwell%20temperament"&gt;orwell temperament&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;/body&gt;&lt;/html&gt;</pre></div>
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 {{EDOs| 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-odd-limit]] ennead, 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 ennead 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 the [[orwell9-12]] scale. Examples of music retuned in this way are given below:
 
== Sound examples ==
* [https://web.archive.org/web/20201127013259/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/k404-orwell9.mp3 Scarlatti K404]
* [https://web.archive.org/web/20201127013106/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/reger135b-fantasie-orwell9.mp3 Reger Fantasie op135b]
* [https://web.archive.org/web/20201127012607/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/swing-orwell9.mp3 Swing, Swing, Swing]
 
== See also ==
* [[Chords of orwell]]
 
[[Category:11-odd-limit chords]]
[[Category:15-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Guanyin]]
[[Category:Orwell]]
[[Category:Tetrads]]
[[Category:Listen]]

Latest revision as of 13:45, 1 January 2025

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 in size, and a major third, of approximately 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. This chord contains two fifths that are flattened by 36/35, which is about a quartertone. Equal temperaments tempering out 1728/1715 and hence containing orwell tetrads include 22, 26, 27, 31, 53, 58, 80, 84, 111 and 137.

Orwell tetrad, in 22edo tuning

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 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-odd-limit ennead, 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 ennead 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 the orwell9-12 scale. Examples of music retuned in this way are given below:

Sound examples

See also

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