View source for Orwell tetrad

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 }}.

[[File:OrwellTetrad22edo.mp3]]

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 [[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]]