Orwell tetrad: Difference between revisions
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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 [[ | 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, 111 and 137. | ||
[[File:OrwellTetrad22edo.mp3]] | [[File:OrwellTetrad22edo.mp3]] | ||
Orwell tetrad, in [[ | Orwell tetrad, in [[22edo]] tuning | ||
The orwell tetrad can in a natural way be extended to the [[ | 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: | 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: | ||
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[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/swing-orwell9.mp3 Swing, Swing, Swing] | [http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/swing-orwell9.mp3 Swing, Swing, Swing] | ||
== | == See also == | ||
<ul><li>[[ | <ul><li>[[Chords of orwell]]</li></ul> [[Category:11-limit]] | ||
[[Category:15-limit]] | [[Category:15-limit]] | ||
[[Category: | [[Category:Chords]] | ||
[[Category: | [[Category:Dyadic]] | ||
[[Category: | [[Category:Guanyin]] | ||
[[Category: | [[Category:Orwell]] | ||
[[Category: | [[Category:Tetrad]] | ||
[[Category: | [[Category:Todo:add links]] | ||
[[Category: | [[Category:Todo:add sound examples]] | ||
Revision as of 23:56, 30 June 2019
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, 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-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 this scale. Examples of music retuned in this way are given below: