Orwell tetrad
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: