22:28:33

22:28:33, the pentacircle major triad, is an 11-limit tertian triad. This triad has a brighter quality than the 4:5:6 classical major triad, though not as much as the 14:18:21 supermajor triad. Here 14/11 functions as a neogothic major third, being between 5/4 and 9/7, in fact being (5 + 9)/(4 + 7), which is the mediant of 5/4 and 9/7, and 33/28 functions as the corresponding neogothic minor third.

Chord information

Harmonics	22:28:33
Subharmonics	1/(42:33:28)
Intervals from root	1/1–14/11–3/2
Cents from root	0¢–418¢–702¢
Step intervals	14/11, 33/28
Step cents	418¢, 284¢
Prime limit	11
Genus	3⋅7⋅11 (231)
Intervallic odd limit	33
Otonal odd limit	33
Utonal odd limit	33
Consistent edos (d ≥ 2)	12edo*, 17edo**, 26edo*, 29edo*, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

We can find another neogothic minor third by taking the mediant of 7/6 and 6/5, which is (7 + 6)/(6 + 5) = 13/11. The triad containing this third and the perfect fifth is 22:26:33. Note that these triads are reduced to the 13-odd-limit and invert to each other if and only if (14/11)⋅(13/11)/(3/2) = 364/363, the minor minthma or gentle comma, is tempered out.

See also

• 28:33:42 – its inverse