22:26:33

22:26:33, the major minthmic minor triad, is a 13-limit tertian triad. This triad has a darker quality than the 10:12:15 classical minor triad, though not as much as the 6:7:9 subminor triad. Here 13/11 functions as a neogothic minor third, being between 7/6 and 6/5, in fact being (7 + 6)/(6 + 5), which is the mediant of 7/6 and 6/5, and 33/26 functions as the corresponding neogothic major third.

Chord information

Harmonics	22:26:33
Subharmonics	1/(39:33:26)
Intervals from root	1/1–13/11–3/2
Cents from root	0¢–289¢–702¢
Step intervals	13/11, 33/26
Step cents	289¢, 413¢
Prime limit	13
Genus	3⋅11⋅13 (429)
Intervallic odd limit	33
Otonal odd limit	33
Utonal odd limit	39
Consistent edos (d ≥ 2)	12edo*, 17edo*, 29edo***, 38edo*, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

We can find another neogothic major third by taking the mediant of 5/4 and 9/7, which is (5 + 9)/(4 + 7) = 14/11. The triad containing this third and the perfect fifth is 22:28:33. 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

• 26:33:39 – its inverse