4:5:6:7:9

4:5:6:7:9, the harmonic ninth chord, is a pentad in 7-limit harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. It is an extension of 4:5:6 and 4:5:6:7.

Chord information

Harmonics	4:5:6:7:9
Subharmonics	1/(315:252:210:180:140)
Intervals from root	1/1–5/4–3/2–7/4–9/4
Cents from root	0¢–386¢–702¢–969¢–1404¢
Step intervals	5/4, 6/5, 7/6, 9/7
Step cents	386¢, 316¢, 267¢, 435¢
Color names	yo zo-7 add-9 or y,z7,9 har-9 or h9
Prime limit	7
Genus	32⋅5⋅7 (315)
Intervallic odd limit	9
Otonal odd limit	9
Utonal odd limit	315
Consistent edos (d ≥ 1.5)	31edo, 41edo*, 46edo, 53edo, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

Its utonal inverse, 1/(9:7:6:5:4), can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by 36/35, so the third becomes 9/7 and the seventh 9/5.

4:5:6:7:9 (1–5/4–3/2–7/4–9/4) can be modified by inflecting the 5/4 down by 25/24, the 7/4 down by 49/48, and the 9/4 down by 33/32 to get an 11-limit utonal minor counterpart 1–6/5–3/2–12/7–24/11. Meanwhile, the utonal inverse above can be voiced as 1–6/5–3/2–12/7–8/3, which has the inverse 1–5/4–3/2–7/4–11/4. These four chords form a quadruplet in the 11-odd-limit, all being subsets of 1–5/4–3/2–7/4–9/4–11/4 and 1–6/5–3/2–12/7–24/11–8/3.

See also

• Otonalpentad – this chord as a scale