4:5:6:7:11

Chord information

Harmonics	4:5:6:7:11
Intervals from root	1/1–5/4–3/2–7/4–11/4
Cents from root	0¢–386¢–702¢–969¢–1751¢
Step intervals	5/4, 6/5, 7/6, 11/7
Step cents	386¢, 316¢, 267¢, 782¢
Prime limit	11
Genus	3⋅5⋅7⋅11 (1155)
Intervallic odd limit	11
Otonal odd limit	11
Utonal odd limit	1155
Consistent edos (d ≥ 1.5)	31edo, 46edo, 72edo*
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

4:5:6:7:11, the harmonic seventh added-eleventh chord, is a pentad in the 11-limit. It is a subset of 4:5:6:7:9:11, the harmonic eleventh chord.

This chord can be modified by inflecting the 5/4 down by 25/24, the 7/4 down by 49/48, and the 11/4 down by 33/32 to get a 7-limit utonal minor counterpart 1–6/5–3/2–12/7–8/3, which is the inverse of 1–5/4–3/2–7/4–9/4. The chord's own inverse is 1–6/5–3/2–12/7–24/11. 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.

Edo approximations for 4:5:6:7:11 ▶
intervals: 5/4, 3/2, 7/4, 11/4 · ≤ 60edo, RMS rel. error ≤ 15%

	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	9	0  3  5  7 13	0.00 400.00 666.67 933.33 1733.33	0.00 +13.69 -35.29 -35.49 -17.98	19.43	14.58
▶	15	0  5  9 12 22	0.00 400.00 720.00 960.00 1760.00	0.00 +13.69 +18.04  -8.83  +8.68	9.66	12.08
▶	22	0  7 13 18 32	0.00 381.82 709.09 981.82 1745.45	0.00  -4.50  +7.14 +12.99  -5.86	7.14	13.10
▶	31	0 10 18 25 45	0.00 387.10 696.77 967.74 1741.94	0.00  +0.78  -5.18  -1.08  -9.38	3.81	9.84
▶	37	0 12 22 30 54	0.00 389.19 713.51 972.97 1751.35	0.00  +2.88 +11.56  +4.15  +0.03	4.24	13.06
▶	41	0 13 24 33 60	0.00 380.49 702.44 965.85 1756.10	0.00  -5.83  +0.48  -2.97  +4.78	3.56	12.16
▶	46	0 15 27 37 67	0.00 391.30 704.35 965.22 1747.83	0.00  +4.99  +2.39  -3.61  -3.49	3.34	12.81
▶	58	0 19 34 47 85	0.00 393.10 703.45 972.41 1758.62	0.00  +6.79  +1.49  +3.59  +7.30	2.86	13.84