4:5:6:7:9:11

4:5:6:7:9:11, the harmonic eleventh chord, is a hexad in 11-limit harmony. It can be considered the fundamental otonal consonance of the 11-odd-limit, voiced in a roughly tertian manner. It is an extension of 4:5:6, 4:5:6:7, and 4:5:6:7:9.

Chord information

Harmonics	4:5:6:7:9:11
Intervals from root	1/1–5/4–3/2–7/4–9/4–11/4
Cents from root	0¢–386¢–702¢–969¢–1404¢–1751¢
Step intervals	5/4, 6/5, 7/6, 9/7, 11/9
Step cents	386¢, 316¢, 267¢, 435¢, 347¢
Prime limit	11
Genus	32⋅5⋅7⋅11 (3465)
Intervallic odd limit	11
Otonal odd limit	11
Utonal odd limit	3465
Consistent edos (d ≥ 1.5)	31edo, 46edo, 72edo*
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

Edo approximations for 4:5:6:7:9:11 ▶
intervals: 5/4, 3/2, 7/4, 9/4, 11/4 · ≤ 60edo, RMS rel. error ≤ 15%

	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	22	0  7 13 18 26 32	0.00 381.82 709.09 981.82 1418.18 1745.45	0.00 -4.50 +7.14 +12.99 +14.27 -5.86	7.98	14.62
▶	31	0 10 18 25 36 45	0.00 387.10 696.77 967.74 1393.55 1741.94	0.00 +0.78 -5.18  -1.08 -10.36 -9.38	4.43	11.45
▶	41	0 13 24 33 48 60	0.00 380.49 702.44 965.85 1404.88 1756.10	0.00 -5.83 +0.48  -2.97  +0.97 +4.78	3.31	11.31
▶	46	0 15 27 37 54 67	0.00 391.30 704.35 965.22 1408.70 1747.83	0.00 +4.99 +2.39  -3.61  +4.79 -3.49	3.52	13.50
▶	58	0 19 34 47 68 85	0.00 393.10 703.45 972.41 1406.90 1758.62	0.00 +6.79 +1.49  +3.59  +2.99 +7.30	2.63	12.73

Related chords

• 1/(11:9:7:6:5:4) – its melodic inverse
• 1/(24:20:16:14:11:9) – the above chord voiced differently
• 4:5:6:7:9 – a subchord of this chord
• 4:5:6:7:11 – another subchord