5:6:7

5:6:7 is a diminished triad found as an upper structure of 4:5:6:7, the harmonic seventh chord. As a 7-odd-limit otonal chord, this is the most consonant JI tuning of a diminished triad.

Edo approximations for 5:6:7 ▶
*intervals: 6/5, 7/5 · ≤ 60edo, RMS rel. error ≤ 15%*
	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	8	`0 2 4`	`0.00 300.00 600.00`	`0.00 -15.64 +17.49`	13.53	9.02
▶	12	`0 3 6`	`0.00 300.00 600.00`	`0.00 -15.64 +17.49`	13.53	13.53
▶	14	`0 4 7`	`0.00 342.86 600.00`	`0.00 +27.22 +17.49`	11.26	13.14
▶	15	`0 4 7`	`0.00 320.00 560.00`	`0.00 +4.36 -22.51`	11.77	14.72
▶	18	`0 5 9`	`0.00 333.33 600.00`	`0.00 +17.69 +17.49`	8.29	12.44
▶	19	`0 5 9`	`0.00 315.79 568.42`	`0.00 +0.15 -14.09`	6.68	10.57
▶	22	`0 6 11`	`0.00 327.27 600.00`	`0.00 +11.63 +17.49`	7.27	13.32
▶	23	`0 6 11`	`0.00 313.04 573.91`	`0.00 -2.60 -8.60`	3.60	6.90
▶	27	`0 7 13`	`0.00 311.11 577.78`	`0.00 -4.53 -4.73`	2.19	4.92
▶	31	`0 8 15`	`0.00 309.68 580.65`	`0.00 -5.96 -1.87`	2.49	6.43
▶	35	`0 9 17`	`0.00 308.57 582.86`	`0.00 -7.07 +0.34`	3.42	9.97
▶	37	`0 10 18`	`0.00 324.32 583.78`	`0.00 +8.68 +1.27`	3.83	11.81
▶	39	`0 10 19`	`0.00 307.69 584.62`	`0.00 -7.95 +2.10`	4.33	14.07
▶	41	`0 11 20`	`0.00 321.95 585.37`	`0.00 +6.31 +2.85`	2.58	8.81
▶	45	`0 12 22`	`0.00 320.00 586.67`	`0.00 +4.36 +4.15`	2.01	7.53
▶	46	`0 12 22`	`0.00 313.04 573.91`	`0.00 -2.60 -8.60`	3.60	13.80
▶	49	`0 13 24`	`0.00 318.37 587.76`	`0.00 +2.73 +5.24`	2.14	8.74
▶	50	`0 13 24`	`0.00 312.00 576.00`	`0.00 -3.64 -6.51`	2.66	11.10
▶	53	`0 14 26`	`0.00 316.98 588.68`	`0.00 +1.34 +6.17`	2.65	11.70
▶	54	`0 14 26`	`0.00 311.11 577.78`	`0.00 -4.53 -4.73`	2.19	9.83
▶	58	`0 15 28`	`0.00 310.34 579.31`	`0.00 -5.30 -3.20`	2.18	10.53
▶	60	`0 16 29`	`0.00 320.00 580.00`	`0.00 +4.36 -2.51`	2.84	14.19

See also