5:6:7:9

5:6:7:9 is a concordant 7-limit interpretation of the half-diminished seventh chord. It can be thought of as the rootless version of the harmonic ninth chord, 4:5:6:7:9. It is found in the Ringer 5 scale. See also its homonym 6:7:9:10, a minor-major sixth chord.

In archytas temperament, this chord is tempered together with 45:54:64:81.

Edo approximations for 5:6:7:9 ▶
*intervals: 6/5, 7/5, 9/5 · ≤ 60edo, RMS rel. error ≤ 15%*
	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	8	`0 2 4 7`	`0.00 300.00 600.00 1050.00`	`0.00 -15.64 +17.49 +32.40`	18.08	12.05
▶	12	`0 3 6 10`	`0.00 300.00 600.00 1000.00`	`0.00 -15.64 +17.49 -17.60`	14.13	14.13
▶	14	`0 4 7 12`	`0.00 342.86 600.00 1028.57`	`0.00 +27.22 +17.49 +10.98`	9.90	11.55
▶	19	`0 5 9 16`	`0.00 315.79 568.42 1010.53`	`0.00 +0.15 -14.09 -7.07`	5.88	9.31
▶	22	`0 6 11 19`	`0.00 327.27 600.00 1036.36`	`0.00 +11.63 +17.49 +18.77`	7.42	13.60
▶	27	`0 7 13 23`	`0.00 311.11 577.78 1022.22`	`0.00 -4.53 -4.73 +4.63`	3.84	8.64
▶	31	`0 8 15 26`	`0.00 309.68 580.65 1006.45`	`0.00 -5.96 -1.87 -11.14`	4.28	11.05
▶	33	`0 9 16 28`	`0.00 327.27 581.82 1018.18`	`0.00 +11.63 -0.69 +0.59`	5.07	13.95
▶	39	`0 10 19 33`	`0.00 307.69 584.62 1015.38`	`0.00 -7.95 +2.10 -2.21`	3.75	12.19
▶	41	`0 11 20 35`	`0.00 321.95 585.37 1024.39`	`0.00 +6.31 +2.85 +6.79`	2.76	9.43
▶	45	`0 12 22 38`	`0.00 320.00 586.67 1013.33`	`0.00 +4.36 +4.15 -4.26`	3.53	13.25
▶	46	`0 12 22 39`	`0.00 313.04 573.91 1017.39`	`0.00 -2.60 -8.60 -0.20`	3.47	13.31
▶	50	`0 13 24 42`	`0.00 312.00 576.00 1008.00`	`0.00 -3.64 -6.51 -9.60`	3.54	14.77
▶	53	`0 14 26 45`	`0.00 316.98 588.68 1018.87`	`0.00 +1.34 +6.17 +1.27`	2.35	10.40
▶	58	`0 15 28 49`	`0.00 310.34 579.31 1013.79`	`0.00 -5.30 -3.20 -3.80`	1.93	9.34
▶	60	`0 16 29 51`	`0.00 320.00 580.00 1020.00`	`0.00 +4.36 -2.51 +2.40`	2.58	12.89

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