10:12:15:18

10:12:15:18, the just, classical, or ptolemaic minor seventh chord, is a minor seventh chord. It is an anomalous saturated suspension in the 9-odd-limit. It is found on the iii (5/4) and vi (5/3) of Ptolemy's intense diatonic scale (Zarlino), perhaps the most common 5-limit diatonic.

Todo: expand, add sound example

Edo approximations for 10:12:15:18 ▶
*intervals: 6/5, 3/2, 9/5 · ≤ 60edo, RMS rel. error ≤ 15%*
	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	7	`0 2 4 6`	`0.00 342.86 685.71 1028.57`	`0.00 +27.22 -16.24 +10.98`	15.85	9.24
▶	12	`0 3 7 10`	`0.00 300.00 700.00 1000.00`	`0.00 -15.64 -1.96 -17.60`	7.88	7.88
▶	15	`0 4 9 13`	`0.00 320.00 720.00 1040.00`	`0.00 +4.36 +18.04 +22.40`	9.28	11.60
▶	19	`0 5 11 16`	`0.00 315.79 694.74 1010.53`	`0.00 +0.15 -7.22 -7.07`	3.61	5.72
▶	22	`0 6 13 19`	`0.00 327.27 709.09 1036.36`	`0.00 +11.63 +7.14 +18.77`	6.82	12.51
▶	26	`0 7 15 22`	`0.00 323.08 692.31 1015.38`	`0.00 +7.44 -9.65 -2.21`	6.09	13.20
▶	27	`0 7 16 23`	`0.00 311.11 711.11 1022.22`	`0.00 -4.53 +9.16 +4.63`	5.11	11.49
▶	31	`0 8 18 26`	`0.00 309.68 696.77 1006.45`	`0.00 -5.96 -5.18 -11.14`	3.95	10.20
▶	34	`0 9 20 29`	`0.00 317.65 705.88 1023.53`	`0.00 +2.01 +3.93 +5.93`	2.20	6.25
▶	38	`0 10 22 32`	`0.00 315.79 694.74 1010.53`	`0.00 +0.15 -7.22 -7.07`	3.61	11.43
▶	41	`0 11 24 35`	`0.00 321.95 702.44 1024.39`	`0.00 +6.31 +0.48 +6.79`	3.16	10.81
▶	46	`0 12 27 39`	`0.00 313.04 704.35 1017.39`	`0.00 -2.60 +2.39 -0.20`	1.77	6.77
▶	50	`0 13 29 42`	`0.00 312.00 696.00 1008.00`	`0.00 -3.64 -5.96 -9.60`	3.49	14.54
▶	53	`0 14 31 45`	`0.00 316.98 701.89 1018.87`	`0.00 +1.34 -0.07 +1.27`	0.67	2.96
▶	58	`0 15 34 49`	`0.00 310.34 703.45 1013.79`	`0.00 -5.30 +1.49 -3.80`	2.75	13.30
▶	60	`0 16 35 51`	`0.00 320.00 700.00 1020.00`	`0.00 +4.36 -1.96 +2.40`	2.39	11.94

See also