20:26:30:39

Chord information
Harmonics	20:26:30:39
Subharmonics	1/(39:30:26:20)
Intervals from root	1/1–13/10–3/2–39/20
Cents from root	0¢–454¢–702¢–1156¢
Step intervals	13/10, 15/13, 13/10
Step cents	454¢, 248¢, 454¢
Prime limit	13
Genus	3⋅5⋅13 (195)
Intervallic odd limit	39
Otonal odd limit	39
Utonal odd limit	39
Consistent edos (d ≥ 2)	5edo, 24edo, 29edo*, 34edo, …
	* 2 ≤ d < 4; 4 ≤ d < 8; * 8 ≤ d < 16; …

20:26:30:39, the ultramajor-7th chord, is a 13-limit 7th chord made by stacking the ultramajor 13/10 and inframinor 15/13 . As they are fifth complements, this tetrad contains a perfect fifth, and is also relatively low complexity making it a very powerful structure in the 13-limit.

Edo approximations for 20:26:30:39 ▶
*intervals: 13/10, 3/2, 39/20 · ≤ 60edo, RMS rel. error ≤ 15%*
	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	10	`0 4 6 10`	`0.00 480.00 720.00 1200.00`	`0.00 +25.79 +18.04 +43.83`	15.74	13.11
▶	19	`0 7 11 18`	`0.00 442.11 694.74 1136.84`	`0.00 -12.11 -7.22 -19.33`	7.05	11.16
▶	21	`0 8 12 20`	`0.00 457.14 685.71 1142.86`	`0.00 +2.93 -16.24 -13.31`	8.25	14.44
▶	24	`0 9 14 23`	`0.00 450.00 700.00 1150.00`	`0.00 -4.21 -1.96 -6.17`	2.32	4.65
▶	26	`0 10 15 25`	`0.00 461.54 692.31 1153.85`	`0.00 +7.32 -9.65 -2.32`	6.06	13.12
▶	29	`0 11 17 28`	`0.00 455.17 703.45 1158.62`	`0.00 +0.96 +1.49 +2.45`	0.89	2.14
▶	31	`0 12 18 30`	`0.00 464.52 696.77 1161.29`	`0.00 +10.30 -5.18 +5.12`	5.77	14.89
▶	34	`0 13 20 33`	`0.00 458.82 705.88 1164.71`	`0.00 +4.61 +3.93 +8.54`	3.03	8.58
▶	48	`0 18 28 46`	`0.00 450.00 700.00 1150.00`	`0.00 -4.21 -1.96 -6.17`	2.32	9.29
▶	50	`0 19 29 48`	`0.00 456.00 696.00 1152.00`	`0.00 +1.79 -5.96 -4.17`	3.11	12.95
▶	53	`0 20 31 51`	`0.00 452.83 701.89 1154.72`	`0.00 -1.38 -0.07 -1.45`	0.69	3.06
▶	55	`0 21 32 53`	`0.00 458.18 698.18 1156.36`	`0.00 +3.97 -3.77 +0.19`	2.74	12.55
▶	58	`0 22 34 56`	`0.00 455.17 703.45 1158.62`	`0.00 +0.96 +1.49 +2.45`	0.89	4.29