3:5:7

Chord information
Harmonics	3:5:7
Subharmonics	1/(35:21:15)
Intervals from root	1/1–5/3–7/3
Cents from root	0¢–884¢–1467¢
Step intervals	5/3, 7/5
Step cents	884¢, 583¢
Prime limit	7
Genus	3⋅5⋅7 (105)
Intervallic odd limit	7
Otonal odd limit	7
Utonal odd limit	35
Consistent edos (d ≥ 2)	4edo*, 8edo, 19edo, 23edo, …
	* 2 ≤ d < 4; 4 ≤ d < 8; * 8 ≤ d < 16; …

3:5:7 is a chord best-known for being emphasized by the Bohlen–Pierce scale and other nonoctave (mainly 3.5.7... subgroup) temperaments. It is also known as the "major triad of the Bohlen–Pierce scale".^[1]

Edo approximations for 3:5:7 ▶
*intervals: 5/3, 7/3 · ≤ 60edo, RMS rel. error ≤ 15%*
	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	8	`0 6 10`	`0.00 900.00 1500.00`	`0.00 +15.64 +33.13`	13.53	9.02
▶	12	`0 9 15`	`0.00 900.00 1500.00`	`0.00 +15.64 +33.13`	13.53	13.53
▶	14	`0 10 17`	`0.00 857.14 1457.14`	`0.00 -27.22 -9.73`	11.26	13.14
▶	15	`0 11 18`	`0.00 880.00 1440.00`	`0.00 -4.36 -26.87`	11.77	14.72
▶	18	`0 13 22`	`0.00 866.67 1466.67`	`0.00 -17.69 -0.20`	8.29	12.44
▶	19	`0 14 23`	`0.00 884.21 1452.63`	`0.00 -0.15 -14.24`	6.68	10.57
▶	22	`0 16 27`	`0.00 872.73 1472.73`	`0.00 -11.63 +5.86`	7.27	13.32
▶	23	`0 17 28`	`0.00 886.96 1460.87`	`0.00 +2.60 -6.00`	3.60	6.90
▶	27	`0 20 33`	`0.00 888.89 1466.67`	`0.00 +4.53 -0.20`	2.19	4.92
▶	31	`0 23 38`	`0.00 890.32 1470.97`	`0.00 +5.96 +4.10`	2.49	6.43
▶	35	`0 26 43`	`0.00 891.43 1474.29`	`0.00 +7.07 +7.41`	3.42	9.97
▶	37	`0 27 45`	`0.00 875.68 1459.46`	`0.00 -8.68 -7.41`	3.83	11.81
▶	39	`0 29 48`	`0.00 892.31 1476.92`	`0.00 +7.95 +10.05`	4.33	14.07
▶	41	`0 30 50`	`0.00 878.05 1463.41`	`0.00 -6.31 -3.46`	2.58	8.81
▶	45	`0 33 55`	`0.00 880.00 1466.67`	`0.00 -4.36 -0.20`	2.01	7.53
▶	46	`0 34 56`	`0.00 886.96 1460.87`	`0.00 +2.60 -6.00`	3.60	13.80
▶	49	`0 36 60`	`0.00 881.63 1469.39`	`0.00 -2.73 +2.52`	2.14	8.74
▶	50	`0 37 61`	`0.00 888.00 1464.00`	`0.00 +3.64 -2.87`	2.66	11.10
▶	53	`0 39 65`	`0.00 883.02 1471.70`	`0.00 -1.34 +4.83`	2.65	11.70
▶	54	`0 40 66`	`0.00 888.89 1466.67`	`0.00 +4.53 -0.20`	2.19	9.83
▶	58	`0 43 71`	`0.00 889.66 1468.97`	`0.00 +5.30 +2.09`	2.18	10.53
▶	60	`0 44 73`	`0.00 880.00 1460.00`	`0.00 -4.36 -6.87`	2.84	14.19

Sources

↑ https://gist.github.com/endolith/3098720

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[1] ttps://gist.github.com/endolith/3098720

[1]