4:5:7

Chord information
Harmonics	4:5:7
Subharmonics	1/(35:28:20)
Intervals from root	1/1–5/4–7/4
Cents from root	0¢–386¢–969¢
Step intervals	5/4, 7/5
Step cents	386¢, 583¢
Color names	yo zo-7 no-5 or y,z7no5; har-7 no-5 or h7no5
Prime limit	7
Genus	5⋅7 (35)
Intervallic odd limit	7
Otonal odd limit	7
Utonal odd limit	35
Consistent edos (d ≥ 2)	6edo, 10edo, 16edo, 21edo, …
	* 2 ≤ d < 4; 4 ≤ d < 8; * 8 ≤ d < 16; …

4:5:7, the fifthless harmonic seventh chord, is a 7-limit chord found as a subset of the harmonic seventh chord, 4:5:6:7. It is used as a tuning target for the Italian augmented sixth chord in septimal meantone.

The open voicing 4:7:10 may be used as a fundamental otonal consonance of the 2.5.7 subgroup. It inverts to 14:20:35 with the middle voice contrasting by 49/40.

Rotations around the octave

4:5:7 "Root position"

5:7:8 "1st inversion"

7:8:10 "2nd inversion"

Edo approximations for 4:5:7 ▶
*intervals: 5/4, 7/4 · ≤ 60edo, RMS rel. error ≤ 15%*
	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	6	`0 2 5`	`0.00 400.00 1000.00`	`0.00 +13.69 +31.17`	12.76	6.38
▶	10	`0 3 8`	`0.00 360.00 960.00`	`0.00 -26.31 -8.83`	10.93	9.11
▶	12	`0 4 10`	`0.00 400.00 1000.00`	`0.00 +13.69 +31.17`	12.76	12.76
▶	15	`0 5 12`	`0.00 400.00 960.00`	`0.00 +13.69 -8.83`	9.26	11.58
▶	16	`0 5 13`	`0.00 375.00 975.00`	`0.00 -11.31 +6.17`	7.24	9.66
▶	19	`0 6 15`	`0.00 378.95 947.37`	`0.00 -7.37 -21.46`	8.90	14.10
▶	21	`0 7 17`	`0.00 400.00 971.43`	`0.00 +13.69 +2.60`	5.93	10.38
▶	22	`0 7 18`	`0.00 381.82 981.82`	`0.00 -4.50 +12.99`	7.41	13.59
▶	25	`0 8 20`	`0.00 384.00 960.00`	`0.00 -2.31 -8.83`	3.74	7.78
▶	27	`0 9 22`	`0.00 400.00 977.78`	`0.00 +13.69 +8.95`	5.68	12.77
▶	31	`0 10 25`	`0.00 387.10 967.74`	`0.00 +0.78 -1.08`	0.77	1.98
▶	35	`0 11 28`	`0.00 377.14 960.00`	`0.00 -9.17 -8.83`	4.24	12.38
▶	37	`0 12 30`	`0.00 389.19 972.97`	`0.00 +2.88 +4.15`	1.73	5.35
▶	41	`0 13 33`	`0.00 380.49 965.85`	`0.00 -5.83 -2.97`	2.38	8.13
▶	43	`0 14 35`	`0.00 390.70 976.74`	`0.00 +4.38 +7.92`	3.24	11.61
▶	46	`0 15 37`	`0.00 391.30 965.22`	`0.00 +4.99 -3.61`	3.53	13.52
▶	47	`0 15 38`	`0.00 382.98 970.21`	`0.00 -3.33 +1.39`	1.98	7.76
▶	52	`0 17 42`	`0.00 392.31 969.23`	`0.00 +5.99 +0.40`	2.74	11.85
▶	53	`0 17 43`	`0.00 384.91 973.58`	`0.00 -1.41 +4.76`	2.64	11.65
▶	56	`0 18 45`	`0.00 385.71 964.29`	`0.00 -0.60 -4.54`	2.01	9.40
▶	58	`0 19 47`	`0.00 393.10 972.41`	`0.00 +6.79 +3.59`	2.77	13.40

Related chords

Chords related to this triad (5-limit except where noted):

4:6:7 – no-fives version
4:5:6:7 – full tetrad
28:35:40 – its inverse