10:13:15

Chord information

Harmonics	10:13:15
Subharmonics	1/(39:30:26)
Intervals from root	1/1–13/10–3/2
Cents from root	0¢–454¢–702¢
Step intervals	13/10, 15/13
Step cents	454¢, 248¢
Prime limit	13
Genus	3⋅5⋅13 (195)
Intervallic odd limit	15
Otonal odd limit	15
Utonal odd limit	39
Consistent edos (d ≥ 2)	5edo**, 10edo*, 19edo*, 24edo**, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

10:13:15, also known as the barbados triad, is a triad in 13-limit just intonation. It is formed by stacking a 13/10 ultramajor third and a 15/13 inframinor third. In terms of harmonics, it is only slightly more complex than 10:12:15, the classical minor triad. It can thus be used as a basis for harmony, for example in barbados temperament.

Edo approximations for 10:13:15 ▶
intervals: 13/10, 3/2 · ≤ 60edo, RMS rel. error ≤ 15%

	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	10	0  4  6	0.00 480.00 720.00	0.00 +25.79 +18.04	10.80	9.00
▶	14	0  5  8	0.00 428.57 685.71	0.00 -25.64 -16.24	10.59	12.36
▶	15	0  6  9	0.00 480.00 720.00	0.00 +25.79 +18.04	10.80	13.50
▶	19	0  7 11	0.00 442.11 694.74	0.00 -12.11  -7.22	4.97	7.88
▶	21	0  8 12	0.00 457.14 685.71	0.00  +2.93 -16.24	8.43	14.76
▶	24	0  9 14	0.00 450.00 700.00	0.00  -4.21  -1.96	1.72	3.44
▶	29	0 11 17	0.00 455.17 703.45	0.00  +0.96  +1.49	0.62	1.49
▶	34	0 13 20	0.00 458.82 705.88	0.00  +4.61  +3.93	2.03	5.76
▶	39	0 15 23	0.00 461.54 707.69	0.00  +7.32  +5.74	3.15	10.22
▶	43	0 16 25	0.00 446.51 697.67	0.00  -7.70  -4.28	3.15	11.29
▶	44	0 17 26	0.00 463.64 709.09	0.00  +9.42  +7.14	4.01	14.71
▶	45	0 17 26	0.00 453.33 693.33	0.00  -0.88  -8.62	3.87	14.53
▶	48	0 18 28	0.00 450.00 700.00	0.00  -4.21  -1.96	1.72	6.89
▶	50	0 19 29	0.00 456.00 696.00	0.00  +1.79  -5.96	3.31	13.79
▶	53	0 20 31	0.00 452.83 701.89	0.00  -1.38  -0.07	0.64	2.81
▶	55	0 21 32	0.00 458.18 698.18	0.00  +3.97  -3.77	3.16	14.49
▶	58	0 22 34	0.00 455.17 703.45	0.00  +0.96  +1.49	0.62	2.99

See also

• 26:30:39 - its utonal inverse