List of root-3rd-P5 triads in JI

The basic structure of major and minor triads—two stacked thirds which total to a perfect fifth—can be generalized to produce an infinity of chords with their own distinct qualities. What follows is a list of all such chords that are possible in 47-prime-limit Just Intonation, assuming a 3/2 perfect fifth.

Wiki authors can feel free to extend this list beyond the 47-limit or leave it at that, but of course, it should be noted that a complete list would be infinite.

The narrowest "third" listed is 27/25, which is decidedly not a third; and the widest "third" is 25/18, which ditto. Thus, the entire conceptual category of a third and then some is covered, and composers can decide for themselves what counts as a "third" and what doesn't.

50:54:7527/25133.23825/18568.717 5 75 12:13:1813/12138.57318/13563.382 13 13 46:50:6925/23144.35369/50557.602 23 69 22:24:3312/11150.63711/8551.318 11 33 42:46:6323/21157.49363/46544.462 23 63 10:11:1511/10165.00415/11536.951 11 15 Suspended submajor second 38:42:5721/19173.26819/14528.687 19 57 18:20:2710/9182.40427/20519.551 5 27 Grave Suspended 2nd 34:38:5119/17192.55851/38509.397 19 51 Quasi-meantone Suspended 2nd 8:9:129/8203.914/3498.045 3 9 Suspended 2nd 30:34:4517/15216.68745/34485.268 17 45 22:25:3325/22221.30933/25480.646 11 33 36:41:5441/36225.15254/41476.803 41 41 14:16:218/7231.17421/16470.781 7 21 Suspended supermajor second 20:23:30 23/20 241.961 30/23 459.994 23 23 26:30:39 15/13 247.741 13/10 454.214 13 15 Inverse "barbados" triad 32:37:48 37/32 251.344 48/37 450.611 37 37 Rooted inframinor triad 6:7:9 7/6 266.871 9/7 435.084 7 9 Septimal subminor 40:47:60 47/40 279.193 60/47 422.762 47 47 28:33:42 33/28 284.447 14/11 417.508 11 33 22:26:33 13/11 289.210 33/26 412.745 13 33 Neo-Gothic minor triad 16:19:24 19/16 297.513 24/19 404.442 19 19 Rooted minor triad 26:31:39 31/26 304.508 39/31 397.447 31 39 36:43:54 43/36 307.608 54/43 394.347 43 43 10:12:15 6/5 315.641 5/4 386.314 5 15 5-limit minor 24:29:36 29/24 327.622 36/29 374.333 29 29 22EDO-esque minor 14:17:21 17/14 336.130 21/17 365.825 17 21 17-limit supraminor 32:39:48 39/32 342.483 16/13 359.472 13 39 Rooted neutral triad 18:22:27 11/9 347.408 27/22 354.547 11 27 Neutral 22:27:33 27/22 354.547 11/9 347.408 11 33 Neutral 26:32:39 16/13 359.472 39/32 342.483 13 39 Rooted neutral triad 30:37:45 37/30 363.075 45/37 338.88 37 45 4:5:6 5/4 386.314 6/5 315.641 5 5 5-limit major 30:38:45 19/15 409.244 45/38 292.711 19 45 26:33:39 33/26 412.745 13/11 289.21 13 39 22:28:33 14/11 417.508 33/28 284.447 11 33 Neo-Gothic major triad 94:120:141 60/47 422.762 47/40 279.193 47 141 18:23:27 23/18 424.364 27/23 277.591 23 27 32:41:48 41/32 429.062 48/41 272.893 41 41 Rooted supermajor triad 14:18:21 9/7 435.084 7/6 266.871 7 9 Septimal supermajor 24:31:36 31/24 443.081 36/31 258.874 31 31 74:96:111 48/37 450.611 37/32 251.344 37 10:13:15 13/10 454.214 15/13 247.741 13 15 "Barbados" triad 36:47:54 47/36 461.597 54/47 240.358 47 47 26:34:3917/13464.42839/34237.527 17 39 16:21:2421/16470.7818/7231.174 7 21 Suspended subfourth 22:29:3329/22478.25933/29223.696 29 28:37:4237/28482.51842/37219.437 37 37 34:45:5145/34485.26817/15216.687 17 51 6:8:94/3498.0459/8203.91 3 9 Suspended 4th 38:51:5751/38509.39719/17192.558 19 57 Quasi-meantone Suspended 4th 20:27:3027/20519.55110/9182.404 5 27 Acute Suspended 4th 14:19:2119/14529.68721/19173.268 19 21 22:30:3315/11536.95111/10165.004 11 33 Suspended superfourth 46:63:6963/46544.46223/21157.493 23 69 8:11:1211/8551.31812/11150.637 11 11 50:69:7569/50557.60225/23144.353 23 75 26:36:3918/13563.38213/12138.573 13 39 18:25:2725/18568.71727/25133.238 5 27 Viennese trichord

chord	first interval (ratio)	first interval (cents)	second interval (ratio)	second interval (cents)	prime limit	odd limit	comments
74:84:111	42/37	219.437	37/28	482.518	37	111
58:66:87	33/29	223.696	29/22	478.259	29	87
34:39:51	39/34	237.527	17/13	464.428	17	51
94:108:141	54/47	240.358	47/36	461.597	47	141
62:72:93	36/31	258.874	31/24	443.081	31	93
82:96:123	48/41	272.893	41/32	429.066	41	41	Rooted subminor triad
46:54:69	27/23	277.591	23/18	424.364	23	69
74:90:111	45/37	338.88	37/30	363.075	37	111
34:42:51	21/17	365.825	17/14	336.13	17	51	17-limit submajor
58:76:87	36/29	374.333	29/24	327.622	29	87	22EDO-esque major
38:48:57	24/19	404.442	19/16	297.513	19	57	Rooted major triad
111 Rooted ultramajor triad
46:60:69	30/23	459.994	23/20	241.961	23	69
33
50:66:75	33/25	480.646	25/22	221.309	11	75