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.

chord	first interval (ratio)	first interval (cents)	second interval (ratio)	second interval (cents)	prime limit	odd limit	comments
50:54:75	27/25	133.238	25/18	568.717	5	75
12:13:18	13/12	138.573	18/13	563.382	13	13
46:50:69	25/23	144.353	69/50	557.602	23	69
22:24:33	12/11	150.637	11/8	551.318	11	33
42:46:63	23/21	157.493	63/46	544.462	23	63
10:11:15	11/10	165.004	15/11	536.951	11	15	Suspended submajor second
38:42:57	21/19	173.268	19/14	528.687	19	57
18:20:27	10/9	182.404	27/20	519.551	5	27	Grave Suspended 2nd
34:38:51	19/17	192.558	51/38	509.397	19	51	Quasi-meantone Suspended 2nd
8:9:12	9/8	203.91	4/3	498.045	3	9	Suspended 2nd
30:34:45	17/15	216.687	45/34	485.268	17	45
74:84:111	42/37	219.437	37/28	482.518	37	111
22:25:33	25/22	221.309	33/25	480.646	11	33
58:66:87	33/29	223.696	29/22	478.259	29	87
36:41:54	41/36	225.152	54/41	476.803	41	41
14:16:21	8/7	231.174	21/16	470.781	7	21	Suspended supermajor second
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
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
62:72:93	36/31	258.874	31/24	443.081	31	93
6:7:9	7/6	266.871	9/7	435.084	7	9	Septimal subminor
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
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
74:90:111	45/37	338.88	37/30	363.075	37	111
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
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
4:5:6	5/4	386.314	6/5	315.641	5	5	5-limit major
38:48:57	24/19	404.442	19/16	297.513	19	57	Rooted major triad
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	111	Rooted ultramajor triad
10:13:15	13/10	454.214	15/13	247.741	13	15	"Barbados" triad
46:60:69	30/23	459.994	23/20	241.961	23	69
36:47:54	47/36	461.597	54/47	240.358	47	47
26:34:39	17/13	464.428	39/34	237.527	17	39
16:21:24	21/16	470.781	8/7	231.174	7	21	Suspended subfourth
22:29:33	29/22	478.259	33/29	223.696	29	33
50:66:75	33/25	480.646	25/22	221.309	11	75
28:37:42	37/28	482.518	42/37	219.437	37	37
34:45:51	45/34	485.268	17/15	216.687	17	51
6:8:9	4/3	498.045	9/8	203.91	3	9	Suspended 4th
38:51:57	51/38	509.397	19/17	192.558	19	57	Quasi-meantone Suspended 4th
20:27:30	27/20	519.551	10/9	182.404	5	27	Acute Suspended 4th
14:19:21	19/14	529.687	21/19	173.268	19	21
22:30:33	15/11	536.951	11/10	165.004	11	33	Suspended superfourth
46:63:69	63/46	544.462	23/21	157.493	23	69
8:11:12	11/8	551.318	12/11	150.637	11	11
50:69:75	69/50	557.602	25/23	144.353	23	75
26:36:39	18/13	563.382	13/12	138.573	13	39
18:25:27	25/18	568.717	27/25	133.238	5	27	Viennese trichord