List of root-3rd-P5 triads in JI

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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" is 27/25, which is decidedly not a third; and the widest "third" is 50/27, 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 second interval prime odd comments
ratio cents ratio cents limit limit
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
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
34:38:51 19/17 192.558 51/38 509.397 19 51 Quasi-meantone Suspended 2nd
8:9:12 9/8 203.910 4/3 498.045 3 9 Suspended 2nd
30:34:45 17/15 216.687 45/34 485.268 17 45
22:25:33 25/22 221.309 33/25 480.646 11 33
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
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 5 5-limit minor
24:29:36 29/24 327.622 36/29 374.333 29 29
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
30:37:45 37/30 363.075 45/37 338.880 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 13/11 289.210 13 33
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 37 Rooted ultramajor triad
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
26:34:39 17/13 464.428 39/34 237.527 17 39
16:21:24 21/16 470.781 8/7 231.174 7 21
22:29:33 29/22 478.259 33/29 223.696 29 29
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 9/8 203.910 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
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
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
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