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" 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 |