User:Hkm/Interval categories
< User:Hkm
The internal logic should be apparent. 9\72 or 1(6) + 3 \72, or any just interval which is reasonably mapped to that interval, could be called a neutral 2nd.
| # | /6 | %6 | Cents | Approximate ratios | name | other names |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0.0 | 1/1 | unison | |
| 1 | 0 | 1 | 16.7 | 81/80, 91/90, 99/98, 100/99, 105/104 | comma | |
| 2 | 0 | 2 | 33.3 | 45/44, 49/48, 50/49, 55/54, 64/63 | sixth-tone | |
| 3 | 0 | 3 | 50.0 | 33/32, 36/35, 40/39 | quarter-tone | |
| 4 | 0 | 4 | 66.7 | 25/24, 26/25, 27/26, 28/27 | subminor 2nd | third-tone |
| 5 | 0 | 5 | 83.3 | 20/19, 21/20, 22/21 | neominor 2nd | |
| 6 | 1 | 0 | 100.0 | 17/16, 18/17, 19/18 | novaminor 2nd | |
| 7 | 1 | 1 | 116.7 | 15/14, 16/15 | pentaminor 2nd | |
| 8 | 1 | 2 | 133.3 | 13/12, 14/13, 27/25 | supraminor 2nd | |
| 9 | 1 | 3 | 150.0 | 12/11 | neutral 2nd | |
| 10 | 1 | 4 | 166.7 | 11/10 | submajor 2nd | |
| 11 | 1 | 5 | 183.3 | 10/9 | pentamajor 2nd | |
| 12 | 2 | 0 | 200.0 | 9/8 | novamajor 2nd | |
| 13 | 2 | 1 | 216.7 | 17/15, 25/22 | neomajor 2nd | |
| 14 | 2 | 2 | 233.3 | 8/7 | supermajor 2nd | |
| 15 | 2 | 3 | 250.0 | 15/13, 22/19 | 2nd-3rd | inframajor 2nd, inframinor 3rd |
| 16 | 2 | 4 | 266.7 | 7/6 | subminor 3nd | |
| 17 | 3 | 5 | 283.3 | 13/11, 20/17 | neominor 3nd | |
| 18 | 3 | 0 | 300.0 | 19/16, 25/21, 32/27 | novaminor 3nd | |
| 19 | 3 | 1 | 316.7 | 6/5 | pentaminor 3nd | |
| 20 | 3 | 2 | 333.3 | 17/14, 39/32, 40/33 | supraminor 3nd | |
| 21 | 3 | 3 | 350.0 | 11/9, 27/22 | neutral 3nd | |
| 22 | 3 | 4 | 366.7 | 16/13, 21/17, 26/21 | submajor 3nd | |
| 23 | 3 | 5 | 383.3 | 5/4 | pentamajor 3nd | |
| 24 | 4 | 0 | 400.0 | 24/19 | novamajor 3nd | |
| 25 | 4 | 1 | 416.7 | 14/11 | neomajor 3nd | |
| 26 | 4 | 2 | 433.3 | 9/7 | supermajor 3nd | |
| 27 | 4 | 3 | 450.0 | 13/10, 22/17 | ultramajor 3rd | 3rd-4th, inframinor 4th |
| 28 | 4 | 4 | 466.7 | 17/13, 21/16 | sub 4th | |
| 29 | 4 | 5 | 483.3 | 33/25 | neo 4th | |
| 30 | 5 | 0 | 500.0 | 4/3 | clear 4th | |
| 31 | 5 | 1 | 516.7 | 27/20 | penta 4th | |
| 32 | 5 | 2 | 533.3 | 15/11, 19/14, 26/19 | supra 4th | |
| 33 | 5 | 3 | 550.0 | 11/8 | neutral 4th | |
| 34 | 5 | 4 | 566.7 | 18/13, 25/18 | subaugmented 4th | |
| 35 | 5 | 5 | 583.3 | 7/5 | pentaugmented 4th | small semioctave, neodiminished 5th |
| 36 | 6 | 0 | 600.0 | 17/12, 24/17 | medium semioctave | novaugmented 4th, novadiminished 5th |
| 37 | 6 | 1 | 616.7 | 10/7 | pentadiminished 5th | large semioctave, pentadiminished 5th |
| 38 | 6 | 2 | 633.3 | 13/9, 36/25 | supradiminished 5th | |
| 39 | 6 | 3 | 650.0 | 16/11 | neutral 5th | |
| 40 | 6 | 4 | 666.7 | 19/13, 22/15, 28/19 | sub 5th | |
| 41 | 6 | 5 | 683.3 | 40/27 | penta 5th | |
| 42 | 7 | 0 | 700.0 | 3/2 | clear 5th | |
| 43 | 7 | 1 | 716.7 | 50/33 | neo 5th | |
| 44 | 7 | 2 | 733.3 | 26/17, 32/21 | super(major) 5th | |
| 45 | 7 | 3 | 750.0 | 17/11, 20/13 | inframinor 6th | 5th-6th, ultramajor 5th |
| 46 | 7 | 4 | 766.7 | 14/9 | subminor 6th | |
| 47 | 7 | 5 | 783.3 | 11/7 | neominor 6th | |
| 48 | 8 | 0 | 800.0 | 19/12 | etc. | etc. |
| 49 | 8 | 1 | 816.7 | 8/5 | etc. | etc. |
| 50 | 8 | 2 | 833.3 | 13/8, 21/13, 34/21 | ||
| 51 | 8 | 3 | 850.0 | 18/11, 44/27 | ||
| 52 | 8 | 4 | 866.7 | 28/17, 33/20, 64/39 | ||
| 53 | 8 | 5 | 883.3 | 5/3 | ||
| 54 | 9 | 0 | 900.0 | 27/16, 32/19, 42/25 | ||
| 55 | 9 | 1 | 916.7 | 17/10, 22/13 | ||
| 56 | 9 | 2 | 933.3 | 12/7 | ||
| 57 | 9 | 3 | 950.0 | 19/11, 26/15 | ||
| 58 | 9 | 4 | 966.7 | 7/4 | ||
| 59 | 9 | 5 | 983.3 | 30/17, 44/25 | ||
| 60 | 10 | 0 | 1000.0 | 16/9 | ||
| 61 | 10 | 1 | 1016.7 | 9/5 | ||
| 62 | 10 | 2 | 1033.3 | 20/11 | ||
| 63 | 10 | 3 | 1050.0 | 11/6 | ||
| 64 | 10 | 4 | 1066.7 | 13/7, 24/13, 50/27 | ||
| 65 | 10 | 5 | 1083.3 | 15/8, 28/15 | ||
| 66 | 11 | 0 | 1100.0 | 17/9, 32/17, 36/19 | ||
| 67 | 11 | 1 | 1116.7 | 19/10, 21/11, 40/21 | ||
| 68 | 11 | 2 | 1133.3 | 25/13, 27/14, 48/25, 52/27 | ||
| 69 | 11 | 3 | 1150.0 | 35/18, 39/20, 64/33 | ||
| 70 | 11 | 4 | 1166.7 | 49/25, 55/28, 63/32, 88/45, 96/49 | ||
| 71 | 11 | 5 | 1183.3 | 99/50, 160/81, 180/91, 196/99, 208/105 | ||
| 72 | 12 | 0 | 1200.0 | 2/1 |