80edo: Difference between revisions
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→Intervals of 80edo: Removed pions column |
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| Line 31: | Line 31: | ||
! | degrees | ! | degrees | ||
! | cents | ! | cents | ||
!7mus | !7mus | ||
! | ratios* | ! | ratios* | ||
|- | |- | ||
| | | colspan="3" | 0 | ||
| | 1/1 | | | 1/1 | ||
|- | |- | ||
| | 1 | | | 1 | ||
| | 15 | | | 15 | ||
|19.2 (13.3<sub>16</sub>) | |19.2 (13.3<sub>16</sub>) | ||
| | 64/63 | | | 64/63 | ||
| Line 46: | Line 44: | ||
| | 2 | | | 2 | ||
| | 30 | | | 30 | ||
|38.4 (26.6<sub>16</sub>) | |38.4 (26.6<sub>16</sub>) | ||
| | 81/80 | | | 81/80 | ||
| Line 52: | Line 49: | ||
| | 3 | | | 3 | ||
| | 45 | | | 45 | ||
|57.6 (39.A<sub>16</sub>) | |57.6 (39.A<sub>16</sub>) | ||
| | 34/33, 36/35 | | | 34/33, 36/35 | ||
| Line 58: | Line 54: | ||
| | 4 | | | 4 | ||
| | 60 | | | 60 | ||
|76.8 (4C.D<sub>16</sub>) | |76.8 (4C.D<sub>16</sub>) | ||
| | 26/25, 28/27, 33/32, 35/34 | | | 26/25, 28/27, 33/32, 35/34 | ||
| Line 64: | Line 59: | ||
| | 5 | | | 5 | ||
| | 75 | | | 75 | ||
|96 (60<sub>16</sub>) | |96 (60<sub>16</sub>) | ||
| | 22/21, 25/24, 27/26 | | | 22/21, 25/24, 27/26 | ||
| Line 70: | Line 64: | ||
| | 6 | | | 6 | ||
| | 90 | | | 90 | ||
|115.2 (73.3<sub>16</sub>) | |115.2 (73.3<sub>16</sub>) | ||
| | 19/18, 20/19, 21/20 | | | 19/18, 20/19, 21/20 | ||
| Line 76: | Line 69: | ||
| | 7 | | | 7 | ||
| | 105 | | | 105 | ||
|134.4 (86.6<sub>16</sub>) | |134.4 (86.6<sub>16</sub>) | ||
| | 16/15, 17/16, 18/17 | | | 16/15, 17/16, 18/17 | ||
| Line 82: | Line 74: | ||
| | 8 | | | 8 | ||
| | 120 | | | 120 | ||
|153.6 (99.A<sub>16</sub>) | |153.6 (99.A<sub>16</sub>) | ||
| | 14/13, 15/14 | | | 14/13, 15/14 | ||
| Line 88: | Line 79: | ||
| | 9 | | | 9 | ||
| | 135 | | | 135 | ||
|172.8 (AC.D<sub>16</sub>) | |172.8 (AC.D<sub>16</sub>) | ||
| | 13/12 | | | 13/12 | ||
| Line 94: | Line 84: | ||
| | 10 | | | 10 | ||
| | 150 | | | 150 | ||
|192 (C0<sub>16</sub>) | |192 (C0<sub>16</sub>) | ||
| | 12/11 | | | 12/11 | ||
| Line 100: | Line 89: | ||
| | 11 | | | 11 | ||
| | 165 | | | 165 | ||
|211.2 (D3.3<sub>16</sub>) | |211.2 (D3.3<sub>16</sub>) | ||
| | 11/10 | | | 11/10 | ||
| Line 106: | Line 94: | ||
| | 12 | | | 12 | ||
| | 180 | | | 180 | ||
|230.4 (E6.6<sub>16</sub>) | |230.4 (E6.6<sub>16</sub>) | ||
| | 10/9, 21/19 | | | 10/9, 21/19 | ||
| Line 112: | Line 99: | ||
| | 13 | | | 13 | ||
| | 195 | | | 195 | ||
|249.6 (F9.A<sub>16</sub>) | |249.6 (F9.A<sub>16</sub>) | ||
| | 19/17 | | | 19/17 | ||
| Line 118: | Line 104: | ||
| | 14 | | | 14 | ||
| | 210 | | | 210 | ||
|268.8 (10C.D<sub>16</sub>) | |268.8 (10C.D<sub>16</sub>) | ||
| | 9/8, 17/15 | | | 9/8, 17/15 | ||
| Line 124: | Line 109: | ||
| | 15 | | | 15 | ||
| | 225 | | | 225 | ||
|288 (120<sub>16</sub>) | |288 (120<sub>16</sub>) | ||
| | 8/7 | | | 8/7 | ||
| Line 130: | Line 114: | ||
| | 16 | | | 16 | ||
| | 240 | | | 240 | ||
|307.2 (133.3<sub>16</sub>) | |307.2 (133.3<sub>16</sub>) | ||
| | | | | | ||
| Line 136: | Line 119: | ||
| | 17 | | | 17 | ||
| | 255 | | | 255 | ||
|326.4 (146.6<sub>16</sub>) | |326.4 (146.6<sub>16</sub>) | ||
| | 15/13, 22/19 | | | 15/13, 22/19 | ||
| Line 142: | Line 124: | ||
| | 18 | | | 18 | ||
| | 270 | | | 270 | ||
|345.6 (159.A<sub>16</sub>) | |345.6 (159.A<sub>16</sub>) | ||
| | 7/6 | | | 7/6 | ||
| Line 148: | Line 129: | ||
| | 19 | | | 19 | ||
| | 285 | | | 285 | ||
|364.8 (16C.D<sub>16</sub>) | |364.8 (16C.D<sub>16</sub>) | ||
| | 13/11, 20/17 | | | 13/11, 20/17 | ||
| Line 154: | Line 134: | ||
| | 20 | | | 20 | ||
| | 300 | | | 300 | ||
|384 (180<sub>16</sub>) | |384 (180<sub>16</sub>) | ||
| | 19/16, 25/21 | | | 19/16, 25/21 | ||
| Line 160: | Line 139: | ||
| | 21 | | | 21 | ||
| | 315 | | | 315 | ||
|403.2 (193.3<sub>16</sub>) | |403.2 (193.3<sub>16</sub>) | ||
| | 6/5 | | | 6/5 | ||
| Line 166: | Line 144: | ||
| | 22 | | | 22 | ||
| | 330 | | | 330 | ||
|422.4 (1A6.6<sub>16</sub>) | |422.4 (1A6.6<sub>16</sub>) | ||
| | 17/14 | | | 17/14 | ||
| Line 172: | Line 149: | ||
| | 23 | | | 23 | ||
| | 345 | | | 345 | ||
|441.6 (1B9.A<sub>16</sub>) | |441.6 (1B9.A<sub>16</sub>) | ||
| | 11/9 | | | 11/9 | ||
| Line 178: | Line 154: | ||
| | 24 | | | 24 | ||
| | 360 | | | 360 | ||
|460.8 (1CC.D<sub>16</sub>) | |460.8 (1CC.D<sub>16</sub>) | ||
| | 16/13, 21/17 | | | 16/13, 21/17 | ||
| Line 184: | Line 159: | ||
| | 25 | | | 25 | ||
| | 375 | | | 375 | ||
|480 (1E0<sub>16</sub>) | |480 (1E0<sub>16</sub>) | ||
| | | | | | ||
| Line 190: | Line 164: | ||
| | 26 | | | 26 | ||
| | 390 | | | 390 | ||
|499.2 (1F3.3<sub>16</sub>) | |499.2 (1F3.3<sub>16</sub>) | ||
| | 5/4 | | | 5/4 | ||
| Line 196: | Line 169: | ||
| | 27 | | | 27 | ||
| | 405 | | | 405 | ||
|518.4 (206.6<sub>16</sub>) | |518.4 (206.6<sub>16</sub>) | ||
| | 19/15, 24/19 | | | 19/15, 24/19 | ||
| Line 202: | Line 174: | ||
| | 28 | | | 28 | ||
| | 420 | | | 420 | ||
|537.6 (219.A<sub>16</sub>) | |537.6 (219.A<sub>16</sub>) | ||
| | 14/11 | | | 14/11 | ||
| Line 208: | Line 179: | ||
| | 29 | | | 29 | ||
| | 435 | | | 435 | ||
|556.8 (22C.D<sub>16</sub>) | |556.8 (22C.D<sub>16</sub>) | ||
| | 9/7 | | | 9/7 | ||
| Line 214: | Line 184: | ||
| | 30 | | | 30 | ||
| | 450 | | | 450 | ||
|576 (240<sub>16</sub>) | |576 (240<sub>16</sub>) | ||
| | 13/10, 22/17 | | | 13/10, 22/17 | ||
| Line 220: | Line 189: | ||
| | 31 | | | 31 | ||
| | 465 | | | 465 | ||
|595.2 (253.3<sub>16</sub>) | |595.2 (253.3<sub>16</sub>) | ||
| | 17/13 | | | 17/13 | ||
| Line 226: | Line 194: | ||
| | 32 | | | 32 | ||
| | 480 | | | 480 | ||
|614.4 (266.6<sub>16</sub>) | |614.4 (266.6<sub>16</sub>) | ||
| | 21/16, 25/19 | | | 21/16, 25/19 | ||
| Line 232: | Line 199: | ||
| | 33 | | | 33 | ||
| | 495 | | | 495 | ||
|633.6 (279.A<sub>16</sub>) | |633.6 (279.A<sub>16</sub>) | ||
| | 4/3 | | | 4/3 | ||
| Line 238: | Line 204: | ||
| | 34 | | | 34 | ||
| | 510 | | | 510 | ||
|652.8 (28C.D<sub>16</sub>) | |652.8 (28C.D<sub>16</sub>) | ||
| | | | | | ||
| Line 244: | Line 209: | ||
| | 35 | | | 35 | ||
| | 525 | | | 525 | ||
|672 (2A0<sub>16</sub>) | |672 (2A0<sub>16</sub>) | ||
| | 19/14 | | | 19/14 | ||
| Line 250: | Line 214: | ||
| | 36 | | | 36 | ||
| | 540 | | | 540 | ||
|691.2 (2B3.3<sub>16</sub>) | |691.2 (2B3.3<sub>16</sub>) | ||
| | 26/19 | | | 26/19 | ||
| Line 256: | Line 219: | ||
| | 37 | | | 37 | ||
| | 555 | | | 555 | ||
|710.4 (2C6.6<sub>16</sub>) | |710.4 (2C6.6<sub>16</sub>) | ||
| | 11/8 | | | 11/8 | ||
| Line 262: | Line 224: | ||
| | 38 | | | 38 | ||
| | 570 | | | 570 | ||
|729.6 (2D9.A<sub>16</sub>) | |729.6 (2D9.A<sub>16</sub>) | ||
| | 18/13 | | | 18/13 | ||
| Line 268: | Line 229: | ||
| | 39 | | | 39 | ||
| | 585 | | | 585 | ||
|748.8 (2EC.D<sub>16</sub>) | |748.8 (2EC.D<sub>16</sub>) | ||
| | 7/5 | | | 7/5 | ||
| Line 274: | Line 234: | ||
| | 40 | | | 40 | ||
| | 600 | | | 600 | ||
|768 (300<sub>16</sub>) | |768 (300<sub>16</sub>) | ||
| | 17/12, 24/17 | | | 17/12, 24/17 | ||
Revision as of 12:34, 12 December 2019
The 80 equal temperament, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 cents. 80et is the first equal temperament that represents the 19-limit tonality diamond consistently (it barely manages to do so).
80 et tempers out 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.
80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:
31&80 <<7 6 15 27 -24 -23 -20 ... ||
72&80 <<24 30 40 24 32 24 0 ... ||
34&80 <<2 -4 -50 22 16 2 -40 ... ||
46&80 <<2 -4 30 22 16 2 40 ... ||
29&80 <<3 34 45 33 24 -37 20 ... ||
12&80 <<4 -8 -20 -36 32 4 0 ... ||
22&80 <<6 -10 12 -14 -32 6 -40 ... ||
58&80 <<6 -10 12 -14 -32 6 40 ... ||
41&80 <<7 26 25 -3 -24 -33 20 ... ||
In each case, the numbers joined by an ampersand represent 19-limit patent vals (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.
Intervals of 80edo
| degrees | cents | 7mus | ratios* |
|---|---|---|---|
| 0 | 1/1 | ||
| 1 | 15 | 19.2 (13.316) | 64/63 |
| 2 | 30 | 38.4 (26.616) | 81/80 |
| 3 | 45 | 57.6 (39.A16) | 34/33, 36/35 |
| 4 | 60 | 76.8 (4C.D16) | 26/25, 28/27, 33/32, 35/34 |
| 5 | 75 | 96 (6016) | 22/21, 25/24, 27/26 |
| 6 | 90 | 115.2 (73.316) | 19/18, 20/19, 21/20 |
| 7 | 105 | 134.4 (86.616) | 16/15, 17/16, 18/17 |
| 8 | 120 | 153.6 (99.A16) | 14/13, 15/14 |
| 9 | 135 | 172.8 (AC.D16) | 13/12 |
| 10 | 150 | 192 (C016) | 12/11 |
| 11 | 165 | 211.2 (D3.316) | 11/10 |
| 12 | 180 | 230.4 (E6.616) | 10/9, 21/19 |
| 13 | 195 | 249.6 (F9.A16) | 19/17 |
| 14 | 210 | 268.8 (10C.D16) | 9/8, 17/15 |
| 15 | 225 | 288 (12016) | 8/7 |
| 16 | 240 | 307.2 (133.316) | |
| 17 | 255 | 326.4 (146.616) | 15/13, 22/19 |
| 18 | 270 | 345.6 (159.A16) | 7/6 |
| 19 | 285 | 364.8 (16C.D16) | 13/11, 20/17 |
| 20 | 300 | 384 (18016) | 19/16, 25/21 |
| 21 | 315 | 403.2 (193.316) | 6/5 |
| 22 | 330 | 422.4 (1A6.616) | 17/14 |
| 23 | 345 | 441.6 (1B9.A16) | 11/9 |
| 24 | 360 | 460.8 (1CC.D16) | 16/13, 21/17 |
| 25 | 375 | 480 (1E016) | |
| 26 | 390 | 499.2 (1F3.316) | 5/4 |
| 27 | 405 | 518.4 (206.616) | 19/15, 24/19 |
| 28 | 420 | 537.6 (219.A16) | 14/11 |
| 29 | 435 | 556.8 (22C.D16) | 9/7 |
| 30 | 450 | 576 (24016) | 13/10, 22/17 |
| 31 | 465 | 595.2 (253.316) | 17/13 |
| 32 | 480 | 614.4 (266.616) | 21/16, 25/19 |
| 33 | 495 | 633.6 (279.A16) | 4/3 |
| 34 | 510 | 652.8 (28C.D16) | |
| 35 | 525 | 672 (2A016) | 19/14 |
| 36 | 540 | 691.2 (2B3.316) | 26/19 |
| 37 | 555 | 710.4 (2C6.616) | 11/8 |
| 38 | 570 | 729.6 (2D9.A16) | 18/13 |
| 39 | 585 | 748.8 (2EC.D16) | 7/5 |
| 40 | 600 | 768 (30016) | 17/12, 24/17 |
- based on treating 80edo as a 19-limit temperament; other approaches are possible.