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'''32EDT''' is the [[Edt|equal division of the third harmonic]] into 32 parts of 59.4361 [[cent|cents]] each, corresponding to 20.1898 [[edo]]. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, and 19 are all sharp. It tempers out 3125/3087 in the 7-limit; 891/875, 1331/1323 and 2475/2401 in the 11-limit; 275/273, 351/343, 729/ | '''32EDT''' is the [[Edt|equal division of the third harmonic]] into 32 parts of 59.4361 [[cent|cents]] each, corresponding to 20.1898 [[edo]]. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, and 19 are all sharp. It tempers out 3125/3087 and 885735/823543 in the 7-limit; 891/875, 1331/1323, and 2475/2401 in the 11-limit; 275/273, 351/343, 729/715, and 847/845 in the 13-limit; 121/119, 189/187, 225/221, 459/455, and 845/833 in the 17-limit; 135/133, 171/169, 247/245, 325/323, and 363/361 in the 19-limit (no-twos subgroup). It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|zeta peak tritave division]]. | ||
=Intervals= | =Intervals= | ||
Revision as of 06:38, 15 February 2019
32EDT is the equal division of the third harmonic into 32 parts of 59.4361 cents each, corresponding to 20.1898 edo. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, and 19 are all sharp. It tempers out 3125/3087 and 885735/823543 in the 7-limit; 891/875, 1331/1323, and 2475/2401 in the 11-limit; 275/273, 351/343, 729/715, and 847/845 in the 13-limit; 121/119, 189/187, 225/221, 459/455, and 845/833 in the 17-limit; 135/133, 171/169, 247/245, 325/323, and 363/361 in the 19-limit (no-twos subgroup). It is the eighth zeta peak tritave division.
Intervals
| step | cents |
|---|---|
| 1 | 59.436 |
| 2 | 118.872 |
| 3 | 178.308 |
| 4 | 237.744 |
| 5 | 297.180 |
| 6 | 356.617 |
| 7 | 416.053 |
| 8 | 475.489 |
| 9 | 534.925 |
| 10 | 594.361 |
| 11 | 653.797 |
| 12 | 713.233 |
| 13 | 772.669 |
| 14 | 832.105 |
| 15 | 891.541 |
| 16 | 950.978 |
| 17 | 1010.414 |
| 18 | 1069.850 |
| 19 | 1129.286 |
| 20 | 1188.722 |
| 21 | 1248.158 |
| 22 | 1307.594 |
| 23 | 1367.030 |
| 24 | 1426.466 |
| 25 | 1485.902 |
| 26 | 1545.338 |
| 27 | 1604.775 |
| 28 | 1664.211 |
| 29 | 1723.647 |
| 30 | 1783.083 |
| 31 | 1842.519 |
| 32 | 1901.955 |