32edt: Difference between revisions
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''32edt'' means the division of 3, the tritave, into 32 equal parts of 59.436 cents each, corresponding to 20.190 edo. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13 and 17 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, 729/714, 847/845 and 1575/1573 in the 13-limit, 121/119, 189/197 and 225/221 in the 17-limit. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|zeta peak tritave division]]. | ''32edt'' means the division of 3, the tritave, into 32 equal parts of 59.436 cents each, corresponding to 20.190 edo. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13 and 17 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, 729/714, 847/845 and 1575/1573 in the 13-limit, 121/119, 189/197 and 225/221 in the 17-limit. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|zeta peak tritave division]]. | ||
= | =Intervals= | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |||
! step | |||
! cents | |||
|- | |- | ||
| | 1 | | | 1 | ||
| | 59. | | | 59.436 | ||
|- | |- | ||
| | 2 | | | 2 | ||
| | 118. | | | 118.872 | ||
|- | |- | ||
| | 3 | | | 3 | ||
| | 178. | | | 178.308 | ||
|- | |- | ||
| | 4 | | | 4 | ||
| | 237. | | | 237.744 | ||
|- | |- | ||
| | 5 | | | 5 | ||
| | 297. | | | 297.180 | ||
|- | |- | ||
| | 6 | | | 6 | ||
| | 356. | | | 356.617 | ||
|- | |- | ||
| | 7 | | | 7 | ||
| | 416. | | | 416.053 | ||
|- | |- | ||
| | 8 | | | 8 | ||
| | 475. | | | 475.489 | ||
|- | |- | ||
| | 9 | | | 9 | ||
| | 534. | | | 534.925 | ||
|- | |- | ||
| | 10 | | | 10 | ||
| | 594. | | | 594.361 | ||
|- | |- | ||
| | 11 | | | 11 | ||
| | 653. | | | 653.797 | ||
|- | |- | ||
| | 12 | | | 12 | ||
| | 713. | | | 713.233 | ||
|- | |- | ||
| | 13 | | | 13 | ||
| | 772. | | | 772.669 | ||
|- | |- | ||
| | 14 | | | 14 | ||
| | 832. | | | 832.105 | ||
|- | |- | ||
| | 15 | | | 15 | ||
| | 891. | | | 891.541 | ||
|- | |- | ||
| | 16 | | | 16 | ||
| | 950. | | | 950.978 | ||
|- | |- | ||
| | 17 | | | 17 | ||
| | 1010. | | | 1010.414 | ||
|- | |- | ||
| | 18 | | | 18 | ||
| | 1069. | | | 1069.850 | ||
|- | |- | ||
| | 19 | | | 19 | ||
| | 1129. | | | 1129.286 | ||
|- | |- | ||
| | 20 | | | 20 | ||
| | 1188. | | | 1188.722 | ||
|- | |- | ||
| | 21 | | | 21 | ||
| | 1248. | | | 1248.158 | ||
|- | |- | ||
| | 22 | | | 22 | ||
| | 1307. | | | 1307.594 | ||
|- | |- | ||
| | 23 | | | 23 | ||
| | 1367. | | | 1367.030 | ||
|- | |- | ||
| | 24 | | | 24 | ||
| | 1426. | | | 1426.466 | ||
|- | |- | ||
| | 25 | | | 25 | ||
| | 1485. | | | 1485.902 | ||
|- | |- | ||
| | 26 | | | 26 | ||
| | 1545. | | | 1545.338 | ||
|- | |- | ||
| | 27 | | | 27 | ||
| | 1604. | | | 1604.775 | ||
|- | |- | ||
| | 28 | | | 28 | ||
| | 1664. | | | 1664.211 | ||
|- | |- | ||
| | 29 | | | 29 | ||
| | 1723. | | | 1723.647 | ||
|- | |- | ||
| | 30 | | | 30 | ||
| | 1783. | | | 1783.083 | ||
|- | |- | ||
| | 31 | | | 31 | ||
| | 1842. | | | 1842.519 | ||
|- | |- | ||
| | 32 | | | 32 | ||
| | 1901.955 | | | 1901.955 | ||
|} | |} |