460edo
The 460 equal divisions of the octave divides the octave into 460 equal parts of 2.609 cents each.
460edo is a very strong 19-limit system and is uniquely consistent to the 21-odd-limit, with harmonics of 3 to 19 all tuned flat. It tempers out the schisma, 32805/32768, in the 5-limit and 4375/4374 and 65536/65625 in the 7-limit, so that it supports pontiac. In the 11-limit it tempers of 43923/43904, 3025/3024 and 9801/9800; in the 13-limit 1001/1000, 4225/4224 and 10648/10647; in the 17-limit 833/832, 1089/1088, 1225/1224, 1701/1700, 2058/2057, 2431/2430, 2601/2600 and 4914/4913; and in the 19-limit 1331/1330, 1445/1444, 1521/1520, 1540/1539, 1729/1728, 2376/2375, 2926/2925, 3136/3135, 3250/3249 and 4200/4199. It serves as the optimal patent val for various temperaments such as the rank five temperament tempering out 833/832 and 1001/1000.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.22 | -0.23 | -1.00 | -0.88 | -0.53 | -0.61 | -0.12 | +0.42 | +0.86 | +0.18 |
| Relative (%) | +0.0 | -8.3 | -8.7 | -38.3 | -33.9 | -20.2 | -23.3 | -4.7 | +16.2 | +32.9 | +7.0 | |
| Steps (reduced) |
460 (0) |
729 (269) |
1068 (148) |
1291 (371) |
1591 (211) |
1702 (322) |
1880 (40) |
1954 (114) |
2081 (241) |
2235 (395) |
2279 (439) | |