460edo
| ← 459edo | 460edo | 461edo → |
Theory
460edo is a very strong 19-limit system and is distinctly consistent to the 21-odd-limit, with harmonics of 3 to 19 all tuned flat.
The equal temperament 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, the 171 & 289 temperament. In the 11-limit it tempers of 3025/3024 and 9801/9800, and 43923/43904; in the 13-limit 1001/1000, 4225/4224 and 10648/10647, so that it supports deca, the 190 & 270 temperament; 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-5 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) | |
Subsets and supersets
Since 460 factors into 22 × 5 × 23, 460edo has subset edos 2, 4, 5, 10, 20, 23, 46, 92, 115, and 230.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-729 460⟩ | [⟨460 729]] | +0.0681 | 0.0681 | 2.61 |- | 2.3.5 | 32805/32768, [6 68 -49⟩ | [⟨460 729 1068]] | +0.0780 | 0.0573 | 2.20 |- | 2.3.5.7 | 4375/4374, 32805/32768, [-4 -2 -9 10⟩ | [⟨460 729 1068 1291]] | +0.1475 | 0.1303 | 4.99 |- | 2.3.5.7.11 | 3025/3024, 4375/4374, 32805/32768, 184877/184320 | [⟨460 729 1068 1291 1591]] | +0.1691 | 0.1243 | 4.76 |- | 2.3.5.7.11.13 | 1001/1000, 3025/3024, 4225/4224, 4375/4374, 26411/26364 | [⟨460 729 1068 1291 1591 1702]] | +0.1647 | 0.1139 | 4.36 |- | 2.3.5.7.11.13.17 | 833/832, 1001/1000, 1089/1088, 1225/1224, 1701/1700, 4225/4224 | [⟨460 729 1068 1291 1591 1702 1880]] | +0.1624 | 0.1056 | 4.05 |- | 2.3.5.7.11.13.17.19 | 833/832, 1001/1000, 1089/1088, 1225/1224, 1331/1330, 1445/1444, 1617/1615 | [⟨460 729 1068 1291 1591 1702 1880 1954]] | +0.1457 | 0.1082 | 4.15 Template:Comma basis end
- 460et has lower absolute errors in the 17- and 19-limit than any previous equal temperaments. It beats 422 in either subgroup, and is bettered by 494 in the 17-limit, and 525 in the 19-limit.
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 9\460
| 23.48
| 531441/524288
| Commatose
|-
| 1
| 121\460
| 315.65
| 6/5
| Egads
|-
| 1
| 191\460
| 498.26
| 4/3
| Pontiac
|-
| 10
| 121\460
(17\460)
| 315.65
(44.35)
| 6/5
(40/39)
| Deca
|-
| 20
| 66\460
(20\460)
| 172.173
(52.173)
| 169/153
(?)
| Calcium
|-
| 20
| 217\460
(10\460)
| 566.086
(26.086)
| 238/165
(?)
| Soviet ferris wheel
Template:Rank-2 end
Template:Orf