463edo
Theory
463et tempers out 184528125/184473632, 4096000/4084101, 703125/702464, 67108864/66976875, 95703125/95551488, 359661568/358722675 and 420175/419904 in the 7-limit; 161280/161051, 25165824/25109315, 820125/819896, 29296875/29218112, 1019215872/1019046875, 4000/3993, 759375/758912, 117649/117612, 2359296/2358125, 6250/6237, 369140625/369098752, 200704/200475, 283115520/282475249, 825000/823543, 180224/180075, 537109375/536870912, 19712/19683, 3025/3024, 199297406/199290375, 1362944/1361367, 532400/531441, 3294225/3294172 and 1771561/1771470 in the 11-limit. It provides the optimal patent val for the temperaments Amity, Trinity until the 11-limit and Undesemi. 463edo is the 90th prime edo.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.42 | -0.14 | +0.50 | +0.73 | -0.79 | -1.28 | +0.54 | -1.06 | -0.64 | +0.54 |
| Relative (%) | +0.0 | +16.2 | -5.3 | +19.5 | +28.3 | -30.4 | -49.5 | +21.0 | -40.9 | -24.5 | +20.7 | |
| Steps (reduced) |
463 (0) |
734 (271) |
1075 (149) |
1300 (374) |
1602 (213) |
1713 (324) |
1892 (40) |
1967 (115) |
2094 (242) |
2249 (397) |
2294 (442) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [734 -463⟩ | ⟨463 734] | -0.1328 | 0.1327 | 5.12 |
| 2.3.5 | [9 -13 5⟩, [91 -12 -31⟩ | ⟨463 734 1075] | -0.0689 | 0.1411 | 5.44 |
| 2.3.5.7 | 420175/419904, 703125/702464, 1600000/1594323 | ⟨463 734 1075 1300] | -0.0966 | 0.1313 | 5.07 |
| 2.3.5.7.11 | 3025/3024, 6250/6237, 19712/19683, 180224/180075 | ⟨463 734 1075 1300 1602] | -0.1197 | 0.1262 | 4.87 |
| 2.3.5.7.11.13 | 3025/3024, 1716/1715, 4096/4095, 676/675, 6250/6237 | ⟨463 734 1075 1300 1602 1713] | -0.0643 | 0.1691 | 6.52 |
| 2.3.5.7.11.13.17 | 442/441, 595/594, 1275/1274, 2601/2600, 3025/3024, 32955/32912, 45500/45441 | ⟨463 734 1075 1300 1602 1713 1892] | -0.0103 | 0.2051 | 7.91 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 131\463 | 339.52 | 243/200 | Amity |
| 1 | 198\463 | 513.17 | 168/125, 121/90 | Trinity |
| 1 | 31\463 | 80.35 | 8575/8192, 22/21 | Undesemi |