641edo
| ← 640edo | 641edo | 642edo → |
Theory
641edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.11.13.17 subgroup, tempering out 625/624, 2431/2430, 1089/1088, 4225/4224 and 1384448000/1382278041.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.073 | -0.666 | +0.909 | +0.146 | -0.928 | +0.034 | -0.593 | -0.119 | +0.147 | -0.890 | +0.743 |
| Relative (%) | +3.9 | -35.6 | +48.5 | +7.8 | -49.6 | +1.8 | -31.7 | -6.4 | +7.8 | -47.5 | +39.7 | |
| Steps (reduced) |
1016 (375) |
1488 (206) |
1800 (518) |
2032 (109) |
2217 (294) |
2372 (449) |
2504 (581) |
2620 (56) |
2723 (159) |
2815 (251) |
2900 (336) | |
Subsets and supersets
641edo is the 116th prime EDO. 1282edo, which doubles it, gives a good correction to the harmonic 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [1016 -641⟩ | [⟨641 1016]] | -0.0231 | 0.0231 | 1.23 |
| 2.3.5 | [24 -21 4⟩, [-56 -13 33⟩ | [⟨641 1016 1488]] | +0.0803 | 0.1474 | 7.87 |
| 2.3.5.11 | 166375/165888, 234375/234256, 10485760000/10460353203 | [⟨641 1016 1488 2217]] | +0.1273 | 0.1514 | 8.09 |
| 2.3.5.11.13 | 625/624, 4225/4224, 17303/17280, 10485760000/10460353203 | [⟨641 1016 1488 2217 2372]] | +0.1000 | 0.1460 | 7.80 |
| 2.3.5.11.13.17 | 625/624, 2431/2430, 1089/1088, 4225/4224, 1384448000/1382278041 | [⟨641 1016 1488 2217 2372 2620]] | +0.0882 | 0.1358 | 7.25 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 254\641 | 475.507 | 320/243 | Vulture |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct