449edo
| ← 448edo | 449edo | 450edo → |
Theory
449edo is consistent to the 7-odd-limit, but the errors of harmonics 3, 5, and 7 are all quite large, giving us the option of treating it as a full 7-limit temperament, or a 2.9.15.21.11.13 subgroup temperament.
Using the patent val, the equal temperament tempers out 4375/4374 and 26873856/26796875 in the 7-limit; 41503/41472, 160083/160000, 539055/537824, 805255/802816, and 825000/823543 in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.94 | +1.21 | +1.33 | -0.79 | -0.76 | -1.33 | -0.52 | -0.72 | -0.85 | -0.40 | -0.21 |
| Relative (%) | +35.2 | +45.4 | +49.8 | -29.6 | -28.5 | -49.7 | -19.4 | -27.1 | -31.9 | -15.1 | -7.9 | |
| Steps (reduced) |
712 (263) |
1043 (145) |
1261 (363) |
1423 (76) |
1553 (206) |
1661 (314) |
1754 (407) |
1835 (39) |
1907 (111) |
1972 (176) |
2031 (235) | |
Subsets and supersets
449edo is the 87th prime edo. 898edo, which doubles it, gives a good correction to the harmonic 3, 5 and 7.
Regular temperament properties
Template:Comma basis begin |- | 2.9 | [-1423 449⟩ | [⟨449 1423]] | 0.1249 | 0.1249 | 4.67 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 127\449 | 339.421 | 243\200 | Amity (7-limit) Template:Rank-2 end Template:Orf
Music
- Little Victorious Dance (2023)