449edo
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Prime factorization
449 (prime)
Step size
2.67261¢
Fifth
263\449 (702.895¢)
Semitones (A1:m2)
45:32 (120.3¢ : 85.52¢)
Dual sharp fifth
263\449 (702.895¢)
Dual flat fifth
262\449 (700.223¢)
Dual major 2nd
76\449 (203.118¢)
Consistency limit
7
Distinct consistency limit
7
| ← 448edo | 449edo | 450edo → |
449 equal divisions of the octave (449edo), or 449-tone equal temperament (449tet), 449 equal temperament (449et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 449 equal parts of about 2.67 ¢ each.
Theory
449et tempers out 26873856/26796875 and 4375/4374 in the 7-limit; 100663296/100656875, 117440512/117406179, 4302592/4296875, 825000/823543, 85937500/85766121, 160083/160000, 41503/41472, 539055/537824 and 805255/802816 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 | +45 | +50 | -30 | -28 | -50 | -19 | -27 | -32 | -15 | -8 | |
| 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
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-1423 449⟩ | ⟨449 1423] | 0.1249 | 0.1249 | 4.67 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 127\449 | 339.421 | 243\200 | Amity (7-limit) |