408edo
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Prime factorization
23 × 3 × 17
Step size
2.94118¢
Fifth
239\408 (702.941¢)
Semitones (A1:m2)
41:29 (120.6¢ : 85.29¢)
Dual sharp fifth
239\408 (702.941¢)
Dual flat fifth
238\408 (700¢) (→7\12)
Dual major 2nd
69\408 (202.941¢) (→23\136)
Consistency limit
3
Distinct consistency limit
3
| ← 407edo | 408edo | 409edo → |
408 equal divisions of the octave (abbreviated 408edo or 408ed2), also called 408-tone equal temperament (408tet) or 408 equal temperament (408et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 408 equal parts of about 2.94 ¢ each. Each step represents a frequency ratio of 21/408, or the 408th root of 2.
408edo is inconsistent to the 5-odd-limit and the errors of the lower harmonics are all quite large. It is mainly notable for being the optimal patent val for the argent temperament, following 169edo, 70edo, 29edo and 12edo.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.99 | -1.02 | -1.18 | -0.97 | -1.32 | +0.65 | -0.03 | +0.93 | -0.45 | -0.19 | +1.14 |
| relative (%) | +34 | -35 | -40 | -33 | -45 | +22 | -1 | +32 | -15 | -7 | +39 | |
| Steps (reduced) |
647 (239) |
947 (131) |
1145 (329) |
1293 (69) |
1411 (187) |
1510 (286) |
1594 (370) |
1668 (36) |
1733 (101) |
1792 (160) |
1846 (214) | |
Subsets and supersets
Since 408 factors into 23 × 3 × 17, 408edo has subset edos 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204.