408edo

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← 407edo408edo409edo →
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

408 equal divisions of the octave (abbreviated 408edo), or 408-tone equal temperament (408tet), 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 of 408edo 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

Approximation of odd harmonics in 408edo
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.