408edo

← 407edo

408edo

409edo →

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 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 2^1/408, 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 (%)	+33.5	-34.7	-40.1	-32.9	-44.8	+22.1	-1.1	+31.5	-15.4	-6.6	+38.7
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.