| 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
|
408edo divides the octave into 408 steps of 2.9411 cents. It is inconsistent in the 5-limit, and mainly notable for being the optimal patent val for Argent Temperament, following after 169edo, 70edo, 29edo and 12edo. It's factors are 2^3, 3 & 17.
Approximation of prime intervals in 408 EDO
| Prime number
|
2
|
3
|
5
|
7
|
11
|
13
|
17
|
19
|
23
|
29
|
31
|
| Error
|
absolute (¢)
|
+0.00
|
+0.99
|
-1.02
|
-1.18
|
-1.32
|
+0.65
|
+0.93
|
-0.45
|
+1.14
|
-0.17
|
-0.92
|
| relative (%)
|
+0
|
+34
|
-35
|
-40
|
-45
|
+22
|
+32
|
-15
|
+39
|
-6
|
-31
|
| Steps (reduced)
|
408 (0)
|
647 (239)
|
947 (131)
|
1145 (329)
|
1411 (187)
|
1510 (286)
|
1668 (36)
|
1733 (101)
|
1846 (214)
|
1982 (350)
|
2021 (389)
|