4650edo
Jump to navigation
Jump to search
Prime factorization
2 × 3 × 52 × 31
Step size
0.258065¢
Fifth
2720\4650 (701.935¢) (→272\465)
Semitones (A1:m2)
440:350 (113.5¢ : 90.32¢)
Consistency limit
15
Distinct consistency limit
15
| ← 4649edo | 4650edo | 4651edo → |
4650 equal divisions of the octave (abbreviated 4650edo or 4650ed2), also called 4650-tone equal temperament (4650tet) or 4650 equal temperament (4650et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4650 equal parts of about 0.258 ¢ each. Each step represents a frequency ratio of 21/4650, or the 4650th root of 2.
4650edo is consistent in the 15-odd-limit, with optional additions of 19 and 31. It provides the optimal patent val for the 30th-octave temperament zinc in the 7-limit and the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.020 | +0.009 | -0.052 | -0.092 | -0.012 | +0.077 | +0.035 | +0.113 | +0.100 | -0.003 |
| relative (%) | +0 | -8 | +3 | -20 | -36 | -4 | +30 | +14 | +44 | +39 | -1 | |
| Steps (reduced) |
4650 (0) |
7370 (2720) |
10797 (1497) |
13054 (3754) |
16086 (2136) |
17207 (3257) |
19007 (407) |
19753 (1153) |
21035 (2435) |
22590 (3990) |
23037 (4437) | |
Subsets and supersets
Since 4650 factors as 2 × 3 × 52 × 31, 4650edo has subset edos 1, 2, 3, 5, 6, 10, 15, 25, 30, 31, 50, 62, 75, 93, 150, 155, 186, 310, 465, 775, 930, 1550, 2325.