4650edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 4649edo4650edo4651edo →
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

4650 equal divisions of the octave (abbreviated 4650edo), or 4650-tone equal temperament (4650tet), 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 of 4650edo 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

Approximation of prime harmonics in 4650edo
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.