4650edo

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4650edo

4651edo →

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 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 2^1/4650, or the 4650th root of 2.

4650edo is consistent in the 15-odd-limit, with optional additions of 19 and 31. Some of the simpler commas it tempers out include 250047/250000 in the 7-limit; 9801/9800 and 151263/151250 in the 11-limit; 10648/10647 and 123201/123200 in the 13-limit. 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 (%)	+0.0	-7.6	+3.4	-20.0	-35.7	-4.5	+29.8	+13.7	+43.7	+38.8	-1.3
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 2, 3, 5, 6, 10, 15, 25, 30, 31, 50, 62, 75, 93, 150, 155, 186, 310, 465, 775, 930, 1550, 2325.