6650edo

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6650edo

6651edo →

Prime factorization	2 × 52 × 7 × 19
Step size	0.180451 ¢
Fifth	3890\6650 (701.955 ¢) (→ 389\665)
Semitones (A1:m2)	630:500 (113.7 ¢ : 90.23 ¢)
Consistency limit	15
Distinct consistency limit	15

6650 equal divisions of the octave (abbreviated 6650edo or 6650ed2), also called 6650-tone equal temperament (6650tet) or 6650 equal temperament (6650et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 6650 equal parts of about 0.18 ¢ each. Each step represents a frequency ratio of 2^1/6650, or the 6650th root of 2.

This system is consistent up to the 15-odd-limit and shares the same super accurate fifth with 665edo. In the 11-limit, it tempers out 9801/9800, and in the 13-limit, 123201/123200.

Prime harmonics

Approximation of prime harmonics in 6650edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	-0.0001	+0.0322	+0.0162	-0.0397	+0.0137	+0.0671	+0.0509	+0.0565	+0.0769	-0.0732
	Relative (%)	+0.0	-0.1	+17.8	+9.0	-22.0	+7.6	+37.2	+28.2	+31.3	+42.6	-40.5
Steps (reduced)		6650 (0)	10540 (3890)	15441 (2141)	18669 (5369)	23005 (3055)	24608 (4658)	27182 (582)	28249 (1649)	30082 (3482)	32306 (5706)	32945 (6345)

Subsets and supersets

Since 6650 factors into 2 × 5² × 7 × 19, 6650edo has subset edos 2, 5, 7, 10, 14, 19, 25, 35, 38, 50, 70, 95, 133, 175, 190, 266, 350, 475, 665, 950, 1330, and 3325.