6ed5

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6ed5

7ed5 →

Prime factorization	2 × 3 (highly composite)
Step size	464.386 ¢
Octave	3\6ed5 (1393.16 ¢) (→ 1\2ed5)
Twelfth	4\6ed5 (1857.54 ¢) (→ 2\3ed5)
Consistency limit	2
Distinct consistency limit	2

6 equal divisions of the 5th harmonic (abbreviated 6ed5) is a nonoctave tuning system that divides the interval of 5/1 into 6 equal parts of about 464 ¢ each. Each step represents a frequency ratio of 5^1/6, or the 6th root of 5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	464.4	9/7, 13/10, 14/11, 17/13, 19/15
2	928.8	5/3, 17/10, 19/11
3	1393.2	11/5, 13/6
4	1857.5	3/1, 17/6
5	2321.9	19/5
6	2786.3	5/1

Harmonics

Approximation of harmonics in 6ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+193	-44	-78	+0	+149	-118	+115	-89	+193	+28	-122
	Relative (%)	+41.6	-9.6	-16.8	+0.0	+32.0	-25.4	+24.8	-19.1	+41.6	+6.1	-26.4
Steps (reduced)		3 (3)	4 (4)	5 (5)	6 (0)	7 (1)	7 (1)	8 (2)	8 (2)	9 (3)	9 (3)	9 (3)

Approximation of harmonics in 6ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+203	+75	-44	-156	+203	+104	+11	-78	-163	+221	+144
	Relative (%)	+43.8	+16.2	-9.6	-33.6	+43.8	+22.5	+2.3	-16.8	-35.0	+47.7	+31.1
Steps (reduced)		10 (4)	10 (4)	10 (4)	10 (4)	11 (5)	11 (5)	11 (5)	11 (5)	11 (5)	12 (0)	12 (0)