6ed7

6 equal divisions of the 7th harmonic (abbreviated 6ed7) is a nonoctave tuning system that divides the interval of 7/1 into 6 equal parts of about 561 ¢ each. Each step represents a frequency ratio of 7^1/6, or the 6th root of 7.

← 5ed7

6ed7

7ed7 →

Prime factorization	2 × 3 (highly composite)
Step size	561.471 ¢
Octave	2\6ed7 (1122.94 ¢) (→ 1\3ed7)
Twelfth	3\6ed7 (1684.41 ¢) (→ 1\2ed7)
Consistency limit	5
Distinct consistency limit	3

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	561.5	7/5, 10/7, 11/8, 15/11, 19/14
2	1122.9	13/7, 15/8, 19/10, 21/11
3	1684.4	8/3, 13/5, 19/7, 21/8
4	2245.9	11/3, 15/4
5	2807.4	5/1
6	3368.8	7/1

Harmonics

Approximation of prime harmonics in 5ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+148	+119	-91	+0	-109	+276	-189	+293	-38	+234	+119
	Relative (%)	+21.9	+17.7	-13.5	+0.0	-16.1	+40.9	-28.0	+43.4	-5.7	+34.8	+17.6
Steps (reduced)		2 (2)	3 (3)	4 (4)	5 (0)	6 (1)	7 (2)	7 (2)	8 (3)	8 (3)	9 (4)	9 (4)

Approximation of prime harmonics in 5ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-187	+309	+226	+72	-136	-322	+295	+132	+32	-16	-153
	Relative (%)	-27.8	+45.8	+33.6	+10.7	-20.2	-47.7	+43.7	+19.6	+4.7	-2.4	-22.7
Steps (reduced)		9 (4)	10 (0)	10 (0)	10 (0)	10 (0)	10 (0)	11 (1)	11 (1)	11 (1)	11 (1)	11 (1)

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