8ed7

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8ed7

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Prime factorization	23
Step size	421.103¢
Octave	3\8ed7 (1263.31¢) (semiconvergent)
Twelfth	5\8ed7 (2105.52¢)
Consistency limit	5
Distinct consistency limit	2

8 equal divisions of the 7th harmonic (abbreviated 8ed7) is a nonoctave tuning system that divides the interval of 7/1 into 8 equal parts of about 421⁠ ⁠¢ each. Each step represents a frequency ratio of 7^1/8, or the 8th root of 7.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	421.1	5/4, 13/10, 14/11, 17/13, 22/17
2	842.2	5/3, 8/5, 13/8, 21/13
3	1263.3	17/8, 21/10
4	1684.4	8/3, 13/5, 19/7, 21/8
5	2105.5	10/3, 17/5
6	2526.6	13/3, 17/4, 21/5, 22/5
7	2947.7	11/2
8	3368.8	7/1

Harmonics

Approximation of prime harmonics in 8ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+63	+204	+161	+0	+60	+192	+148	-44	+46	+66	-50
	Relative (%)	+15.0	+48.3	+38.3	+0.0	+14.2	+45.5	+35.2	-10.5	+10.9	+15.6	-11.8
Steps (reduced)		3 (3)	5 (5)	7 (7)	8 (0)	10 (2)	11 (3)	12 (4)	12 (4)	13 (5)	14 (6)	14 (6)

Approximation of prime harmonics in 8ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+65	-113	-195	+72	-136	+100	+42	-121	+200	+152	+15
	Relative (%)	+15.5	-26.7	-46.3	+17.1	-32.3	+23.6	+9.9	-28.6	+47.5	+36.1	+3.6
Steps (reduced)		15 (7)	15 (7)	15 (7)	16 (0)	16 (0)	17 (1)	17 (1)	17 (1)	18 (2)	18 (2)	18 (2)

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