9ed7

← 8ed7

9ed7

10ed7 →

Prime factorization	32
Step size	374.314¢
Octave	3\9ed7 (1122.94¢) (→1\3ed7)
Twelfth	5\9ed7 (1871.57¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	3

9 equal divisions of the 7th harmonic (abbreviated 9ed7) is a nonoctave tuning system that divides the interval of 7/1 into 9 equal parts of about 374⁠ ⁠¢ each. Each step represents a frequency ratio of 7^1/9, or the 9th root of 7.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	374.3	5/4, 11/9, 17/14, 21/17
2	748.6	11/7, 14/9, 17/11
3	1122.9	15/8, 17/9, 21/11
4	1497.3	7/3, 12/5, 17/7
5	1871.6	3/1
6	2245.9	11/3, 18/5
7	2620.2	9/2
8	2994.5	17/3
9	3368.8	7/1

Harmonics

Approximation of prime harmonics in 9ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-77	-30	-166	+0	-34	+51	-39	+143	+186	+159	+44
	Relative (%)	-20.6	-8.1	-44.4	+0.0	-9.0	+13.7	-10.4	+38.2	+49.8	+42.6	+11.8
Steps (reduced)		3 (3)	5 (5)	7 (7)	9 (0)	11 (2)	12 (3)	13 (4)	14 (5)	15 (6)	16 (7)	16 (7)

Approximation of prime harmonics in 9ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+112	-66	-148	+72	-136	+53	-5	-167	+107	+58	-78
	Relative (%)	+29.9	-17.6	-39.6	+19.3	-36.3	+14.1	-1.3	-44.7	+28.5	+15.6	-20.9
Steps (reduced)		17 (8)	17 (8)	17 (8)	18 (0)	18 (0)	19 (1)	19 (1)	19 (1)	20 (2)	20 (2)	20 (2)

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