9ed5

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9ed5

10ed5 →

Prime factorization	32
Step size	309.59 ¢
Octave	4\9ed5 (1238.36 ¢) (semiconvergent)
Twelfth	6\9ed5 (1857.54 ¢) (→ 2\3ed5)
Consistency limit	7
Distinct consistency limit	3

9 equal divisions of the 5th harmonic (abbreviated 9ed5) is a nonoctave tuning system that divides the interval of 5/1 into 9 equal parts of about 310 ¢ each. Each step represents a frequency ratio of 5^1/9, or the 9th root of 5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	309.6	6/5, 11/9, 13/11, 17/14, 20/17
2	619.2	7/5, 10/7, 13/9, 17/12, 19/13
3	928.8	12/7, 17/10, 19/11, 22/13
4	1238.4	2/1
5	1548	5/2, 12/5, 17/7, 22/9
6	1857.5
7	2167.1	7/2
8	2476.7	17/4, 21/5
9	2786.3	5/1

Harmonics

Approximation of harmonics in 9ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+38	-44	+77	+0	-6	+37	+115	-89	+38	-127	+32
	Relative (%)	+12.4	-14.3	+24.8	+0.0	-2.0	+11.8	+37.2	-28.7	+12.4	-40.9	+10.4
Steps (reduced)		4 (4)	6 (6)	8 (8)	9 (0)	10 (1)	11 (2)	12 (3)	12 (3)	13 (4)	13 (4)	14 (5)

Approximation of harmonics in 9ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-106	+75	-44	+153	+48	-50	-144	+77	-8	-88	+144
	Relative (%)	-34.3	+24.2	-14.3	+49.6	+15.7	-16.3	-46.5	+24.8	-2.5	-28.5	+46.6
Steps (reduced)		14 (5)	15 (6)	15 (6)	16 (7)	16 (7)	16 (7)	16 (7)	17 (8)	17 (8)	17 (8)	18 (0)