9ed5/2

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9ed5/2

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Prime factorization	32
Step size	176.257 ¢
Octave	7\9ed5/2 (1233.8 ¢) (semiconvergent)
Twelfth	11\9ed5/2 (1938.83 ¢)
Consistency limit	6
Distinct consistency limit	5

9 equal divisions of 5/2 (abbreviated 9ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 9 equal parts of about 176 ¢ each. Each step represents a frequency ratio of (5/2)^1/9, or the 9th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	176.3	9/8, 10/9, 11/10, 12/11, 19/17, 21/19
2	352.5	5/4, 6/5, 11/9, 17/14, 21/17
3	528.8	4/3, 11/8, 15/11, 19/14
4	705	3/2
5	881.3	5/3, 17/10, 18/11
6	1057.5	11/6, 13/7, 15/8, 20/11
7	1233.8	2/1
8	1410.1	9/4, 20/9
9	1586.3	5/2, 22/9

Harmonics

Approximation of harmonics in 9ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+33.8	+36.9	+67.6	+33.8	+70.7	-19.9	-74.9	+73.7	+67.6	+78.9	-71.8
	Relative (%)	+19.2	+20.9	+38.4	+19.2	+40.1	-11.3	-42.5	+41.8	+38.4	+44.7	-40.7
Steps (reduced)		7 (7)	11 (2)	14 (5)	16 (7)	18 (0)	19 (1)	20 (2)	22 (4)	23 (5)	24 (6)	24 (6)

Approximation of harmonics in 9ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-34.1	+13.9	+70.7	-41.1	+30.2	-68.7	+13.9	-74.9	+16.9	-63.6	+35.7
	Relative (%)	-19.3	+7.9	+40.1	-23.3	+17.2	-39.0	+7.9	-42.5	+9.6	-36.1	+20.3
Steps (reduced)		25 (7)	26 (8)	27 (0)	27 (0)	28 (1)	28 (1)	29 (2)	29 (2)	30 (3)	30 (3)	31 (4)