12ed9/5

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12ed9/5

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Prime factorization	22 × 3
Step size	84.7997¢
Octave	14\12ed9/5 (1187.2¢) (→7\6ed9/5)
Twelfth	22\12ed9/5 (1865.59¢) (→11\6ed9/5)
Consistency limit	4
Distinct consistency limit	2
Special properties	Highly composite

12 equal divisions of 9/5 (abbreviated 12ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 12 equal parts of about 84.8 ¢ each. Each step represents a frequency ratio of (9/5)^1/12, or the 12th root of 9/5.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	84.8	16/15, 20/19, 21/20, 22/21, 23/22
2	169.599	11/10, 19/17, 21/19, 23/21
3	254.399	15/13, 20/17, 22/19, 23/20
4	339.199	16/13, 17/14, 21/17, 23/19
5	423.998	14/11, 19/15, 22/17
6	508.798	4/3, 15/11, 19/14, 23/17
7	593.598	7/5, 10/7
8	678.398	3/2, 19/13, 22/15
9	763.197	11/7, 17/11, 20/13, 23/15
10	847.997	13/8, 21/13, 23/14
11	932.797	17/10, 19/11, 22/13
12	1017.596	16/9, 20/11

Harmonics

Approximation of harmonics in 12ed9/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-12.8	-36.4	-25.6	+12.1	+35.6	+23.2	-38.4	+12.1	-0.7	+3.9	+22.8
	Relative (%)	-15.1	-42.9	-30.2	+14.2	+42.0	+27.3	-45.3	+14.2	-0.9	+4.6	+26.9
Steps (reduced)		14 (2)	22 (10)	28 (4)	33 (9)	37 (1)	40 (4)	42 (6)	45 (9)	47 (11)	49 (1)	51 (3)

Approximation of harmonics in 12ed9/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-30.9	+10.4	-24.3	+33.6	+13.4	-0.7	-9.5	-13.5	-13.2	-8.9	-1.1
	Relative (%)	-36.5	+12.2	-28.6	+39.6	+15.8	-0.9	-11.2	-16.0	-15.6	-10.5	-1.3
Steps (reduced)		52 (4)	54 (6)	55 (7)	57 (9)	58 (10)	59 (11)	60 (0)	61 (1)	62 (2)	63 (3)	64 (4)