12ed5/3

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12ed5/3

13ed5/3 →

Prime factorization	22 × 3
Step size	73.6966¢
Octave	16\12ed5/3 (1179.14¢) (→4\3ed5/3)
Twelfth	26\12ed5/3 (1916.11¢) (→13\6ed5/3)
Consistency limit	3
Distinct consistency limit	2
Special properties	Highly composite

12 equal divisions of 5/3 (abbreviated 12ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 12 equal parts of about 73.7 ¢ each. Each step represents a frequency ratio of (5/3)^1/12, or the 12th root of 5/3.

One step of this tuning is extremely close to 24/23, being 0.016 cents sharp of that interval.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	73.697	18/17, 19/18, 20/19
2	147.393	11/10, 12/11, 13/12, 14/13, 15/14, 23/21
3	221.09	17/15
4	294.786	6/5, 7/6, 13/11
5	368.483	21/17
6	442.179	9/7, 13/10, 14/11, 23/18
7	515.876	19/14, 23/17
8	589.572	7/5, 10/7, 18/13
9	663.269	19/13
10	736.966	14/9, 20/13, 23/15
11	810.662	19/12
12	884.359	5/3, 22/13, 23/14

Harmonics

Approximation of harmonics in 12ed5/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-20.9	+14.2	+32.0	+14.2	-6.7	+21.2	+11.1	+28.3	-6.7	-24.3	-27.6
	Relative (%)	-28.3	+19.2	+43.4	+19.2	-9.1	+28.8	+15.1	+38.4	-9.1	-33.0	-37.4
Steps (reduced)		16 (4)	26 (2)	33 (9)	38 (2)	42 (6)	46 (10)	49 (1)	52 (4)	54 (6)	56 (8)	58 (10)

Approximation of harmonics in 12ed5/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-18.7	+0.4	+28.3	-9.7	+32.7	+7.5	-12.5	-27.6	+35.4	+28.5	+25.3
	Relative (%)	-25.4	+0.5	+38.4	-13.2	+44.4	+10.1	-16.9	-37.4	+48.0	+38.7	+34.3
Steps (reduced)		60 (0)	62 (2)	64 (4)	65 (5)	67 (7)	68 (8)	69 (9)	70 (10)	72 (0)	73 (1)	74 (2)