4ed5/3

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4ed5/3

5ed5/3 →

Prime factorization	22 (highly composite)
Step size	221.09 ¢
Octave	5\4ed5/3 (1105.45 ¢)
Twelfth	9\4ed5/3 (1989.81 ¢)
Consistency limit	2
Distinct consistency limit	2

4 equal divisions of 5/3 (abbreviated 4ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 4 equal parts of about 221 ¢ each. Each step represents a frequency ratio of (5/3)^1/4, or the 4th root of 5/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1, 19/18, 20/19
1	221.1	6/5, 7/6, 11/10, 13/11, 13/12, 19/17, 20/17, 21/19
2	442.2	13/10, 17/13, 21/17
3	663.3	10/7, 17/11, 17/12, 19/13, 20/13
4	884.4	5/3, 12/7, 17/10, 18/11, 19/11, 19/12, 21/13

Harmonics

Approximation of harmonics in 4ed5/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-94.6	+87.9	+32.0	+87.9	-6.7	-52.5	-62.6	-45.4	-6.7	+49.4	-101.3
	Relative (%)	-42.8	+39.7	+14.5	+39.7	-3.0	-23.7	-28.3	-20.5	-3.0	+22.3	-45.8
Steps (reduced)		5 (1)	9 (1)	11 (3)	13 (1)	14 (2)	15 (3)	16 (0)	17 (1)	18 (2)	19 (3)	19 (3)

Approximation of harmonics in 4ed5/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-18.7	+74.1	-45.4	+64.0	-41.0	+81.2	-12.5	-101.3	+35.4	-45.2	+99.0
	Relative (%)	-8.5	+33.5	-20.5	+28.9	-18.5	+36.7	-5.6	-45.8	+16.0	-20.4	+44.8
Steps (reduced)		20 (0)	21 (1)	21 (1)	22 (2)	22 (2)	23 (3)	23 (3)	23 (3)	24 (0)	24 (0)	25 (1)