28ed5/2

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28ed5/2

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Prime factorization	22 × 7
Step size	56.6541¢
Octave	21\28ed5/2 (1189.74¢) (→3\4ed5/2)
Twelfth	34\28ed5/2 (1926.24¢) (→17\14ed5/2)
Consistency limit	2
Distinct consistency limit	2

28 equal divisions of 5/2 (abbreviated 28ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 28 equal parts of about 56.7 ¢ each. Each step represents a frequency ratio of (5/2)^1/28, or the 28th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	56.654
2	113.308
3	169.962	11/10, 21/19
4	226.616	8/7, 17/15, 25/22
5	283.27	13/11
6	339.924	23/19
7	396.578	5/4, 24/19
8	453.232	13/10
9	509.887
10	566.541
11	623.195	10/7
12	679.849
13	736.503	20/13, 23/15
14	793.157	11/7, 19/12
15	849.811	13/8
16	906.465	22/13
17	963.119	7/4
18	1019.773
19	1076.427	13/7
20	1133.081	23/12, 25/13
21	1189.735	2/1
22	1246.389
23	1303.043
24	1359.697	11/5, 24/11
25	1416.352	25/11
26	1473.006
27	1529.66
28	1586.314	5/2

Harmonics

Approximation of harmonics in 28ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-10.3	+24.3	-20.5	-10.3	+14.0	-26.2	+25.9	-8.1	-20.5	-15.6	+3.8
	Relative (%)	-18.1	+42.9	-36.2	-18.1	+24.7	-46.3	+45.6	-14.3	-36.2	-27.5	+6.6
Steps (reduced)		21 (21)	34 (6)	42 (14)	49 (21)	55 (27)	59 (3)	64 (8)	67 (11)	70 (14)	73 (17)	76 (20)

Approximation of harmonics in 28ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-21.5	+20.2	+14.0	+15.6	+23.9	-18.4	+1.4	+25.9	-2.0	-25.8	+10.5
	Relative (%)	-38.0	+35.6	+24.7	+27.5	+42.3	-32.4	+2.4	+45.6	-3.4	-45.6	+18.6
Steps (reduced)		78 (22)	81 (25)	83 (27)	85 (1)	87 (3)	88 (4)	90 (6)	92 (8)	93 (9)	94 (10)	96 (12)