28ed11/5

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28ed11/5

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Prime factorization	22 × 7
Step size	48.7502¢
Octave	25\28ed11/5 (1218.75¢)
Twelfth	39\28ed11/5 (1901.26¢) (convergent)
Consistency limit	3
Distinct consistency limit	2

28 equal divisions of 11/5 (abbreviated 28ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 28 equal parts of about 48.8 ¢ each. Each step represents a frequency ratio of (11/5)^1/28, or the 28th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	48.75
2	97.5	18/17, 19/18, 20/19
3	146.25	25/23
4	195.001	19/17
5	243.751	15/13, 22/19
6	292.501	13/11, 25/21
7	341.251	11/9, 17/14
8	390.001
9	438.751	9/7, 22/17
10	487.502
11	536.252	15/11, 19/14, 26/19
12	585.002	7/5
13	633.752	13/9
14	682.502
15	731.252	23/15, 26/17
16	780.002	11/7
17	828.753	21/13
18	877.503	5/3
19	926.253	17/10
20	975.003
21	1023.753	9/5
22	1072.503	13/7
23	1121.253	19/10, 21/11, 25/13
24	1170.004
25	1218.754
26	1267.504	23/11, 27/13
27	1316.254	15/7
28	1365.004	11/5

Harmonics

Approximation of harmonics in 28ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+18.8	-0.7	-11.2	-7.6	+18.1	-5.1	+7.5	-1.4	+11.2	-7.6	-11.9
	Relative (%)	+38.5	-1.4	-23.1	-15.5	+37.0	-10.4	+15.4	-2.9	+23.0	-15.5	-24.5
Steps (reduced)		25 (25)	39 (11)	49 (21)	57 (1)	64 (8)	69 (13)	74 (18)	78 (22)	82 (26)	85 (1)	88 (4)

Approximation of harmonics in 28ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.3	+13.7	-8.3	-22.5	+18.8	+17.4	+21.3	-18.8	-5.8	+11.2	-17.0
	Relative (%)	-8.7	+28.1	-16.9	-46.1	+38.6	+35.6	+43.6	-38.6	-11.8	+23.0	-34.9
Steps (reduced)		91 (7)	94 (10)	96 (12)	98 (14)	101 (17)	103 (19)	105 (21)	106 (22)	108 (24)	110 (26)	111 (27)