28ed5/4

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28ed5/4

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Prime factorization	22 × 7
Step size	13.7969¢
Octave	87\28ed5/4 (1200.33¢) (semiconvergent)
Twelfth	138\28ed5/4 (1903.97¢) (→69\14ed5/4)
Consistency limit	16
Distinct consistency limit	6

28 equal divisions of 5/4 (abbreviated 28ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 28 equal parts of about 13.8 ¢ each. Each step represents a frequency ratio of (5/4)^1/28, or the 28th root of 5/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	13.797
2	27.594
3	41.391
4	55.188
5	68.985	23/22, 25/24, 26/25, 27/26
6	82.782	19/18, 21/20, 22/21, 24/23
7	96.578	18/17, 20/19
8	110.375	16/15, 17/16
9	124.172	14/13, 15/14
10	137.969	13/12, 27/25
11	151.766	12/11, 23/21, 25/23
12	165.563	11/10
13	179.36	10/9, 21/19
14	193.157
15	206.954	9/8
16	220.751	17/15, 25/22, 26/23
17	234.548	8/7, 23/20
18	248.345	15/13
19	262.141	7/6, 22/19
20	275.938	20/17
21	289.735	13/11, 19/16
22	303.532	25/21
23	317.329	6/5
24	331.126	23/19
25	344.923	11/9, 17/14
26	358.72	16/13, 21/17, 27/22
27	372.517	26/21
28	386.314	5/4

Harmonics

Approximation of harmonics in 28ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.33	+2.02	+0.66	+0.66	+2.35	-2.38	+1.00	+4.04	+1.00	+1.55	+2.68
	Relative (%)	+2.4	+14.6	+4.8	+4.8	+17.0	-17.2	+7.2	+29.3	+7.2	+11.3	+19.5
Steps (reduced)		87 (3)	138 (26)	174 (6)	202 (6)	225 (1)	244 (20)	261 (9)	276 (24)	289 (9)	301 (21)	312 (4)

Approximation of harmonics in 28ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.08	-2.05	+2.68	+1.33	+6.75	+4.37	-6.45	+1.33	-0.36	+1.89	-6.09
	Relative (%)	+15.1	-14.8	+19.5	+9.6	+48.9	+31.7	-46.8	+9.6	-2.6	+13.7	-44.1
Steps (reduced)		322 (14)	331 (23)	340 (4)	348 (12)	356 (20)	363 (27)	369 (5)	376 (12)	382 (18)	388 (24)	393 (1)