28ed7/4

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28ed7/4

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Prime factorization	22 × 7
Step size	34.6009¢
Octave	35\28ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth	55\28ed7/4 (1903.05¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	3

28 equal divisions of 7/4 (abbreviated 28ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 28 equal parts of about 34.6 ¢ each. Each step represents a frequency ratio of (7/4)^1/28, or the 28th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	34.601
2	69.202	23/22, 25/24, 27/26
3	103.803	18/17
4	138.404	14/13
5	173.005	21/19
6	207.606	17/15, 26/23
7	242.206
8	276.807	27/23
9	311.408	6/5
10	346.009	11/9, 17/14, 27/22
11	380.61	5/4, 26/21
12	415.211	14/11, 23/18
13	449.812	22/17
14	484.413
15	519.014	19/14, 23/17
16	553.615	26/19
17	588.216
18	622.817
19	657.418	19/13, 22/15
20	692.019	3/2
21	726.619	26/17
22	761.22	14/9, 17/11
23	795.821	27/17
24	830.422	21/13
25	865.023	23/14
26	899.624
27	934.225
28	968.826

Harmonics

Approximation of harmonics in 28ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.0	+1.1	-12.5	+16.4	+12.1	-12.5	-1.5	+2.2	-7.2	+0.8	-11.4
	Relative (%)	+31.9	+3.2	-36.2	+47.3	+35.1	-36.2	-4.3	+6.3	-20.8	+2.3	-33.1
Steps (reduced)		35 (7)	55 (27)	69 (13)	81 (25)	90 (6)	97 (13)	104 (20)	110 (26)	115 (3)	120 (8)	124 (12)

Approximation of harmonics in 28ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-11.6	-1.5	-17.1	+9.5	+8.4	+13.2	-11.2	+3.8	-11.4	+11.8	+4.1
	Relative (%)	-33.6	-4.3	-49.5	+27.5	+24.2	+38.2	-32.3	+11.1	-33.1	+34.2	+11.8
Steps (reduced)		128 (16)	132 (20)	135 (23)	139 (27)	142 (2)	145 (5)	147 (7)	150 (10)	152 (12)	155 (15)	157 (17)