28ed7/3

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28ed7/3

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Prime factorization	22 × 7
Step size	52.3882¢
Octave	23\28ed7/3 (1204.93¢)
Twelfth	36\28ed7/3 (1885.98¢) (→9\7ed7/3)
Consistency limit	6
Distinct consistency limit	3

28 equal divisions of 7/3 (abbreviated 28ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 28 equal parts of about 52.4 ¢ each. Each step represents a frequency ratio of (7/3)^1/28, or the 28th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	52.388
2	104.776	17/16
3	157.165	11/10, 12/11
4	209.553	26/23
5	261.941	7/6, 22/19
6	314.329	6/5
7	366.718	16/13
8	419.106	14/11, 19/15
9	471.494	17/13, 25/19
10	523.882	19/14, 23/17
11	576.271	7/5, 25/18
12	628.659	23/16
13	681.047
14	733.435	26/17
15	785.824	11/7, 19/12
16	838.212	13/8
17	890.6	5/3
18	942.988	12/7, 19/11
19	995.377	23/13, 25/14
20	1047.765	11/6
21	1100.153
22	1152.541
23	1204.93	2/1
24	1257.318
25	1309.706	15/7, 17/8
26	1362.094	11/5
27	1414.483	25/11
28	1466.871	7/3

Harmonics

Approximation of harmonics in 28ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.9	-16.0	+9.9	-9.7	-11.0	-16.0	+14.8	+20.4	-4.8	-12.6	-6.1
	Relative (%)	+9.4	-30.5	+18.8	-18.6	-21.1	-30.5	+28.2	+39.0	-9.2	-24.1	-11.7
Steps (reduced)		23 (23)	36 (8)	46 (18)	53 (25)	59 (3)	64 (8)	69 (13)	73 (17)	76 (20)	79 (23)	82 (26)

Approximation of harmonics in 28ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+12.5	-11.0	-25.7	+19.7	+19.5	+25.4	-15.9	+0.1	+20.4	-7.7	+20.1
	Relative (%)	+23.8	-21.1	-49.1	+37.6	+37.3	+48.4	-30.3	+0.2	+39.0	-14.7	+38.4
Steps (reduced)		85 (1)	87 (3)	89 (5)	92 (8)	94 (10)	96 (12)	97 (13)	99 (15)	101 (17)	102 (18)	104 (20)