52ed7/3

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52ed7/3

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Prime factorization	22 × 13
Step size	28.2091¢
Octave	43\52ed7/3 (1212.99¢)
Twelfth	67\52ed7/3 (1890.01¢)
Consistency limit	2
Distinct consistency limit	2

52 equal divisions of 7/3 (abbreviated 52ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 52 equal parts of about 28.2⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/52, or the 52nd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	28.2
2	56.4	29/28, 30/29, 31/30
3	84.6
4	112.8	31/29
5	141
6	169.3
7	197.5	19/17, 28/25
8	225.7	25/22
9	253.9	22/19, 29/25
10	282.1
11	310.3
12	338.5	17/14
13	366.7
14	394.9
15	423.1	23/18
16	451.3	22/17
17	479.6	25/19, 29/22
18	507.8
19	536	15/11
20	564.2	18/13
21	592.4	31/22
22	620.6	33/23
23	648.8
24	677
25	705.2
26	733.4	26/17, 29/19
27	761.6
28	789.9	30/19
29	818.1
30	846.3	31/19
31	874.5
32	902.7
33	930.9
34	959.1
35	987.3	23/13, 30/17
36	1015.5
37	1043.7	31/17
38	1071.9	13/7
39	1100.2
40	1128.4
41	1156.6
42	1184.8
43	1213
44	1241.2
45	1269.4	25/12
46	1297.6
47	1325.8
48	1354
49	1382.2
50	1410.5
51	1438.7
52	1466.9	7/3

Harmonics

Approximation of harmonics in 52ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+13.0	-11.9	-2.2	+6.4	+1.0	-11.9	+10.8	+4.3	-8.8	-4.6	+14.0
	Relative (%)	+46.0	-42.4	-7.9	+22.6	+3.7	-42.4	+38.1	+15.3	-31.3	-16.3	+49.7
Steps (reduced)		43 (43)	67 (15)	85 (33)	99 (47)	110 (6)	119 (15)	128 (24)	135 (31)	141 (37)	147 (43)	153 (49)

Approximation of harmonics in 52ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-11.7	+1.0	-5.6	-4.5	+3.4	-10.9	+8.3	+4.2	+4.3	+8.4	-12.1
	Relative (%)	-41.5	+3.7	-19.7	-15.8	+12.1	-38.7	+29.5	+14.7	+15.3	+29.8	-43.0
Steps (reduced)		157 (1)	162 (6)	166 (10)	170 (14)	174 (18)	177 (21)	181 (25)	184 (28)	187 (31)	190 (34)	192 (36)