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	28.209
2	56.418	29/28, 30/29, 31/30
3	84.627
4	112.836	31/29
5	141.045
6	169.254
7	197.463	19/17, 28/25
8	225.672	25/22
9	253.882	22/19, 29/25
10	282.091
11	310.3
12	338.509	17/14
13	366.718
14	394.927
15	423.136	23/18
16	451.345	22/17
17	479.554	25/19, 29/22
18	507.763
19	535.972	15/11
20	564.181	18/13
21	592.39	31/22
22	620.599	33/23
23	648.808
24	677.017
25	705.226
26	733.435	26/17, 29/19
27	761.645
28	789.854	30/19
29	818.063
30	846.272	31/19
31	874.481
32	902.69
33	930.899
34	959.108
35	987.317	23/13, 30/17
36	1015.526
37	1043.735	31/17
38	1071.944	13/7
39	1100.153
40	1128.362
41	1156.571
42	1184.78
43	1212.989
44	1241.198
45	1269.408	25/12
46	1297.617
47	1325.826
48	1354.035
49	1382.244
50	1410.453
51	1438.662
52	1466.871	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)