52ed7/3

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← 51ed7/3 52ed7/3 53ed7/3 →
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)