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
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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
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) |
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) |