32ed7/3
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Prime factorization
25
Step size
45.8397¢
Octave
26\32ed7/3 (1191.83¢) (→13\16ed7/3)
Twelfth
41\32ed7/3 (1879.43¢)
Consistency limit
4
Distinct consistency limit
4
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← 31ed7/3 | 32ed7/3 | 33ed7/3 → |
32 equal divisions of 7/3 (abbreviated 32ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 32 equal parts of about 45.8 ¢ each. Each step represents a frequency ratio of (7/3)1/32, or the 32nd root of 7/3.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 45.84 | |
2 | 91.679 | 20/19 |
3 | 137.519 | |
4 | 183.359 | 19/17 |
5 | 229.199 | 8/7, 25/22 |
6 | 275.038 | 7/6, 20/17 |
7 | 320.878 | |
8 | 366.718 | |
9 | 412.557 | 19/15 |
10 | 458.397 | 13/10, 17/13 |
11 | 504.237 | 4/3 |
12 | 550.077 | 26/19 |
13 | 595.916 | |
14 | 641.756 | |
15 | 687.596 | |
16 | 733.435 | 23/15, 26/17 |
17 | 779.275 | |
18 | 825.115 | |
19 | 870.955 | |
20 | 916.794 | 17/10, 22/13 |
21 | 962.634 | 7/4 |
22 | 1008.474 | |
23 | 1054.313 | |
24 | 1100.153 | |
25 | 1145.993 | |
26 | 1191.833 | 2/1 |
27 | 1237.672 | |
28 | 1283.512 | |
29 | 1329.352 | |
30 | 1375.191 | |
31 | 1421.031 | 25/11 |
32 | 1466.871 | 7/3 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -8.2 | -22.5 | -16.3 | +9.9 | +15.1 | -22.5 | +21.3 | +0.8 | +1.7 | +20.1 | +7.0 |
Relative (%) | -17.8 | -49.1 | -35.6 | +21.6 | +33.0 | -49.1 | +46.5 | +1.7 | +3.8 | +43.8 | +15.2 | |
Steps (reduced) |
26 (26) |
41 (9) |
52 (20) |
61 (29) |
68 (4) |
73 (9) |
79 (15) |
83 (19) |
87 (23) |
91 (27) |
94 (30) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +5.9 | +15.1 | -12.6 | +13.2 | -0.1 | -7.4 | -9.3 | -6.4 | +0.8 | +11.9 | -19.2 |
Relative (%) | +12.9 | +33.0 | -27.5 | +28.7 | -0.2 | -16.1 | -20.3 | -14.0 | +1.7 | +26.0 | -41.9 | |
Steps (reduced) |
97 (1) |
100 (4) |
102 (6) |
105 (9) |
107 (11) |
109 (13) |
111 (15) |
113 (17) |
115 (19) |
117 (21) |
118 (22) |