33ed5/2
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Prime factorization
3 × 11
Step size
48.0701¢
Octave
25\33ed5/2 (1201.75¢)
(semiconvergent)
Twelfth
40\33ed5/2 (1922.8¢)
Consistency limit
6
Distinct consistency limit
6
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← 32ed5/2 | 33ed5/2 | 34ed5/2 → |
(semiconvergent)
33 equal divisions of 5/2 (abbreviated 33ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 33 equal parts of about 48.1 ¢ each. Each step represents a frequency ratio of (5/2)1/33, or the 33rd root of 5/2.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 48.07 | |
2 | 96.14 | 17/16, 20/19 |
3 | 144.21 | 25/23 |
4 | 192.28 | 19/17, 28/25 |
5 | 240.351 | 23/20 |
6 | 288.421 | 13/11, 20/17 |
7 | 336.491 | 17/14, 23/19, 28/23 |
8 | 384.561 | 5/4 |
9 | 432.631 | |
10 | 480.701 | 25/19 |
11 | 528.771 | 19/14, 23/17 |
12 | 576.841 | 7/5 |
13 | 624.911 | 10/7, 23/16 |
14 | 672.982 | 25/17, 28/19 |
15 | 721.052 | |
16 | 769.122 | 25/16 |
17 | 817.192 | 8/5 |
18 | 865.262 | 23/14, 28/17 |
19 | 913.332 | 17/10, 22/13 |
20 | 961.402 | 7/4 |
21 | 1009.472 | 25/14 |
22 | 1057.542 | |
23 | 1105.613 | 19/10 |
24 | 1153.683 | |
25 | 1201.753 | 2/1 |
26 | 1249.823 | |
27 | 1297.893 | 17/8 |
28 | 1345.963 | |
29 | 1394.033 | |
30 | 1442.103 | 23/10 |
31 | 1490.173 | 19/8, 26/11 |
32 | 1538.244 | 17/7 |
33 | 1586.314 | 5/2 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +1.8 | +20.8 | +3.5 | +1.8 | +22.6 | -3.9 | +5.3 | -6.4 | +3.5 | -17.3 | -23.7 |
Relative (%) | +3.6 | +43.4 | +7.3 | +3.6 | +47.0 | -8.2 | +10.9 | -13.3 | +7.3 | -36.0 | -49.3 | |
Steps (reduced) |
25 (25) |
40 (7) |
50 (17) |
58 (25) |
65 (32) |
70 (4) |
75 (9) |
79 (13) |
83 (17) |
86 (20) |
89 (23) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -18.1 | -2.2 | +22.6 | +7.0 | -1.8 | -4.6 | -2.1 | +5.3 | +16.9 | -15.5 | +3.6 |
Relative (%) | -37.6 | -4.5 | +47.0 | +14.6 | -3.8 | -9.6 | -4.3 | +10.9 | +35.2 | -32.3 | +7.6 | |
Steps (reduced) |
92 (26) |
95 (29) |
98 (32) |
100 (1) |
102 (3) |
104 (5) |
106 (7) |
108 (9) |
110 (11) |
111 (12) |
113 (14) |