32ed11/5
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Prime factorization
25
Step size
42.6564¢
Octave
28\32ed11/5 (1194.38¢) (→7\8ed11/5)
Twelfth
45\32ed11/5 (1919.54¢)
Consistency limit
2
Distinct consistency limit
2
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← 31ed11/5 | 32ed11/5 | 33ed11/5 → |
32 equal divisions of 11/5 (abbreviated 32ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 32 equal parts of about 42.7 ¢ each. Each step represents a frequency ratio of (11/5)1/32, or the 32nd root of 11/5.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 42.656 | |
2 | 85.313 | 19/18, 23/22 |
3 | 127.969 | 14/13, 15/14 |
4 | 170.626 | 11/10, 21/19 |
5 | 213.282 | 17/15, 25/22, 26/23 |
6 | 255.938 | 15/13 |
7 | 298.595 | |
8 | 341.251 | 17/14, 28/23 |
9 | 383.907 | 5/4 |
10 | 426.564 | 14/11 |
11 | 469.22 | 17/13 |
12 | 511.877 | |
13 | 554.533 | 11/8 |
14 | 597.189 | 17/12, 24/17 |
15 | 639.846 | 16/11 |
16 | 682.502 | |
17 | 725.158 | |
18 | 767.815 | 25/16 |
19 | 810.471 | 8/5 |
20 | 853.128 | 23/14 |
21 | 895.784 | |
22 | 938.44 | 12/7 |
23 | 981.097 | 23/13 |
24 | 1023.753 | |
25 | 1066.41 | 13/7, 24/13 |
26 | 1109.066 | |
27 | 1151.722 | |
28 | 1194.379 | 2/1 |
29 | 1237.035 | |
30 | 1279.691 | 23/11 |
31 | 1322.348 | 15/7, 28/13 |
32 | 1365.004 | 11/5 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -5.6 | +17.6 | -11.2 | -13.6 | +12.0 | +1.0 | -16.9 | -7.5 | -19.3 | -13.6 | +6.3 |
Relative (%) | -13.2 | +41.2 | -26.4 | -32.0 | +28.0 | +2.4 | -39.5 | -17.6 | -45.2 | -32.0 | +14.9 | |
Steps (reduced) |
28 (28) |
45 (13) |
56 (24) |
65 (1) |
73 (9) |
79 (15) |
84 (20) |
89 (25) |
93 (29) |
97 (1) |
101 (5) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -4.3 | -4.6 | +3.9 | +20.2 | +0.5 | -13.1 | +21.3 | +17.8 | +18.6 | -19.3 | -10.9 |
Relative (%) | -10.0 | -10.8 | +9.2 | +47.3 | +1.2 | -30.7 | +49.8 | +41.6 | +43.6 | -45.2 | -25.6 | |
Steps (reduced) |
104 (8) |
107 (11) |
110 (14) |
113 (17) |
115 (19) |
117 (21) |
120 (24) |
122 (26) |
124 (28) |
125 (29) |
127 (31) |