41ed11/5
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Prime factorization
41 (prime)
Step size
33.2928¢
Octave
36\41ed11/5 (1198.54¢)
Twelfth
57\41ed11/5 (1897.69¢)
Consistency limit
8
Distinct consistency limit
6
 |
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| ← 40ed11/5 | 41ed11/5 | 42ed11/5 → |
41 equal divisions of 11/5 (abbreviated 41ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 41 equal parts of about 33.3 ¢ each. Each step represents a frequency ratio of (11/5)1/41, or the 41st root of 11/5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 33.293 | |
| 2 | 66.586 | 27/26, 28/27, 29/28 |
| 3 | 99.878 | 17/16, 18/17, 19/18 |
| 4 | 133.171 | 13/12, 14/13 |
| 5 | 166.464 | 11/10, 21/19 |
| 6 | 199.757 | 9/8 |
| 7 | 233.05 | 8/7 |
| 8 | 266.342 | 7/6 |
| 9 | 299.635 | 19/16 |
| 10 | 332.928 | 17/14, 23/19, 29/24 |
| 11 | 366.221 | 16/13, 21/17, 26/21 |
| 12 | 399.513 | 24/19, 29/23 |
| 13 | 432.806 | 9/7 |
| 14 | 466.099 | 17/13, 21/16, 30/23 |
| 15 | 499.392 | 4/3 |
| 16 | 532.685 | 15/11, 19/14 |
| 17 | 565.977 | 18/13 |
| 18 | 599.27 | 17/12, 24/17 |
| 19 | 632.563 | 13/9, 23/16 |
| 20 | 665.856 | 22/15, 28/19 |
| 21 | 699.149 | 3/2 |
| 22 | 732.441 | 26/17, 29/19 |
| 23 | 765.734 | 14/9 |
| 24 | 799.027 | 19/12, 27/17 |
| 25 | 832.32 | 21/13, 29/18 |
| 26 | 865.612 | 23/14, 28/17 |
| 27 | 898.905 | 27/16 |
| 28 | 932.198 | 12/7 |
| 29 | 965.491 | 7/4 |
| 30 | 998.784 | 16/9 |
| 31 | 1032.076 | 20/11, 29/16 |
| 32 | 1065.369 | 13/7, 24/13 |
| 33 | 1098.662 | 17/9 |
| 34 | 1131.955 | 23/12, 27/14 |
| 35 | 1165.248 | |
| 36 | 1198.54 | 2/1 |
| 37 | 1231.833 | |
| 38 | 1265.126 | 27/13, 29/14 |
| 39 | 1298.419 | 17/8, 19/9 |
| 40 | 1331.711 | 13/6, 28/13 |
| 41 | 1365.004 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.5 | -4.3 | -2.9 | +10.3 | -5.7 | -6.3 | -4.4 | -8.5 | +8.8 | +10.3 | -7.2 |
| Relative (%) | -4.4 | -12.8 | -8.8 | +30.9 | -17.2 | -18.8 | -13.2 | -25.6 | +26.5 | +30.9 | -21.6 | |
| Steps (reduced) |
36 (36) |
57 (16) |
72 (31) |
84 (2) |
93 (11) |
101 (19) |
108 (26) |
114 (32) |
120 (38) |
125 (2) |
129 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.6 | -7.7 | +6.0 | -5.8 | -10.9 | -10.0 | -3.7 | +7.4 | -10.5 | +8.8 | -1.6 |
| Relative (%) | -37.8 | -23.2 | +18.1 | -17.5 | -32.8 | -30.0 | -11.2 | +22.1 | -31.6 | +26.5 | -4.7 | |
| Steps (reduced) |
133 (10) |
137 (14) |
141 (18) |
144 (21) |
147 (24) |
150 (27) |
153 (30) |
156 (33) |
158 (35) |
161 (38) |
163 (40) | |