33ed11/5
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Prime factorization
3 × 11
Step size
41.3638¢
Octave
29\33ed11/5 (1199.55¢)
(convergent)
Twelfth
46\33ed11/5 (1902.73¢)
(semiconvergent)
Consistency limit
16
Distinct consistency limit
4
 |
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| ← 32ed11/5 | 33ed11/5 | 34ed11/5 → |
(convergent)
(semiconvergent)
33 equal divisions of 11/5 (abbreviated 33ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 33 equal parts of about 41.4 ¢ each. Each step represents a frequency ratio of (11/5)1/33, or the 33rd root of 11/5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 41.364 | |
| 2 | 82.728 | 20/19, 21/20, 22/21, 23/22 |
| 3 | 124.091 | 14/13, 15/14 |
| 4 | 165.455 | 11/10, 21/19, 23/21 |
| 5 | 206.819 | 9/8, 26/23 |
| 6 | 248.183 | 15/13, 22/19, 23/20 |
| 7 | 289.546 | 13/11, 19/16 |
| 8 | 330.91 | 23/19 |
| 9 | 372.274 | 26/21 |
| 10 | 413.638 | 14/11, 19/15 |
| 11 | 455.001 | 13/10 |
| 12 | 496.365 | 4/3 |
| 13 | 537.729 | 15/11, 26/19 |
| 14 | 579.093 | 7/5 |
| 15 | 620.456 | 10/7, 23/16 |
| 16 | 661.82 | 19/13, 22/15 |
| 17 | 703.184 | 3/2 |
| 18 | 744.548 | 20/13, 23/15 |
| 19 | 785.912 | 11/7 |
| 20 | 827.275 | 21/13 |
| 21 | 868.639 | |
| 22 | 910.003 | 22/13, 27/16 |
| 23 | 951.367 | 19/11, 26/15 |
| 24 | 992.73 | 16/9, 23/13 |
| 25 | 1034.094 | 20/11 |
| 26 | 1075.458 | 13/7, 28/15 |
| 27 | 1116.822 | 19/10, 21/11 |
| 28 | 1158.185 | |
| 29 | 1199.549 | 2/1 |
| 30 | 1240.913 | |
| 31 | 1282.277 | 21/10, 23/11 |
| 32 | 1323.64 | 15/7, 28/13 |
| 33 | 1365.004 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.5 | +0.8 | -0.9 | -14.9 | +0.3 | -18.4 | -1.4 | +1.6 | -15.4 | -14.9 | -0.1 |
| Relative (%) | -1.1 | +1.9 | -2.2 | -36.1 | +0.8 | -44.4 | -3.3 | +3.8 | -37.2 | -36.1 | -0.3 | |
| Steps (reduced) |
29 (29) |
46 (13) |
58 (25) |
67 (1) |
75 (9) |
81 (15) |
87 (21) |
92 (26) |
96 (30) |
100 (1) |
104 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -14.6 | -18.8 | -14.2 | -1.8 | +17.3 | +1.1 | -9.8 | -15.8 | -17.6 | -15.4 | -9.6 |
| Relative (%) | -35.3 | -45.5 | -34.2 | -4.4 | +41.9 | +2.7 | -23.6 | -38.3 | -42.5 | -37.2 | -23.3 | |
| Steps (reduced) |
107 (8) |
110 (11) |
113 (14) |
116 (17) |
119 (20) |
121 (22) |
123 (24) |
125 (26) |
127 (28) |
129 (30) |
131 (32) | |