46ed11/5
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Prime factorization
2 × 23
Step size
29.674¢
Octave
40\46ed11/5 (1186.96¢) (→20\23ed11/5)
Twelfth
64\46ed11/5 (1899.14¢) (→32\23ed11/5)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 45ed11/5 | 46ed11/5 | 47ed11/5 → |
46 equal divisions of 11/5 (abbreviated 46ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 46 equal parts of about 29.7 ¢ each. Each step represents a frequency ratio of (11/5)1/46, or the 46th root of 11/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 29.674 | |
| 2 | 59.348 | 27/26, 28/27, 29/28, 30/29, 31/30 |
| 3 | 89.022 | |
| 4 | 118.696 | 15/14, 29/27, 31/29 |
| 5 | 148.37 | 25/23 |
| 6 | 178.044 | 10/9, 21/19, 31/28 |
| 7 | 207.718 | 26/23 |
| 8 | 237.392 | 31/27 |
| 9 | 267.066 | |
| 10 | 296.74 | 25/21 |
| 11 | 326.414 | 23/19 |
| 12 | 356.088 | 27/22 |
| 13 | 385.762 | |
| 14 | 415.436 | 14/11 |
| 15 | 445.11 | 22/17 |
| 16 | 474.784 | 25/19, 29/22 |
| 17 | 504.458 | |
| 18 | 534.132 | 15/11, 19/14 |
| 19 | 563.806 | |
| 20 | 593.48 | 31/22 |
| 21 | 623.154 | |
| 22 | 652.828 | 19/13 |
| 23 | 682.502 | |
| 24 | 712.176 | |
| 25 | 741.85 | 23/15 |
| 26 | 771.524 | |
| 27 | 801.198 | 27/17 |
| 28 | 830.872 | 21/13, 29/18 |
| 29 | 860.546 | 23/14, 28/17 |
| 30 | 890.22 | 5/3 |
| 31 | 919.894 | 17/10, 29/17 |
| 32 | 949.568 | 19/11, 26/15 |
| 33 | 979.242 | 30/17 |
| 34 | 1008.916 | 25/14 |
| 35 | 1038.59 | 31/17 |
| 36 | 1068.264 | 13/7 |
| 37 | 1097.938 | 17/9 |
| 38 | 1127.612 | 25/13 |
| 39 | 1157.286 | |
| 40 | 1186.96 | |
| 41 | 1216.634 | |
| 42 | 1246.308 | |
| 43 | 1275.982 | 23/11 |
| 44 | 1305.656 | |
| 45 | 1335.33 | |
| 46 | 1365.004 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -13.0 | -2.8 | +3.6 | +3.0 | +13.8 | +14.0 | -9.4 | -5.6 | -10.0 | +3.0 | +0.8 |
| Relative (%) | -43.9 | -9.5 | +12.1 | +10.3 | +46.6 | +47.2 | -31.8 | -19.0 | -33.7 | +10.3 | +2.6 | |
| Steps (reduced) |
40 (40) |
64 (18) |
81 (35) |
94 (2) |
105 (13) |
114 (22) |
121 (29) |
128 (36) |
134 (42) |
140 (2) |
145 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.6 | +1.0 | +0.2 | +7.2 | -8.7 | +11.0 | +6.4 | +6.6 | +11.2 | -10.0 | +2.1 |
| Relative (%) | +35.6 | +3.3 | +0.8 | +24.2 | -29.5 | +37.1 | +21.6 | +22.4 | +37.7 | -33.7 | +7.0 | |
| Steps (reduced) |
150 (12) |
154 (16) |
158 (20) |
162 (24) |
165 (27) |
169 (31) |
172 (34) |
175 (37) |
178 (40) |
180 (42) |
183 (45) | |