48ed11/5
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Prime factorization
24 × 3
Step size
28.4376¢
Octave
42\48ed11/5 (1194.38¢) (→7\8ed11/5)
Twelfth
67\48ed11/5 (1905.32¢)
Consistency limit
3
Distinct consistency limit
3
Special properties
 |
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| ← 47ed11/5 | 48ed11/5 | 49ed11/5 → |
48 equal divisions of 11/5 (abbreviated 48ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 48 equal parts of about 28.4 ¢ each. Each step represents a frequency ratio of (11/5)1/48, or the 48th root of 11/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 28.438 | |
| 2 | 56.875 | 30/29, 31/30 |
| 3 | 85.313 | 20/19, 21/20, 22/21 |
| 4 | 113.75 | 31/29 |
| 5 | 142.188 | 13/12, 25/23 |
| 6 | 170.626 | 11/10, 21/19 |
| 7 | 199.063 | |
| 8 | 227.501 | 8/7 |
| 9 | 255.938 | 22/19, 29/25 |
| 10 | 284.376 | 13/11, 20/17 |
| 11 | 312.813 | 6/5 |
| 12 | 341.251 | 17/14 |
| 13 | 369.689 | 21/17, 26/21, 31/25 |
| 14 | 398.126 | 29/23 |
| 15 | 426.564 | 23/18 |
| 16 | 455.001 | 13/10, 30/23 |
| 17 | 483.439 | 29/22 |
| 18 | 511.877 | 31/23 |
| 19 | 540.314 | 15/11, 26/19 |
| 20 | 568.752 | 18/13, 25/18 |
| 21 | 597.189 | 17/12, 24/17, 31/22 |
| 22 | 625.627 | |
| 23 | 654.065 | 19/13 |
| 24 | 682.502 | |
| 25 | 710.94 | |
| 26 | 739.377 | 23/15, 26/17 |
| 27 | 767.815 | |
| 28 | 796.252 | 19/12, 30/19 |
| 29 | 824.69 | 21/13, 29/18 |
| 30 | 853.128 | 18/11, 31/19 |
| 31 | 881.565 | 5/3 |
| 32 | 910.003 | 22/13 |
| 33 | 938.44 | 12/7, 31/18 |
| 34 | 966.878 | 7/4 |
| 35 | 995.316 | |
| 36 | 1023.753 | |
| 37 | 1052.191 | 11/6 |
| 38 | 1080.628 | |
| 39 | 1109.066 | 19/10 |
| 40 | 1137.504 | 25/13, 29/15 |
| 41 | 1165.941 | |
| 42 | 1194.379 | 2/1 |
| 43 | 1222.816 | |
| 44 | 1251.254 | 31/15 |
| 45 | 1279.691 | 21/10, 23/11 |
| 46 | 1308.129 | 17/8 |
| 47 | 1336.567 | 13/6 |
| 48 | 1365.004 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.6 | +3.4 | -11.2 | +0.6 | -2.3 | -13.2 | +11.6 | +6.7 | -5.1 | +0.6 | -7.9 |
| Relative (%) | -19.8 | +11.8 | -39.5 | +2.0 | -7.9 | -46.4 | +40.7 | +23.7 | -17.8 | +2.0 | -27.7 | |
| Steps (reduced) |
42 (42) |
67 (19) |
84 (36) |
98 (2) |
109 (13) |
118 (22) |
127 (31) |
134 (38) |
140 (44) |
146 (2) |
151 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.3 | +9.6 | +3.9 | +6.0 | -13.7 | +1.1 | -7.2 | -10.7 | -9.8 | -5.1 | +3.3 |
| Relative (%) | -15.0 | +33.8 | +13.8 | +20.9 | -48.1 | +3.9 | -25.3 | -37.5 | -34.6 | -17.8 | +11.6 | |
| Steps (reduced) |
156 (12) |
161 (17) |
165 (21) |
169 (25) |
172 (28) |
176 (32) |
179 (35) |
182 (38) |
185 (41) |
188 (44) |
191 (47) | |