40ed11/5
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Prime factorization
23 × 5
Step size
34.1251¢
Octave
35\40ed11/5 (1194.38¢) (→7\8ed11/5)
Twelfth
56\40ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 39ed11/5 | 40ed11/5 | 41ed11/5 → |
40 equal divisions of 11/5 (abbreviated 40ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 40 equal parts of about 34.1 ¢ each. Each step represents a frequency ratio of (11/5)1/40, or the 40th root of 11/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 34.125 | |
| 2 | 68.25 | 24/23 |
| 3 | 102.375 | 18/17 |
| 4 | 136.5 | 13/12, 27/25 |
| 5 | 170.626 | 11/10 |
| 6 | 204.751 | |
| 7 | 238.876 | 23/20 |
| 8 | 273.001 | 7/6 |
| 9 | 307.126 | 25/21 |
| 10 | 341.251 | 11/9, 17/14, 28/23 |
| 11 | 375.376 | |
| 12 | 409.501 | 24/19 |
| 13 | 443.626 | 22/17 |
| 14 | 477.751 | 29/22 |
| 15 | 511.877 | |
| 16 | 546.002 | 26/19 |
| 17 | 580.127 | 7/5 |
| 18 | 614.252 | 10/7 |
| 19 | 648.377 | 29/20 |
| 20 | 682.502 | |
| 21 | 716.627 | |
| 22 | 750.752 | 17/11, 20/13 |
| 23 | 784.877 | 11/7 |
| 24 | 819.003 | 29/18 |
| 25 | 853.128 | 18/11, 23/14 |
| 26 | 887.253 | 5/3 |
| 27 | 921.378 | 17/10, 29/17 |
| 28 | 955.503 | |
| 29 | 989.628 | 23/13, 30/17 |
| 30 | 1023.753 | 9/5 |
| 31 | 1057.878 | 24/13 |
| 32 | 1092.003 | |
| 33 | 1126.128 | 21/11, 23/12 |
| 34 | 1160.254 | |
| 35 | 1194.379 | 2/1 |
| 36 | 1228.504 | |
| 37 | 1262.629 | 29/14 |
| 38 | 1296.754 | |
| 39 | 1330.879 | 28/13 |
| 40 | 1365.004 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.6 | +9.1 | -11.2 | +11.9 | +3.4 | +9.6 | -16.9 | -16.0 | +6.3 | +11.9 | -2.2 |
| Relative (%) | -16.5 | +26.5 | -32.9 | +35.0 | +10.1 | +28.0 | -49.4 | -47.0 | +18.5 | +35.0 | -6.4 | |
| Steps (reduced) |
35 (35) |
56 (16) |
70 (30) |
82 (2) |
91 (11) |
99 (19) |
105 (25) |
111 (31) |
117 (37) |
122 (2) |
126 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.3 | +3.9 | -13.1 | +11.6 | +9.1 | +12.5 | -12.9 | +0.7 | -15.5 | +6.3 | -2.4 |
| Relative (%) | -12.5 | +11.5 | -38.5 | +34.1 | +26.5 | +36.6 | -37.7 | +2.1 | -45.5 | +18.5 | -7.0 | |
| Steps (reduced) |
130 (10) |
134 (14) |
137 (17) |
141 (21) |
144 (24) |
147 (27) |
149 (29) |
152 (32) |
154 (34) |
157 (37) |
159 (39) | |