41ed7/3
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Prime factorization
41 (prime)
Step size
35.7773¢
Octave
34\41ed7/3 (1216.43¢)
Twelfth
53\41ed7/3 (1896.2¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 40ed7/3 | 41ed7/3 | 42ed7/3 → |
41 equal divisions of 7/3 (abbreviated 41ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 41 equal parts of about 35.8 ¢ each. Each step represents a frequency ratio of (7/3)1/41, or the 41st root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 35.777 | |
| 2 | 71.555 | 23/22, 26/25 |
| 3 | 107.332 | |
| 4 | 143.109 | 25/23 |
| 5 | 178.887 | 21/19 |
| 6 | 214.664 | 17/15, 25/22, 26/23 |
| 7 | 250.441 | 15/13, 29/25 |
| 8 | 286.219 | 13/11 |
| 9 | 321.996 | 6/5 |
| 10 | 357.773 | |
| 11 | 393.551 | |
| 12 | 429.328 | 9/7, 23/18 |
| 13 | 465.105 | 17/13, 30/23 |
| 14 | 500.883 | |
| 15 | 536.66 | 15/11 |
| 16 | 572.437 | 25/18 |
| 17 | 608.215 | 27/19 |
| 18 | 643.992 | |
| 19 | 679.769 | |
| 20 | 715.547 | |
| 21 | 751.324 | 17/11 |
| 22 | 787.101 | 11/7 |
| 23 | 822.879 | 29/18 |
| 24 | 858.656 | 18/11, 23/14 |
| 25 | 894.433 | |
| 26 | 930.211 | 29/17 |
| 27 | 965.988 | |
| 28 | 1001.765 | 25/14 |
| 29 | 1037.543 | |
| 30 | 1073.32 | 13/7 |
| 31 | 1109.098 | |
| 32 | 1144.875 | 29/15 |
| 33 | 1180.652 | |
| 34 | 1216.43 | |
| 35 | 1252.207 | |
| 36 | 1287.984 | 19/9 |
| 37 | 1323.762 | 15/7 |
| 38 | 1359.539 | 11/5 |
| 39 | 1395.316 | 29/13 |
| 40 | 1431.094 | |
| 41 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +16.4 | -5.8 | -2.9 | +4.3 | +10.7 | -5.8 | +13.5 | -11.5 | -15.0 | -1.1 | -8.7 |
| Relative (%) | +45.9 | -16.1 | -8.2 | +12.1 | +29.8 | -16.1 | +37.8 | -32.2 | -42.0 | -3.2 | -24.2 | |
| Steps (reduced) |
34 (34) |
53 (12) |
67 (26) |
78 (37) |
87 (5) |
94 (12) |
101 (19) |
106 (24) |
111 (29) |
116 (34) |
120 (38) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.1 | +10.7 | -1.4 | -5.8 | -3.5 | +4.9 | -17.1 | +1.4 | -11.5 | +15.3 | +9.9 |
| Relative (%) | -11.6 | +29.8 | -4.0 | -16.3 | -9.7 | +13.7 | -47.9 | +3.9 | -32.2 | +42.7 | +27.6 | |
| Steps (reduced) |
124 (1) |
128 (5) |
131 (8) |
134 (11) |
137 (14) |
140 (17) |
142 (19) |
145 (22) |
147 (24) |
150 (27) |
152 (29) | |