41ed5/2
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Prime factorization
41 (prime)
Step size
38.6906¢
Octave
31\41ed5/2 (1199.41¢)
(semiconvergent)
Twelfth
49\41ed5/2 (1895.84¢)
(semiconvergent)
Consistency limit
12
Distinct consistency limit
7
 |
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| ← 40ed5/2 | 41ed5/2 | 42ed5/2 → |
(semiconvergent)
(semiconvergent)
41 equal divisions of 5/2 (abbreviated 41ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 41 equal parts of about 38.7 ¢ each. Each step represents a frequency ratio of (5/2)1/41, or the 41st root of 5/2.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 38.691 | |
| 2 | 77.381 | 22/21, 23/22, 24/23, 25/24 |
| 3 | 116.072 | 15/14, 16/15 |
| 4 | 154.762 | 12/11, 23/21 |
| 5 | 193.453 | 19/17, 28/25, 29/26 |
| 6 | 232.143 | 8/7 |
| 7 | 270.834 | 7/6, 27/23 |
| 8 | 309.525 | 6/5 |
| 9 | 348.215 | 11/9, 27/22 |
| 10 | 386.906 | 5/4 |
| 11 | 425.596 | 23/18 |
| 12 | 464.287 | 17/13, 21/16, 30/23 |
| 13 | 502.978 | 4/3 |
| 14 | 541.668 | 15/11, 26/19 |
| 15 | 580.359 | 7/5 |
| 16 | 619.049 | 10/7 |
| 17 | 657.74 | 19/13, 22/15 |
| 18 | 696.43 | 3/2 |
| 19 | 735.121 | 23/15, 26/17, 29/19 |
| 20 | 773.812 | 25/16 |
| 21 | 812.502 | 8/5 |
| 22 | 851.193 | 18/11 |
| 23 | 889.883 | 5/3 |
| 24 | 928.574 | 12/7, 29/17 |
| 25 | 967.264 | 7/4 |
| 26 | 1005.955 | 25/14 |
| 27 | 1044.646 | 11/6 |
| 28 | 1083.336 | 15/8, 28/15 |
| 29 | 1122.027 | 21/11, 23/12 |
| 30 | 1160.717 | |
| 31 | 1199.408 | 2/1 |
| 32 | 1238.099 | |
| 33 | 1276.789 | 23/11, 25/12 |
| 34 | 1315.48 | 15/7 |
| 35 | 1354.17 | 24/11 |
| 36 | 1392.861 | 29/13 |
| 37 | 1431.551 | 16/7 |
| 38 | 1470.242 | 7/3 |
| 39 | 1508.933 | 12/5 |
| 40 | 1547.623 | 22/9, 27/11 |
| 41 | 1586.314 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.6 | -6.1 | -1.2 | -0.6 | -6.7 | -2.7 | -1.8 | -12.2 | -1.2 | -11.4 | -7.3 |
| Relative (%) | -1.5 | -15.8 | -3.1 | -1.5 | -17.3 | -7.1 | -4.6 | -31.6 | -3.1 | -29.5 | -18.9 | |
| Steps (reduced) |
31 (31) |
49 (8) |
62 (21) |
72 (31) |
80 (39) |
87 (5) |
93 (11) |
98 (16) |
103 (21) |
107 (25) |
111 (29) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.9 | -3.3 | -6.7 | -2.4 | +8.7 | -12.8 | +9.6 | -1.8 | -8.9 | -12.0 | -11.6 |
| Relative (%) | +23.0 | -8.6 | -17.3 | -6.1 | +22.6 | -33.1 | +24.9 | -4.6 | -22.9 | -31.1 | -30.0 | |
| Steps (reduced) |
115 (33) |
118 (36) |
121 (39) |
124 (1) |
127 (4) |
129 (6) |
132 (9) |
134 (11) |
136 (13) |
138 (15) |
140 (17) | |