71ed4
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Prime factorization
71 (prime)
Step size
33.8028¢
Octave
36\71ed4 (1216.9¢)
Twelfth
56\71ed4 (1892.96¢)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 69ed4 | 71ed4 | 73ed4 → |
71 equal divisions of the 4th harmonic (abbreviated 71ed4) is a nonoctave tuning system that divides the interval of 4/1 into 71 equal parts of about 33.8 ¢ each. Each step represents a frequency ratio of 41/71, or the 71st root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 33.803 | |
| 2 | 67.606 | |
| 3 | 101.408 | 18/17, 35/33 |
| 4 | 135.211 | 27/25 |
| 5 | 169.014 | |
| 6 | 202.817 | |
| 7 | 236.62 | |
| 8 | 270.423 | 7/6 |
| 9 | 304.225 | 31/26, 37/31 |
| 10 | 338.028 | |
| 11 | 371.831 | 26/21 |
| 12 | 405.634 | |
| 13 | 439.437 | |
| 14 | 473.239 | |
| 15 | 507.042 | |
| 16 | 540.845 | 26/19 |
| 17 | 574.648 | |
| 18 | 608.451 | 37/26 |
| 19 | 642.254 | |
| 20 | 676.056 | 31/21, 34/23 |
| 21 | 709.859 | |
| 22 | 743.662 | |
| 23 | 777.465 | 36/23 |
| 24 | 811.268 | |
| 25 | 845.07 | 31/19 |
| 26 | 878.873 | |
| 27 | 912.676 | |
| 28 | 946.479 | 19/11 |
| 29 | 980.282 | 30/17, 37/21 |
| 30 | 1014.085 | 9/5 |
| 31 | 1047.887 | 11/6 |
| 32 | 1081.69 | |
| 33 | 1115.493 | |
| 34 | 1149.296 | 33/17, 35/18 |
| 35 | 1183.099 | |
| 36 | 1216.901 | |
| 37 | 1250.704 | 35/17, 37/18 |
| 38 | 1284.507 | 21/10 |
| 39 | 1318.31 | |
| 40 | 1352.113 | |
| 41 | 1385.915 | 29/13 |
| 42 | 1419.718 | |
| 43 | 1453.521 | |
| 44 | 1487.324 | 26/11 |
| 45 | 1521.127 | |
| 46 | 1554.93 | |
| 47 | 1588.732 | |
| 48 | 1622.535 | |
| 49 | 1656.338 | 13/5 |
| 50 | 1690.141 | |
| 51 | 1723.944 | |
| 52 | 1757.746 | |
| 53 | 1791.549 | 31/11 |
| 54 | 1825.352 | |
| 55 | 1859.155 | |
| 56 | 1892.958 | |
| 57 | 1926.761 | |
| 58 | 1960.563 | 31/10 |
| 59 | 1994.366 | 19/6 |
| 60 | 2028.169 | 29/9 |
| 61 | 2061.972 | 23/7 |
| 62 | 2095.775 | |
| 63 | 2129.577 | |
| 64 | 2163.38 | |
| 65 | 2197.183 | |
| 66 | 2230.986 | |
| 67 | 2264.789 | 37/10 |
| 68 | 2298.592 | |
| 69 | 2332.394 | |
| 70 | 2366.197 | |
| 71 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +16.9 | -9.0 | +0.0 | -14.5 | +7.9 | +11.5 | +16.9 | +15.8 | +2.4 | +6.4 | -9.0 |
| Relative (%) | +50.0 | -26.6 | +0.0 | -42.8 | +23.4 | +33.9 | +50.0 | +46.8 | +7.2 | +19.0 | -26.6 | |
| Steps (reduced) |
36 (36) |
56 (56) |
71 (0) |
82 (11) |
92 (21) |
100 (29) |
107 (36) |
113 (42) |
118 (47) |
123 (52) |
127 (56) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.4 | -5.4 | +10.3 | +0.0 | -3.5 | -1.1 | +6.7 | -14.5 | +2.5 | -10.5 | +14.0 |
| Relative (%) | -36.6 | -16.1 | +30.5 | +0.0 | -10.5 | -3.2 | +19.9 | -42.8 | +7.3 | -31.0 | +41.4 | |
| Steps (reduced) |
131 (60) |
135 (64) |
139 (68) |
142 (0) |
145 (3) |
148 (6) |
151 (9) |
153 (11) |
156 (14) |
158 (16) |
161 (19) | |