71ed4
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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 | 33.8 | |
| 2 | 67.6 | |
| 3 | 101.4 | 18/17, 35/33 |
| 4 | 135.2 | 27/25 |
| 5 | 169 | |
| 6 | 202.8 | |
| 7 | 236.6 | |
| 8 | 270.4 | 7/6 |
| 9 | 304.2 | 31/26, 37/31 |
| 10 | 338 | |
| 11 | 371.8 | 26/21 |
| 12 | 405.6 | |
| 13 | 439.4 | |
| 14 | 473.2 | |
| 15 | 507 | |
| 16 | 540.8 | 26/19 |
| 17 | 574.6 | |
| 18 | 608.5 | 37/26 |
| 19 | 642.3 | |
| 20 | 676.1 | 31/21, 34/23 |
| 21 | 709.9 | |
| 22 | 743.7 | |
| 23 | 777.5 | 36/23 |
| 24 | 811.3 | |
| 25 | 845.1 | 31/19 |
| 26 | 878.9 | |
| 27 | 912.7 | |
| 28 | 946.5 | 19/11 |
| 29 | 980.3 | 30/17, 37/21 |
| 30 | 1014.1 | 9/5 |
| 31 | 1047.9 | 11/6 |
| 32 | 1081.7 | |
| 33 | 1115.5 | |
| 34 | 1149.3 | 33/17, 35/18 |
| 35 | 1183.1 | |
| 36 | 1216.9 | |
| 37 | 1250.7 | 35/17, 37/18 |
| 38 | 1284.5 | 21/10 |
| 39 | 1318.3 | |
| 40 | 1352.1 | |
| 41 | 1385.9 | 29/13 |
| 42 | 1419.7 | |
| 43 | 1453.5 | |
| 44 | 1487.3 | 26/11 |
| 45 | 1521.1 | |
| 46 | 1554.9 | |
| 47 | 1588.7 | |
| 48 | 1622.5 | |
| 49 | 1656.3 | 13/5 |
| 50 | 1690.1 | |
| 51 | 1723.9 | |
| 52 | 1757.7 | |
| 53 | 1791.5 | 31/11 |
| 54 | 1825.4 | |
| 55 | 1859.2 | |
| 56 | 1893 | |
| 57 | 1926.8 | |
| 58 | 1960.6 | 31/10 |
| 59 | 1994.4 | 19/6 |
| 60 | 2028.2 | 29/9 |
| 61 | 2062 | 23/7 |
| 62 | 2095.8 | |
| 63 | 2129.6 | |
| 64 | 2163.4 | |
| 65 | 2197.2 | |
| 66 | 2231 | |
| 67 | 2264.8 | 37/10 |
| 68 | 2298.6 | |
| 69 | 2332.4 | |
| 70 | 2366.2 | |
| 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) | |