93ed4
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93 equal divisions of the 4th harmonic (abbreviated 93ed4) is a nonoctave tuning system that divides the interval of 4/1 into 93 equal parts of about 25.8 ¢ each. Each step represents a frequency ratio of 41/93, or the 93rd root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 25.8 | |
| 2 | 51.6 | 34/33, 35/34 |
| 3 | 77.4 | |
| 4 | 103.2 | 35/33 |
| 5 | 129 | |
| 6 | 154.8 | |
| 7 | 180.6 | 10/9 |
| 8 | 206.5 | |
| 9 | 232.3 | |
| 10 | 258.1 | 29/25, 43/37 |
| 11 | 283.9 | |
| 12 | 309.7 | |
| 13 | 335.5 | |
| 14 | 361.3 | |
| 15 | 387.1 | |
| 16 | 412.9 | 33/26 |
| 17 | 438.7 | |
| 18 | 464.5 | 17/13 |
| 19 | 490.3 | |
| 20 | 516.1 | 31/23, 35/26 |
| 21 | 541.9 | 26/19 |
| 22 | 567.7 | 43/31 |
| 23 | 593.5 | 38/27 |
| 24 | 619.4 | 10/7 |
| 25 | 645.2 | |
| 26 | 671 | |
| 27 | 696.8 | |
| 28 | 722.6 | |
| 29 | 748.4 | |
| 30 | 774.2 | |
| 31 | 800 | |
| 32 | 825.8 | |
| 33 | 851.6 | |
| 34 | 877.4 | |
| 35 | 903.2 | |
| 36 | 929 | |
| 37 | 954.8 | 26/15, 33/19 |
| 38 | 980.6 | |
| 39 | 1006.5 | 34/19 |
| 40 | 1032.3 | |
| 41 | 1058.1 | 35/19 |
| 42 | 1083.9 | 43/23 |
| 43 | 1109.7 | 19/10 |
| 44 | 1135.5 | 27/14 |
| 45 | 1161.3 | |
| 46 | 1187.1 | |
| 47 | 1212.9 | |
| 48 | 1238.7 | |
| 49 | 1264.5 | |
| 50 | 1290.3 | |
| 51 | 1316.1 | |
| 52 | 1341.9 | |
| 53 | 1367.7 | |
| 54 | 1393.5 | |
| 55 | 1419.4 | 25/11, 34/15 |
| 56 | 1445.2 | |
| 57 | 1471 | |
| 58 | 1496.8 | |
| 59 | 1522.6 | 41/17 |
| 60 | 1548.4 | 22/9 |
| 61 | 1574.2 | |
| 62 | 1600 | |
| 63 | 1625.8 | |
| 64 | 1651.6 | 13/5 |
| 65 | 1677.4 | 29/11 |
| 66 | 1703.2 | |
| 67 | 1729 | 19/7 |
| 68 | 1754.8 | |
| 69 | 1780.6 | |
| 70 | 1806.5 | |
| 71 | 1832.3 | |
| 72 | 1858.1 | |
| 73 | 1883.9 | |
| 74 | 1909.7 | |
| 75 | 1935.5 | |
| 76 | 1961.3 | |
| 77 | 1987.1 | 41/13 |
| 78 | 2012.9 | |
| 79 | 2038.7 | |
| 80 | 2064.5 | 33/10 |
| 81 | 2090.3 | |
| 82 | 2116.1 | 17/5 |
| 83 | 2141.9 | |
| 84 | 2167.7 | 7/2 |
| 85 | 2193.5 | 39/11 |
| 86 | 2219.4 | |
| 87 | 2245.2 | |
| 88 | 2271 | 26/7 |
| 89 | 2296.8 | |
| 90 | 2322.6 | |
| 91 | 2348.4 | |
| 92 | 2374.2 | |
| 93 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.9 | +7.7 | +0.0 | +0.8 | -5.2 | +11.8 | +12.9 | -10.4 | -12.1 | +3.5 | +7.7 |
| Relative (%) | +50.0 | +29.9 | +0.0 | +3.0 | -20.1 | +45.8 | +50.0 | -40.2 | -47.0 | +13.6 | +29.9 | |
| Steps (reduced) |
47 (47) |
74 (74) |
93 (0) |
108 (15) |
120 (27) |
131 (38) |
140 (47) |
147 (54) |
154 (61) |
161 (68) |
167 (74) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.8 | -1.1 | +8.5 | +0.0 | -1.7 | +2.5 | +12.2 | +0.8 | -6.3 | -9.4 | -8.9 |
| Relative (%) | -7.0 | -4.2 | +33.0 | +0.0 | -6.7 | +9.8 | +47.1 | +3.0 | -24.3 | -36.4 | -34.6 | |
| Steps (reduced) |
172 (79) |
177 (84) |
182 (89) |
186 (0) |
190 (4) |
194 (8) |
198 (12) |
201 (15) |
204 (18) |
207 (21) |
210 (24) | |