73ed4
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73 equal divisions of the 4th harmonic (abbreviated 73ed4) is a nonoctave tuning system that divides the interval of 4/1 into 73 equal parts of about 32.9 ¢ each. Each step represents a frequency ratio of 41/73, or the 73rd root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 32.9 | |
| 2 | 65.8 | 26/25, 27/26, 28/27 |
| 3 | 98.6 | 35/33, 37/35 |
| 4 | 131.5 | 14/13, 27/25 |
| 5 | 164.4 | |
| 6 | 197.3 | 28/25, 37/33 |
| 7 | 230.1 | |
| 8 | 263 | |
| 9 | 295.9 | |
| 10 | 328.8 | 23/19, 35/29 |
| 11 | 361.6 | |
| 12 | 394.5 | |
| 13 | 427.4 | |
| 14 | 460.3 | |
| 15 | 493.2 | |
| 16 | 526 | 19/14, 23/17 |
| 17 | 558.9 | 29/21 |
| 18 | 591.8 | 31/22, 38/27 |
| 19 | 624.7 | 33/23 |
| 20 | 657.5 | 19/13 |
| 21 | 690.4 | |
| 22 | 723.3 | 35/23, 38/25 |
| 23 | 756.2 | 17/11 |
| 24 | 789 | |
| 25 | 821.9 | 37/23 |
| 26 | 854.8 | |
| 27 | 887.7 | 5/3 |
| 28 | 920.5 | |
| 29 | 953.4 | 26/15, 33/19 |
| 30 | 986.3 | 23/13 |
| 31 | 1019.2 | 9/5 |
| 32 | 1052.1 | |
| 33 | 1084.9 | |
| 34 | 1117.8 | 21/11 |
| 35 | 1150.7 | 33/17, 37/19 |
| 36 | 1183.6 | |
| 37 | 1216.4 | |
| 38 | 1249.3 | 35/17 |
| 39 | 1282.2 | |
| 40 | 1315.1 | |
| 41 | 1347.9 | 37/17 |
| 42 | 1380.8 | |
| 43 | 1413.7 | 34/15 |
| 44 | 1446.6 | |
| 45 | 1479.5 | |
| 46 | 1512.3 | |
| 47 | 1545.2 | 22/9 |
| 48 | 1578.1 | |
| 49 | 1611 | 33/13, 38/15 |
| 50 | 1643.8 | |
| 51 | 1676.7 | 29/11 |
| 52 | 1709.6 | |
| 53 | 1742.5 | |
| 54 | 1775.3 | |
| 55 | 1808.2 | 37/13 |
| 56 | 1841.1 | |
| 57 | 1874 | |
| 58 | 1906.8 | |
| 59 | 1939.7 | |
| 60 | 1972.6 | |
| 61 | 2005.5 | 35/11 |
| 62 | 2038.4 | |
| 63 | 2071.2 | |
| 64 | 2104.1 | |
| 65 | 2137 | |
| 66 | 2169.9 | |
| 67 | 2202.7 | |
| 68 | 2235.6 | |
| 69 | 2268.5 | |
| 70 | 2301.4 | 34/9 |
| 71 | 2334.2 | |
| 72 | 2367.1 | |
| 73 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +16.4 | +4.9 | +0.0 | +8.2 | -11.5 | -15.4 | +16.4 | +9.8 | -8.2 | -8.9 | +4.9 |
| Relative (%) | +50.0 | +14.9 | +0.0 | +25.0 | -35.1 | -46.8 | +50.0 | +29.8 | -25.0 | -26.9 | +14.9 | |
| Steps (reduced) |
37 (37) |
58 (58) |
73 (0) |
85 (12) |
94 (21) |
102 (29) |
110 (37) |
116 (43) |
121 (48) |
126 (53) |
131 (58) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.2 | +1.0 | +13.1 | +0.0 | -6.3 | -6.6 | -1.6 | +8.2 | -10.5 | +7.6 | -3.6 |
| Relative (%) | -6.6 | +3.2 | +39.8 | +0.0 | -19.2 | -20.2 | -4.9 | +25.0 | -32.0 | +23.1 | -11.0 | |
| Steps (reduced) |
135 (62) |
139 (66) |
143 (70) |
146 (0) |
149 (3) |
152 (6) |
155 (9) |
158 (12) |
160 (14) |
163 (17) |
165 (19) | |