81ed4
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Prime factorization
34
Step size
29.6296¢
Octave
41\81ed4 (1214.81¢)
Twelfth
64\81ed4 (1896.3¢)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 79ed4 | 81ed4 | 83ed4 → |
81 equal divisions of the 4th harmonic (abbreviated 81ed4) is a nonoctave tuning system that divides the interval of 4/1 into 81 equal parts of about 29.6 ¢ each. Each step represents a frequency ratio of 41/81, or the 81st root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 29.6 | |
| 2 | 59.3 | 30/29, 31/30 |
| 3 | 88.9 | 39/37 |
| 4 | 118.5 | 31/29 |
| 5 | 148.1 | |
| 6 | 177.8 | |
| 7 | 207.4 | 35/31 |
| 8 | 237 | |
| 9 | 266.7 | 7/6 |
| 10 | 296.3 | |
| 11 | 325.9 | 35/29 |
| 12 | 355.6 | 38/31 |
| 13 | 385.2 | |
| 14 | 414.8 | |
| 15 | 444.4 | 22/17 |
| 16 | 474.1 | 25/19 |
| 17 | 503.7 | |
| 18 | 533.3 | |
| 19 | 563 | 18/13 |
| 20 | 592.6 | 31/22 |
| 21 | 622.2 | 33/23 |
| 22 | 651.9 | |
| 23 | 681.5 | 37/25 |
| 24 | 711.1 | |
| 25 | 740.7 | 23/15 |
| 26 | 770.4 | 39/25 |
| 27 | 800 | |
| 28 | 829.6 | 21/13 |
| 29 | 859.3 | |
| 30 | 888.9 | |
| 31 | 918.5 | 17/10 |
| 32 | 948.1 | 19/11 |
| 33 | 977.8 | 37/21 |
| 34 | 1007.4 | |
| 35 | 1037 | 31/17 |
| 36 | 1066.7 | |
| 37 | 1096.3 | |
| 38 | 1125.9 | |
| 39 | 1155.6 | 37/19 |
| 40 | 1185.2 | |
| 41 | 1214.8 | |
| 42 | 1244.4 | 37/18, 39/19 |
| 43 | 1274.1 | 23/11 |
| 44 | 1303.7 | |
| 45 | 1333.3 | |
| 46 | 1363 | 11/5 |
| 47 | 1392.6 | 38/17 |
| 48 | 1422.2 | 25/11 |
| 49 | 1451.9 | |
| 50 | 1481.5 | |
| 51 | 1511.1 | |
| 52 | 1540.7 | |
| 53 | 1570.4 | |
| 54 | 1600 | |
| 55 | 1629.6 | |
| 56 | 1659.3 | |
| 57 | 1688.9 | |
| 58 | 1718.5 | |
| 59 | 1748.1 | |
| 60 | 1777.8 | |
| 61 | 1807.4 | |
| 62 | 1837 | |
| 63 | 1866.7 | |
| 64 | 1896.3 | |
| 65 | 1925.9 | |
| 66 | 1955.6 | 31/10 |
| 67 | 1985.2 | 22/7 |
| 68 | 2014.8 | |
| 69 | 2044.4 | |
| 70 | 2074.1 | |
| 71 | 2103.7 | |
| 72 | 2133.3 | |
| 73 | 2163 | |
| 74 | 2192.6 | 39/11 |
| 75 | 2222.2 | |
| 76 | 2251.9 | 11/3 |
| 77 | 2281.5 | |
| 78 | 2311.1 | 19/5 |
| 79 | 2340.7 | |
| 80 | 2370.4 | |
| 81 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +14.8 | -5.7 | +0.0 | -1.1 | +9.2 | +9.0 | +14.8 | -11.3 | +13.7 | -3.2 | -5.7 |
| Relative (%) | +50.0 | -19.1 | +0.0 | -3.8 | +30.9 | +30.2 | +50.0 | -38.2 | +46.2 | -10.7 | -19.1 | |
| Steps (reduced) |
41 (41) |
64 (64) |
81 (0) |
94 (13) |
105 (24) |
114 (33) |
122 (41) |
128 (47) |
135 (54) |
140 (59) |
145 (64) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.9 | -5.9 | -6.8 | +0.0 | +13.6 | +3.5 | -1.2 | -1.1 | +3.3 | +11.6 | -6.1 |
| Relative (%) | +13.2 | -19.8 | -22.9 | +0.0 | +45.8 | +11.8 | -4.1 | -3.8 | +11.1 | +39.3 | -20.4 | |
| Steps (reduced) |
150 (69) |
154 (73) |
158 (77) |
162 (0) |
166 (4) |
169 (7) |
172 (10) |
175 (13) |
178 (16) |
181 (19) |
183 (21) | |