109ed4
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Prime factorization
109 (prime)
Step size
22.0183¢
Octave
55\109ed4 (1211.01¢)
Twelfth
86\109ed4 (1893.58¢)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 107ed4 | 109ed4 | 111ed4 → |
109 equal divisions of the 4th harmonic (abbreviated 109ed4) is a nonoctave tuning system that divides the interval of 4/1 into 109 equal parts of about 22 ¢ each. Each step represents a frequency ratio of 41/109, or the 109th root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 22.018 | |
| 2 | 44.037 | |
| 3 | 66.055 | 26/25 |
| 4 | 88.073 | 41/39 |
| 5 | 110.092 | 33/31 |
| 6 | 132.11 | |
| 7 | 154.128 | 47/43 |
| 8 | 176.147 | 41/37 |
| 9 | 198.165 | 28/25, 37/33 |
| 10 | 220.183 | 25/22, 42/37 |
| 11 | 242.202 | |
| 12 | 264.22 | |
| 13 | 286.239 | |
| 14 | 308.257 | 37/31, 43/36 |
| 15 | 330.275 | 23/19 |
| 16 | 352.294 | |
| 17 | 374.312 | 36/29, 41/33 |
| 18 | 396.33 | 39/31 |
| 19 | 418.349 | 14/11 |
| 20 | 440.367 | |
| 21 | 462.385 | 17/13, 47/36 |
| 22 | 484.404 | 41/31 |
| 23 | 506.422 | |
| 24 | 528.44 | 19/14 |
| 25 | 550.459 | |
| 26 | 572.477 | |
| 27 | 594.495 | |
| 28 | 616.514 | |
| 29 | 638.532 | |
| 30 | 660.55 | |
| 31 | 682.569 | 43/29 |
| 32 | 704.587 | |
| 33 | 726.606 | 35/23, 38/25 |
| 34 | 748.624 | |
| 35 | 770.642 | |
| 36 | 792.661 | 30/19 |
| 37 | 814.679 | |
| 38 | 836.697 | 47/29 |
| 39 | 858.716 | 23/14 |
| 40 | 880.734 | |
| 41 | 902.752 | |
| 42 | 924.771 | 29/17 |
| 43 | 946.789 | 19/11 |
| 44 | 968.807 | |
| 45 | 990.826 | |
| 46 | 1012.844 | |
| 47 | 1034.862 | |
| 48 | 1056.881 | 35/19, 46/25 |
| 49 | 1078.899 | |
| 50 | 1100.917 | |
| 51 | 1122.936 | |
| 52 | 1144.954 | |
| 53 | 1166.972 | |
| 54 | 1188.991 | |
| 55 | 1211.009 | |
| 56 | 1233.028 | |
| 57 | 1255.046 | 31/15 |
| 58 | 1277.064 | 23/11 |
| 59 | 1299.083 | 36/17 |
| 60 | 1321.101 | 15/7 |
| 61 | 1343.119 | |
| 62 | 1365.138 | 11/5 |
| 63 | 1387.156 | 29/13 |
| 64 | 1409.174 | |
| 65 | 1431.193 | |
| 66 | 1453.211 | |
| 67 | 1475.229 | |
| 68 | 1497.248 | |
| 69 | 1519.266 | |
| 70 | 1541.284 | |
| 71 | 1563.303 | 37/15 |
| 72 | 1585.321 | 5/2 |
| 73 | 1607.339 | 43/17 |
| 74 | 1629.358 | |
| 75 | 1651.376 | |
| 76 | 1673.394 | |
| 77 | 1695.413 | |
| 78 | 1717.431 | |
| 79 | 1739.45 | 41/15 |
| 80 | 1761.468 | 36/13, 47/17 |
| 81 | 1783.486 | 14/5 |
| 82 | 1805.505 | |
| 83 | 1827.523 | |
| 84 | 1849.541 | |
| 85 | 1871.56 | |
| 86 | 1893.578 | |
| 87 | 1915.596 | |
| 88 | 1937.615 | |
| 89 | 1959.633 | |
| 90 | 1981.651 | |
| 91 | 2003.67 | 35/11 |
| 92 | 2025.688 | |
| 93 | 2047.706 | |
| 94 | 2069.725 | 43/13 |
| 95 | 2091.743 | |
| 96 | 2113.761 | |
| 97 | 2135.78 | |
| 98 | 2157.798 | |
| 99 | 2179.817 | |
| 100 | 2201.835 | |
| 101 | 2223.853 | 47/13 |
| 102 | 2245.872 | |
| 103 | 2267.89 | |
| 104 | 2289.908 | |
| 105 | 2311.927 | 19/5 |
| 106 | 2333.945 | |
| 107 | 2355.963 | |
| 108 | 2377.982 | |
| 109 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +11.01 | -8.38 | +0.00 | +10.02 | +2.63 | -0.02 | +11.01 | +5.26 | -0.99 | +10.15 | -8.38 |
| Relative (%) | +50.0 | -38.0 | +0.0 | +45.5 | +12.0 | -0.1 | +50.0 | +23.9 | -4.5 | +46.1 | -38.0 | |
| Steps (reduced) |
55 (55) |
86 (86) |
109 (0) |
127 (18) |
141 (32) |
153 (44) |
164 (55) |
173 (64) |
181 (72) |
189 (80) |
195 (86) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.18 | +10.99 | +1.64 | +0.00 | +5.14 | -5.74 | +10.74 | +10.02 | -8.40 | -0.86 | +10.26 |
| Relative (%) | +32.6 | +49.9 | +7.4 | +0.0 | +23.3 | -26.1 | +48.8 | +45.5 | -38.1 | -3.9 | +46.6 | |
| Steps (reduced) |
202 (93) |
208 (99) |
213 (104) |
218 (0) |
223 (5) |
227 (9) |
232 (14) |
236 (18) |
239 (21) |
243 (25) |
247 (29) | |