107edt
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Prime factorization
107 (prime)
Step size
17.7753¢
Octave
68\107edt (1208.72¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 106edt | 107edt | 108edt → |
107 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 107edt or 107ed3), is a nonoctave tuning system that divides the interval of 3/1 into 107 equal parts of about 17.8 ¢ each. Each step represents a frequency ratio of 31/107, or the 107th root of 3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 17.775 | |
| 2 | 35.551 | |
| 3 | 53.326 | 34/33 |
| 4 | 71.101 | |
| 5 | 88.876 | 39/37 |
| 6 | 106.652 | |
| 7 | 124.427 | 29/27 |
| 8 | 142.202 | 38/35 |
| 9 | 159.978 | 45/41 |
| 10 | 177.753 | 41/37 |
| 11 | 195.528 | |
| 12 | 213.303 | |
| 13 | 231.079 | |
| 14 | 248.854 | 15/13 |
| 15 | 266.629 | 7/6 |
| 16 | 284.404 | 46/39 |
| 17 | 302.18 | 25/21 |
| 18 | 319.955 | |
| 19 | 337.73 | 45/37 |
| 20 | 355.506 | |
| 21 | 373.281 | |
| 22 | 391.056 | |
| 23 | 408.831 | 19/15 |
| 24 | 426.607 | |
| 25 | 444.382 | |
| 26 | 462.157 | 17/13 |
| 27 | 479.933 | 33/25 |
| 28 | 497.708 | |
| 29 | 515.483 | 31/23, 35/26 |
| 30 | 533.258 | 34/25 |
| 31 | 551.034 | |
| 32 | 568.809 | 25/18 |
| 33 | 586.584 | |
| 34 | 604.36 | |
| 35 | 622.135 | |
| 36 | 639.91 | |
| 37 | 657.685 | 19/13 |
| 38 | 675.461 | |
| 39 | 693.236 | |
| 40 | 711.011 | |
| 41 | 728.786 | |
| 42 | 746.562 | |
| 43 | 764.337 | |
| 44 | 782.112 | 11/7 |
| 45 | 799.888 | 27/17, 46/29 |
| 46 | 817.663 | |
| 47 | 835.438 | 34/21 |
| 48 | 853.213 | 18/11 |
| 49 | 870.989 | |
| 50 | 888.764 | |
| 51 | 906.539 | |
| 52 | 924.315 | 29/17, 46/27 |
| 53 | 942.09 | |
| 54 | 959.865 | |
| 55 | 977.64 | |
| 56 | 995.416 | |
| 57 | 1013.191 | |
| 58 | 1030.966 | |
| 59 | 1048.742 | 11/6 |
| 60 | 1066.517 | |
| 61 | 1084.292 | 43/23 |
| 62 | 1102.067 | 17/9 |
| 63 | 1119.843 | 21/11 |
| 64 | 1137.618 | |
| 65 | 1155.393 | 37/19 |
| 66 | 1173.169 | |
| 67 | 1190.944 | |
| 68 | 1208.719 | |
| 69 | 1226.494 | |
| 70 | 1244.27 | 39/19 |
| 71 | 1262.045 | |
| 72 | 1279.82 | |
| 73 | 1297.595 | |
| 74 | 1315.371 | |
| 75 | 1333.146 | 41/19 |
| 76 | 1350.921 | |
| 77 | 1368.697 | |
| 78 | 1386.472 | |
| 79 | 1404.247 | |
| 80 | 1422.022 | 25/11 |
| 81 | 1439.798 | 39/17 |
| 82 | 1457.573 | |
| 83 | 1475.348 | |
| 84 | 1493.124 | 45/19 |
| 85 | 1510.899 | |
| 86 | 1528.674 | 46/19 |
| 87 | 1546.449 | |
| 88 | 1564.225 | 37/15 |
| 89 | 1582 | |
| 90 | 1599.775 | |
| 91 | 1617.551 | |
| 92 | 1635.326 | 18/7 |
| 93 | 1653.101 | 13/5 |
| 94 | 1670.876 | |
| 95 | 1688.652 | |
| 96 | 1706.427 | |
| 97 | 1724.202 | 46/17 |
| 98 | 1741.977 | 41/15 |
| 99 | 1759.753 | |
| 100 | 1777.528 | |
| 101 | 1795.303 | |
| 102 | 1813.079 | 37/13 |
| 103 | 1830.854 | |
| 104 | 1848.629 | |
| 105 | 1866.404 | |
| 106 | 1884.18 | |
| 107 | 1901.955 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.72 | +0.00 | -0.34 | +4.41 | +8.72 | +8.48 | +8.38 | +0.00 | -4.65 | +8.10 | -0.34 |
| Relative (%) | +49.1 | +0.0 | -1.9 | +24.8 | +49.1 | +47.7 | +47.2 | +0.0 | -26.2 | +45.6 | -1.9 | |
| Steps (reduced) |
68 (68) |
107 (0) |
135 (28) |
157 (50) |
175 (68) |
190 (83) |
203 (96) |
214 (0) |
224 (10) |
234 (20) |
242 (28) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.29 | -0.58 | +4.41 | -0.67 | +1.02 | +8.72 | +3.99 | +4.07 | +8.48 | -0.96 | -6.81 |
| Relative (%) | +18.5 | -3.3 | +24.8 | -3.8 | +5.7 | +49.1 | +22.5 | +22.9 | +47.7 | -5.4 | -38.3 | |
| Steps (reduced) |
250 (36) |
257 (43) |
264 (50) |
270 (56) |
276 (62) |
282 (68) |
287 (73) |
292 (78) |
297 (83) |
301 (87) |
305 (91) | |