107ed11
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| ← 106ed11 | 107ed11 | 108ed11 → |
(semiconvergent)
107 equal divisions of the 11th harmonic (abbreviated 107ed11) is a nonoctave tuning system that divides the interval of 11/1 into 107 equal parts of about 38.8 ¢ each. Each step represents a frequency ratio of 111/107, or the 107th root of 11.
Theory
107ed11 is related to 31edo, but with the 11/1 rather than the 2/1 being just. The octave is stretched by 2.718 ¢, which is interesting in that it is almost exactly e cents. Like 31edo, 107ed11 is consistent through the 12-integer-limit, but unlike 31edo it has a discrepancy for the 13th harmonic.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.7 | -0.9 | +5.4 | +7.1 | +1.8 | +6.5 | +8.2 | -1.8 | +9.8 | +0.0 | +4.6 |
| Relative (%) | +7.0 | -2.3 | +14.0 | +18.3 | +4.7 | +16.9 | +21.0 | -4.6 | +25.3 | +0.0 | +11.7 | |
| Steps (reduced) |
31 (31) |
49 (49) |
62 (62) |
72 (72) |
80 (80) |
87 (87) |
93 (93) |
98 (98) |
103 (103) |
107 (0) |
111 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.6 | +9.3 | +6.2 | +10.9 | -16.5 | +0.9 | -15.1 | +12.5 | +5.7 | +2.7 | +3.4 | +7.3 |
| Relative (%) | -45.4 | +23.9 | +16.0 | +28.0 | -42.5 | +2.4 | -38.8 | +32.3 | +14.6 | +7.0 | +8.7 | +18.7 | |
| Steps (reduced) |
114 (7) |
118 (11) |
121 (14) |
124 (17) |
126 (19) |
129 (22) |
131 (24) |
134 (27) |
136 (29) |
138 (31) |
140 (33) |
142 (35) | |
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 38.8 | 43/42, 44/43, 45/44, 46/45 |
| 2 | 77.6 | 23/22, 45/43 |
| 3 | 116.4 | 31/29, 46/43 |
| 4 | 155.2 | 35/32 |
| 5 | 194 | 19/17, 28/25 |
| 6 | 232.8 | 8/7 |
| 7 | 271.6 | |
| 8 | 310.4 | |
| 9 | 349.2 | 11/9 |
| 10 | 388 | 5/4 |
| 11 | 426.8 | 32/25, 41/32 |
| 12 | 465.6 | 17/13 |
| 13 | 504.4 | |
| 14 | 543.2 | 26/19 |
| 15 | 582 | 7/5 |
| 16 | 620.8 | |
| 17 | 659.6 | 41/28 |
| 18 | 698.4 | |
| 19 | 737.1 | 26/17 |
| 20 | 775.9 | 36/23 |
| 21 | 814.7 | 8/5 |
| 22 | 853.5 | 18/11 |
| 23 | 892.3 | |
| 24 | 931.1 | 12/7 |
| 25 | 969.9 | 7/4 |
| 26 | 1008.7 | 34/19, 43/24 |
| 27 | 1047.5 | 11/6 |
| 28 | 1086.3 | 15/8 |
| 29 | 1125.1 | 23/12, 44/23 |
| 30 | 1163.9 | 45/23 |
| 31 | 1202.7 | |
| 32 | 1241.5 | 41/20, 43/21 |
| 33 | 1280.3 | 44/21 |
| 34 | 1319.1 | 15/7 |
| 35 | 1357.9 | 46/21 |
| 36 | 1396.7 | |
| 37 | 1435.5 | 39/17 |
| 38 | 1474.3 | |
| 39 | 1513.1 | |
| 40 | 1551.9 | |
| 41 | 1590.7 | |
| 42 | 1629.5 | 41/16 |
| 43 | 1668.3 | |
| 44 | 1707.1 | |
| 45 | 1745.9 | |
| 46 | 1784.7 | 14/5 |
| 47 | 1823.5 | 43/15 |
| 48 | 1862.3 | 41/14, 44/15 |
| 49 | 1901.1 | 3/1 |
| 50 | 1939.9 | 46/15 |
| 51 | 1978.7 | |
| 52 | 2017.5 | |
| 53 | 2056.3 | |
| 54 | 2095.1 | |
| 55 | 2133.9 | 24/7 |
| 56 | 2172.7 | |
| 57 | 2211.4 | 43/12 |
| 58 | 2250.2 | 11/3 |
| 59 | 2289 | 15/4 |
| 60 | 2327.8 | 23/6 |
| 61 | 2366.6 | |
| 62 | 2405.4 | |
| 63 | 2444.2 | 41/10 |
| 64 | 2483 | 21/5 |
| 65 | 2521.8 | |
| 66 | 2560.6 | |
| 67 | 2599.4 | |
| 68 | 2638.2 | |
| 69 | 2677 | |
| 70 | 2715.8 | 24/5 |
| 71 | 2754.6 | |
| 72 | 2793.4 | |
| 73 | 2832.2 | |
| 74 | 2871 | 21/4 |
| 75 | 2909.8 | 43/8 |
| 76 | 2948.6 | |
| 77 | 2987.4 | |
| 78 | 3026.2 | 23/4 |
| 79 | 3065 | |
| 80 | 3103.8 | 6/1 |
| 81 | 3142.6 | 43/7 |
| 82 | 3181.4 | 44/7 |
| 83 | 3220.2 | 45/7 |
| 84 | 3259 | 46/7 |
| 85 | 3297.8 | |
| 86 | 3336.6 | |
| 87 | 3375.4 | |
| 88 | 3414.2 | |
| 89 | 3453 | |
| 90 | 3491.8 | |
| 91 | 3530.6 | |
| 92 | 3569.4 | |
| 93 | 3608.2 | |
| 94 | 3647 | |
| 95 | 3685.7 | 42/5 |
| 96 | 3724.5 | 43/5 |
| 97 | 3763.3 | 44/5 |
| 98 | 3802.1 | 9/1 |
| 99 | 3840.9 | 46/5 |
| 100 | 3879.7 | |
| 101 | 3918.5 | |
| 102 | 3957.3 | |
| 103 | 3996.1 | |
| 104 | 4034.9 | |
| 105 | 4073.7 | |
| 106 | 4112.5 | 43/4 |
| 107 | 4151.3 | 11/1 |