3889edo
| ← 3888edo | 3889edo | 3890edo → |
Theory
3889edo is consistent to the 27-odd-limit, tempering out 12376/12375, 14400/14399, 6175/6174, 8625/8624, 89376/89375, 123201/123200, 1549184/1549125 and 1990656/1990625 in the 23-limit. It is strong in the 2.3.5.7.13.17.19.23.31 subgroup, tempering out 6175/6174, 14365/14364, 426496/426465, 52326/52325, 52003/52000, 1549184/1549125, 1990656/1990625 and 22816/22815. The equal temperament also tempers out 19251/19250 in the 2.3.5.7.11.23.31 subgroup and 5440/5439 in the 2.3.5.7.17.37 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.025 | +0.007 | +0.061 | +0.083 | -0.003 | -0.044 | -0.059 | -0.041 | +0.096 | +0.040 |
| Relative (%) | +0.0 | +8.1 | +2.2 | +19.7 | +27.0 | -1.0 | -14.3 | -19.0 | -13.2 | +31.2 | +13.1 | |
| Steps (reduced) |
3889 (0) |
6164 (2275) |
9030 (1252) |
10918 (3140) |
13454 (1787) |
14391 (2724) |
15896 (340) |
16520 (964) |
17592 (2036) |
18893 (3337) |
19267 (3711) | |
Subsets and supersets
3889edo is the 539th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [6164 -3889⟩ | [⟨3889 6164]] | −0.0079 | 0.0079 | 2.56 |
| 2.3.5 | [-90 -15 49⟩, [56 -91 38⟩ | [⟨3889 6164 9030]] | −0.0062 | 0.0068 | 2.20 |
| 2.3.5.7 | [-4 17 1 -9⟩, [2 -20 14 -1⟩, [46 -14 -3 -6⟩ | [⟨3889 6164 9030 10918]] | −0.0101 | 0.0089 | 2.88 |
| 2.3.5.7.11 | 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259 | [⟨3889 6164 9030 10918 13454]] | −0.0129 | 0.0098 | 3.18 |
| 2.3.5.7.11.13 | 123201/123200, 6656/6655, 1990656/1990625, 492128/492075, 29046875/29042496 | [⟨3889 6164 9030 10918 13454 14391]] | −0.0106 | 0.0103 | 3.34 |
| 2.3.5.7.11.13.17 | 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179 | [⟨3889 6164 9030 10918 13454 14391 15896]] | −0.0075 | 0.0121 | 3.92 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 602\3889 | 185.755 | [24 4 -13⟩ | Pirate |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct