2243edo
| ← 2242edo | 2243edo | 2244edo → |
2243 equal divisions of the octave (abbreviated 2243edo or 2243ed2), also called 2243-tone equal temperament (2243tet) or 2243 equal temperament (2243et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2243 equal parts of about 0.535 ¢ each. Each step represents a frequency ratio of 21/2243, or the 2243rd root of 2.
Theory
2243edo is consistent to the 9-odd-limit tempering out 43046721/43025920, 78125000/78121827 and 281484423828125/281474976710656 in the 7-limit. It is strong in the 2.3.5.7.13.17.19 subgroup, tempering out 5832/5831, 6175/6174, 14365/14364, 121875/121856, 1003833/1003520 and 1101600/1101373. Using the 2.3.5.17.19 subgroup it tempers out the lakisma. Using the 2.3.7.13.31.37 subgroup, it tempers out 3627/3626. It supports hemiegads.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.038 | -0.045 | +0.055 | +0.265 | -0.046 | -0.096 | -0.054 | -0.187 | -0.241 | -0.140 |
| Relative (%) | +0.0 | -7.1 | -8.5 | +10.3 | +49.5 | -8.6 | -17.9 | -10.1 | -34.9 | -45.1 | -26.2 | |
| Steps (reduced) |
2243 (0) |
3555 (1312) |
5208 (722) |
6297 (1811) |
7760 (1031) |
8300 (1571) |
9168 (196) |
9528 (556) |
10146 (1174) |
10896 (1924) |
11112 (2140) | |
Subsets and supersets
2243edo is the 334th prime edo. 4486edo, which doubles it, gives a good correction to its harmonic 11.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-3555 2243⟩ | [⟨2243 3555]] | 0.0120 | 0.0120 | 2.24 |
| 2.3.5 | [-69 45 -1⟩, [-36 -52 51⟩ | [⟨2243 3555 5208]] | 0.0145 | 0.0104 | 1.94 |
| 2.3.5.7 | 43046721/43025920, 78125000/78121827, [-48 0 11 8⟩ | [⟨2243 3555 5208 6297]] | 0.0060 | 0.0173 | 3.23 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 590\2243 | 315.649 | 6/5 | Egads |
| 1 | 931\2243 | 498.083 | 4/3 | Counterschismic |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct