983edo
| ← 982edo | 983edo | 984edo → |
983 equal divisions of the octave (abbreviated 983edo or 983ed2), also called 983-tone equal temperament (983tet) or 983 equal temperament (983et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 983 equal parts of about 1.22 ¢ each. Each step represents a frequency ratio of 21/983, or the 983rd root of 2.
983edo is consistent in the 5-limit and has a good approximation to the harmonic 3, but it performs poorer in higher limits. It can be used as a high-precision 2.3.11/7.17.31 subgroup tuning, where it tempers out 327726/327701. 983c val, ⟨983 1558 2283 2760 3401], is better tuned than the patent val in the 11-limit, where it is a tuning for the majvamic temperament.
In the 11-limit nonetheless, the patent val supports the 983 & 1848 rank-2 temperament which divides the perfect fifth, 3/2, into 23 even steps. However, the higher harmonics take hundreds of steps to reach. One may instead consider the comma 2.3.11/7 [-99 53 23⟩, with 3/2 reaching in 23 steps and 11/7 in 53, which is more playable.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.022 | -0.556 | +0.452 | +0.462 | +0.571 | +0.029 | +0.351 | +0.413 | -0.483 | +0.031 |
| Relative (%) | +0.0 | -1.8 | -45.5 | +37.0 | +37.9 | +46.8 | +2.4 | +28.7 | +33.9 | -39.5 | +2.5 | |
| Steps (reduced) |
983 (0) |
1558 (575) |
2282 (316) |
2760 (794) |
3401 (452) |
3638 (689) |
4018 (86) |
4176 (244) |
4447 (515) |
4775 (843) |
4870 (938) | |