2200edo
| ← 2199edo | 2200edo | 2201edo → |
2200 equal divisions of the octave (abbreviated 2200edo or 2200ed2), also called 2200-tone equal temperament (2200tet) or 2200 equal temperament (2200et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2200 equal parts of about 0.545 ¢ each. Each step represents a frequency ratio of 21/2200, or the 2200th root of 2.
2200edo is consistent in the 15-odd-limit. In higher limits, it is good as an add-23 system. The patent val doesn't tune any famous or previously named temperaments. Nonetheless, it does temper out 420175/419904 and the septiruthenia in the 7-limit, and 4225/4224 and 6656/6655 in the 13-limit.
Using the 2200c val, ⟨2200 3487 5109 6176], while worse in error, enables the tuning of period-22 major arcana and period-44 ruthenium temperaments.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.045 | -0.132 | -0.099 | +0.137 | +0.018 | -0.228 | -0.240 | +0.089 | +0.241 | -0.126 |
| relative (%) | +0 | +8 | -24 | -18 | +25 | +3 | -42 | -44 | +16 | +44 | -23 | |
| Steps (reduced) |
2200 (0) |
3487 (1287) |
5108 (708) |
6176 (1776) |
7611 (1011) |
8141 (1541) |
8992 (192) |
9345 (545) |
9952 (1152) |
10688 (1888) |
10899 (2099) | |
2200edo factors as 23 × 52 × 11, having subset edos 1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100.
As 2200 = 22 × 100, one step of 2200edo is the relative cent for 22edo.