2200edo

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← 2199edo2200edo2201edo →
Prime factorization 23 × 52 × 11
Step size 0.545455¢
Fifth 1287\2200 (702¢) (→117\200)
Semitones (A1:m2) 209:165 (114¢ : 90¢)
Consistency limit 15
Distinct consistency limit 15

2200 equal divisions of the octave (abbreviated 2200edo), or 2200-tone equal temperament (2200tet), 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 of 2200edo 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

Approximation of prime harmonics in 2200edo
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.