# 2554edo

 ← 2553edo 2554edo 2555edo →
Prime factorization 2 × 1277
Step size 0.469851¢
Fifth 1494\2554 (701.958¢) (→747\1277)
Semitones (A1:m2) 242:192 (113.7¢ : 90.21¢)
Consistency limit 41
Distinct consistency limit 41

2554 equal divisions of the octave (abbreviated 2554edo or 2554ed2), also called 2554-tone equal temperament (2554tet) or 2554 equal temperament (2554et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2554 equal parts of about 0.47 ¢ each. Each step represents a frequency ratio of 21/2554, or the 2554th root of 2.

2554edo is a remarkable very high limit equal temperament. It is consistent through the 41-odd-limit distinctly, tempering out 3025/3024, 4675/4674, 6325/6324, 7106/7105, 7216/7215, 7905/7904, 12155/12152, 13300/13299, 13950/13949, 14652/14651, 56265/56252, and 92701/92690. It provides the optimal patent val for the rank-4 temperament tempering out 3025/3024, the lehmerisma, and thor, the rank-3 temperament also tempering out 4375/4374. It is enfactored in the 7-limit, with the same mapping as 1277edo.

### Prime harmonics

Approximation of prime harmonics in 2554edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) +0.000 +0.003 -0.096 +0.007 -0.182 +0.036 -0.179 -0.097 -0.083 -0.133 -0.008 +0.026 -0.088
Relative (%) +0.0 +0.6 -20.4 +1.6 -38.8 +7.7 -38.0 -20.7 -17.7 -28.3 -1.7 +5.6 -18.8
Steps
(reduced)
2554
(0)
4048
(1494)
5930
(822)
7170
(2062)
8835
(1173)
9451
(1789)
10439
(223)
10849
(633)
11553
(1337)
12407
(2191)
12653
(2437)
13305
(535)
13683
(913)

### Subsets and supersets

Since 2554 factors into 2 × 1277, 2554edo contains 2edo and 1277edo as subsets.