# 2554edo

← 2553edo | 2554edo | 2555edo → |

**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 2^{1/2554}, 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

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 | +1 | -20 | +2 | -39 | +8 | -38 | -21 | -18 | -28 | -2 | +6 | -19 | |

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.