# 3125edo

 ← 3124edo 3125edo 3126edo →
Prime factorization 55
Step size 0.384¢
Fifth 1828\3125 (701.952¢)
Semitones (A1:m2) 296:235 (113.7¢ : 90.24¢)
Consistency limit 15
Distinct consistency limit 15

3125 equal divisions of the octave (abbreviated 3125edo or 3125ed2), also called 3125-tone equal temperament (3125tet) or 3125 equal temperament (3125et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3125 equal parts of exactly 0.384 ¢ each. Each step represents a frequency ratio of 21/3125, or the 3125th root of 2.

## Theory

3125edo is distinctly consistent through the 15-odd-limit. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and 117440512/117406179 are tempered out – it should be noted this edo is so far the only one known to have been confirmed as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five 33/32 quartertones and one 7/6 subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.

In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.

### Prime harmonics

Approximation of prime harmonics in 3125edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.003 -0.010 +0.006 +0.106 +0.048 -0.123 +0.087 -0.050 -0.073 +0.052
Relative (%) +0.0 -0.8 -2.5 +1.6 +27.6 +12.6 -32.1 +22.7 -13.1 -19.1 +13.7
Steps
(reduced)
3125
(0)
4953
(1828)
7256
(1006)
8773
(2523)
10811
(1436)
11564
(2189)
12773
(273)
13275
(775)
14136
(1636)
15181
(2681)
15482
(2982)

### Subsets and supersets

3125 = 55, and as such it is the 5th edo of the form nn. It has subset edos 5, 25, 125, and 625.

## Regular temperament properties

3125et is notable for being an extremely strong 7-limit system, being the first equal division past 171edo with a lower relative error.

### Rank-2 temperaments

Periods
per 8ve
Generator* Cents* Associated
Ratio
Temperaments
1 139\3125 53.376 33/32 Prequartismic