# 1861edo

 ← 1860edo 1861edo 1862edo →
Prime factorization 1861 (prime)
Step size 0.644815¢
Fifth 1089\1861 (702.203¢)
Semitones (A1:m2) 179:138 (115.4¢ : 88.98¢)
Dual sharp fifth 1089\1861 (702.203¢)
Dual flat fifth 1088\1861 (701.558¢)
Dual major 2nd 316\1861 (203.761¢)
Consistency limit 5
Distinct consistency limit 5

1861 equal divisions of the octave (abbreviated 1861edo or 1861ed2), also called 1861-tone equal temperament (1861tet) or 1861 equal temperament (1861et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1861 equal parts of about 0.645 ¢ each. Each step represents a frequency ratio of 21/1861, or the 1861st root of 2.

## Theory

1861edo is only consistent to the 5-odd-limit, and the harmonic 3 is about halfway between its steps. It has a reasonable approximation of the 2.9.5.21.11 subgroup.

### Odd harmonics

Approximation of odd harmonics in 1861edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.248 -0.070 -0.314 -0.149 -0.001 +0.311 +0.178 +0.149 -0.253 -0.066 -0.225
Relative (%) +38.5 -10.8 -48.8 -23.0 -0.2 +48.2 +27.7 +23.2 -39.3 -10.3 -34.9
Steps
(reduced)
2950
(1089)
4321
(599)
5224
(1502)
5899
(316)
6438
(855)
6887
(1304)
7271
(1688)
7607
(163)
7905
(461)
8174
(730)
8418
(974)

### Subsets and supersets

1861edo is the 284th prime edo. 3722edo, which doubles it, provides a good correction to harmonics 3, 7, and 13.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [-5899 1861 [1861 5899]] +0.0234 0.0234 3.63

Francium