# 2019edo

 ← 2018edo 2019edo 2020edo →
Prime factorization 3 × 673
Step size 0.594354¢
Fifth 1181\2019 (701.932¢)
Semitones (A1:m2) 191:152 (113.5¢ : 90.34¢)
Consistency limit 11
Distinct consistency limit 11

2019 equal divisions of the octave (abbreviated 2019edo or 2019ed2), also called 2019-tone equal temperament (2019tet) or 2019 equal temperament (2019et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2019 equal parts of about 0.594 ¢ each. Each step represents a frequency ratio of 21/2019, or the 2019th root of 2.

## Theory

2019edo is excellent in the 7-limit, and with such small errors it supports a noticeable amount of very high accuracy temperaments. While it is consistent in the 11-odd-limit, there is a large relative error on the representation of the 11th harmonic.

In higher limits, it tunes 23/16 and 59/32 with the comparable relative accuracy to the 2.3.5.7 subgroup (less than 7% error). A comma basis for the 2.3.5.7.23.59 subgroup is {14337/14336, 25921/25920, 250047/250000, 48234496/48234375, 843396867/843308032}.

### Prime harmonics

Approximation of prime harmonics in 2019edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.023 +0.016 -0.029 +0.242 -0.112 +0.245 +0.258 -0.043 -0.157 +0.284
Relative (%) +0.0 -3.9 +2.7 -5.0 +40.8 -18.8 +41.3 +43.4 -7.2 -26.4 +47.8
Steps
(reduced)
2019
(0)
3200
(1181)
4688
(650)
5668
(1630)
6985
(928)
7471
(1414)
8253
(177)
8577
(501)
9133
(1057)
9808
(1732)
10003
(1927)

### Subsets and supersets

Since 2019 factors into 3 × 673, 2019 contains 3edo and 673edo as subsets.

## Regular temperament properties

### Rank-2 temperaments

Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 154\2019 91.530 [46 -7 -15 Gross
1 307\2019 182.467 10/9 Minortone
3 307\2019 182.467 10/9 Domain

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct