2019edo

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← 2018edo2019edo2020edo →
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 2019-tone equal temperament (2019tet), 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 of 2019edo 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 -4 +3 -5 +41 -19 +41 +43 -7 -26 +48
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