2019edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 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 (2019edo), or 2019-tone equal temperament (2019tet), 2019 equal temperament (2019et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 2019 equal parts of about 0.594 ¢ each.

Theory

2019edo is excellent in the 2.3.5.7 subgroup, 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)

Regular temperament properties

Rank-2 temperaments

Periods
per 8ve
Generator
(Reduced)
Cents
(Reduced)
Associated
Ratio
Temperaments
1 154\2019 91.530 1953125000000000/1853020188851841 Gross
1 307\2019 182.467 10/9 Minortone
3 307\2019 182.467 10/9 Domain