# 619edo

 ← 618edo 619edo 620edo →
Prime factorization 619 (prime)
Step size 1.93861¢
Fifth 362\619 (701.777¢)
Semitones (A1:m2) 58:47 (112.4¢ : 91.11¢)
Consistency limit 5
Distinct consistency limit 5

619 equal divisions of the octave (abbreviated 619edo or 619ed2), also called 619-tone equal temperament (619tet) or 619 equal temperament (619et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 619 equal parts of about 1.94 ¢ each. Each step represents a frequency ratio of 21/619, or the 619th root of 2.

## Theory

619edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.11.17.19.23.29.41 subgroup, tempering out 2025/2024, 1089/1088, 3520/3519, 1045/1044, 2755/2754, 71875/71808, 374000/373977 and 1025/1024.

### Prime harmonics

Approximation of prime harmonics in 619edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.178 -0.530 +0.479 -0.753 +0.829 -0.270 -0.906 -0.164 -0.175 +0.683
Relative (%) +0.0 -9.2 -27.3 +24.7 -38.8 +42.8 -13.9 -46.7 -8.5 -9.0 +35.2
Steps
(reduced)
619
(0)
981
(362)
1437
(199)
1738
(500)
2141
(284)
2291
(434)
2530
(54)
2629
(153)
2800
(324)
3007
(531)
3067
(591)

### Subsets and supersets

619edo is the 114th prime EDO.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-981 619 [619 981]] 0.0561 0.0561 2.89
2.3.5 32805/32768, [-54 -67 69 [619 981 1437]] 0.1135 0.0932 4.81
2.3.5.11 32805/32768, 234375/234256, 314552734375/313456656384 [619 981 1437 2141]] 0.1395 0.0925 4.77

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 257\619 498.223 4/3 Helmholtz

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