619edo

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← 618edo619edo620edo →
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