# 2619edo

 ← 2618edo 2619edo 2620edo →
Prime factorization 33 × 97
Step size 0.45819¢
Fifth 1532\2619 (701.947¢)
Semitones (A1:m2) 248:197 (113.6¢ : 90.26¢)
Consistency limit 33
Distinct consistency limit 33

2619 equal divisions of the octave (abbreviated 2619edo or 2619ed2), also called 2619-tone equal temperament (2619tet) or 2619 equal temperament (2619et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2619 equal parts of about 0.458 ¢ each. Each step represents a frequency ratio of 21/2619, or the 2619th root of 2.

2619edo tempers out the ennealimma in the 5-limit, as well as providing the optimal patent val for the rank-3 ennealimmic in the 11-limit. The equal temperament tempers out 2401/2400, 4375/4374, 250047/250000, 420175/419904, 40353607/40310784, 78125000/78121827 in the 7-limit, 214358881/214326000, 1879453125/1879048192 in the 11-limit, 4225/4224, 105644/105625, 123201/123200 in the 13-limit, 12376/12375, 224939/224910, 778855/778752 in the 17-limit, 5929/5928, 5985/5984, 10985/10952 in the 19-limit, 21736/21735, 36179/36176, 42757/42750, 45448/45441, 52003/52000 in the 23-limit.

While not a strong higher-limit system, it is distinctly consistent through the 33-odd-limit, being a flat system, and it is a strong 2.3.5.17.29.31 subgroup tuning. In the 2.3.5.13.17.23.29.31 it tunes the berkelium temperament, dividing the octave in 97 parts, and the berkelium-248 extension for the full 31-limit.

### Prime harmonics

Approximation of prime harmonics in 2619edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.008 -0.059 -0.212 -0.115 -0.207 -0.030 -0.148 -0.096 -0.024 -0.018
Relative (%) +0.0 -1.7 -13.0 -46.3 -25.1 -45.2 -6.5 -32.2 -20.9 -5.2 -4.0
Steps
(reduced)
2619
(0)
4151
(1532)
6081
(843)
7352
(2114)
9060
(1203)
9691
(1834)
10705
(229)
11125
(649)
11847
(1371)
12723
(2247)
12975
(2499)