2619edo
| ← 2618edo | 2619edo | 2620edo → |
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
| 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) | |