1619edo
| Prime factorization | 1619 (prime) |
| Step size | 0.741198¢ |
| Fifth | 947\1619 (701.915¢) |
| Major 2nd | 275\1619 (203.830¢) |
| Semitones (A1:m2) | 153:122 (113.403¢ : 90.426¢) |
1619edo divides the octave into parts of about 0.741 cents each.
Theory
1619edo is excellent in the 13-limit, where it tempers out 4225/4224, 4375/4374, 6656/6655, 78125/78078, and 117649/117612. It also notably tempers out 123201/123200. It supports vidar, which has the comma basis 4225/4224, 4375/4374, and 6656/6655, and other unnamed expansions of the ragismic temperament such as the 270 & 441 & 1619, tempering out 4225/4224, 4375/4374, 655473/655360, or the 72 & 270 & 494 & 1619 temperament tempering out 6656/6655 and 2912000/2910897.
1619edo has 7/6 on 360th step, a highly divisible number, 27/25 on 180th, and 33/32 on 72nd as a consequence of tempering out the commas. This means that 72ed33/32 is virtually equivalent to 1619edo. When it comes to using 33/32 as the generator, 1619edo supports the 832 & 1619 temperament, which tempers out 196625/196608, 200000/199927, 2912000/2910897, and 3764768/3764475.
1619edo is the 256th Prime edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.040 | -0.149 | -0.080 | +0.134 | -0.009 | +0.295 | -0.293 | +0.262 | -0.053 |
| relative (%) | +0 | -5 | -20 | -11 | +18 | -1 | +40 | -39 | +35 | -7 | |
| Steps (reduced) |
1619 (0) |
2566 (947) |
3759 (521) |
4545 (1307) |
5601 (744) |
5991 (1134) |
6618 (142) |
6877 (401) |
7324 (848) |
7865 (1389) | |
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2566 1619⟩ | [⟨1619 2566]] | +0.0127 | 0.0127 | 1.71 |
| 2.3.5 | [-69 45 -1⟩, [-82 -1 36⟩ | [⟨1619 2566 3759]] | +0.0299 | 0.0265 | 3.57 |
| 2.3.5.7 | 4375/4374, 52734375/52706752, [-67 14 6 11⟩ | [⟨1619 2566 3759 4545]] | +0.0295 | 0.0229 | 3.09 |
| 2.3.5.7.11 | 4375/4374, 117649/117612, 759375/758912, [24 -6 0 1 -5⟩ | [⟨1619 2566 3759 4545 5601]] | +0.0159 | 0.0341 | 4.60 |
| 2.3.5.7.11.13 | 4225/4224, 4375/4374, 6656/6655, 78125/78078, 117649/117612 | [⟨1619 2566 3759 4545 5601 5991]] | +0.0136 | 0.0315 | 4.26 |