1619edo

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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

Approximation of prime harmonics in 1619edo
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