1619edo: Difference between revisions
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| Line 27: | Line 27: | ||
|- | |- | ||
|2.3.5 | |2.3.5 | ||
| | |{{monzo|-69, 45, -1}}, {{monzo|-82, -1, 36}} | ||
| | |[{{val|1619 2566 3759}}] | ||
| | |0.030 | ||
| | |0.026 | ||
| | |3.5 | ||
|- | |- | ||
|2.3.5.7 | |2.3.5.7 | ||
| | |4375/4374, {{monzo|-6 3 9 -7}}, {{monzo|-67 14 6 11}} | ||
| | |[{{val|1619 2566 3759 4545}}] | ||
| | |0.030 | ||
| | |0.023 | ||
| | |3.1 | ||
|- | |- | ||
|2.3.5.7.11 | |2.3.5.7.11 | ||
| | |117649/117612, 151263/151250, 759375/758912, [[117440512/117406179]] | ||
| | |[{{val|1619 2566 3759 4545 5601}}] | ||
| | |0.016 | ||
| | |0.034 | ||
| | |4.0 | ||
|- | |- | ||
|2.3.5.7.11.13 | |2.3.5.7.11.13 | ||
| | |4225/4224, 43940/43923, 151263/151250, 91125/91091, 123201/123200 | ||
| | |[{{val|1619 2566 3759 4545 5601 5991}}] | ||
| | |0.013 | ||
| | |0.032 | ||
| | |4.2 | ||
|- | |- | ||
|} | |} | ||
[[Category:Ragismic family]] | [[Category:Ragismic family]] | ||
Revision as of 08:18, 12 March 2022
1619edo divides the octave into parts of 741 millicents each. It is the 256th Prime EDO.
Theory
| 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 (%) | +0.0 | -5.4 | -20.2 | -10.8 | +18.0 | -1.2 | +39.8 | -39.5 | +35.3 | -7.1 | |
| Steps (reduced) |
1619 (0) |
2566 (947) |
3759 (521) |
4545 (1307) |
5601 (744) |
5991 (1134) |
6618 (142) |
6877 (401) |
7324 (848) |
7865 (1389) | |
1619edo is excellent in the 13-limit. It supports an extension of the ragismic temperament with 2 extra dimensions in several ways. First, it supports the 441 & 270 & 1619 rank 3 temperament tempering out 4225/4224, 4375/4374, 123201/123200, 655473/655360, 1664000/1663893, and 6470695/6469632. Second, it supports 72 & 494 & 270 & 1619 temperament tempering out 6656/6655, 2912000/2910897, and 29115625/29113344.
In general, 1619edo supports vidar, with the comma set 4225/4224, 4375/4374, and 6656/6655.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal
8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2566 1619⟩ | [⟨1619 2566]] | 0.013 | 0.013 | 1.7 |
| 2.3.5 | [-69, 45, -1⟩, [-82, -1, 36⟩ | [⟨1619 2566 3759]] | 0.030 | 0.026 | 3.5 |
| 2.3.5.7 | 4375/4374, [-6 3 9 -7⟩, [-67 14 6 11⟩ | [⟨1619 2566 3759 4545]] | 0.030 | 0.023 | 3.1 |
| 2.3.5.7.11 | 117649/117612, 151263/151250, 759375/758912, 117440512/117406179 | [⟨1619 2566 3759 4545 5601]] | 0.016 | 0.034 | 4.0 |
| 2.3.5.7.11.13 | 4225/4224, 43940/43923, 151263/151250, 91125/91091, 123201/123200 | [⟨1619 2566 3759 4545 5601 5991]] | 0.013 | 0.032 | 4.2 |