1619edo: Difference between revisions
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In general, 1619edo supports vidar, with the comma set 4225/4224, 4375/4374, and 6656/6655. | In general, 1619edo supports vidar, with the comma set 4225/4224, 4375/4374, and 6656/6655. | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |Subgroup | |||
! rowspan="2" |[[Comma list]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal | |||
8ve stretch (¢) | |||
! colspan="2" |Tuning error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{monzo|-2566 1619}} | |||
|[{{val|1619 2566}}] | |||
|0.013 | |||
|0.013 | |||
|1.7 | |||
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|2.3.5 | |||
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|2.3.5.7 | |||
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|2.3.5.7.11 | |||
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|2.3.5.7.11.13 | |||
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|2.3.5.7.11.13.17 | |||
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|2.3.5.7.11.13.17 | |||
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[[Category:Ragismic family]] | [[Category:Ragismic family]] | ||
Revision as of 07:40, 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 | |||||
| 2.3.5.7 | |||||
| 2.3.5.7.11 | |||||
| 2.3.5.7.11.13 | |||||
| 2.3.5.7.11.13.17 | |||||
| 2.3.5.7.11.13.17 | |||||