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{{Infobox ET
{{Infobox ET
| Prime factorization = 1619 (is prime)
| Prime factorization = 1619 (prime)
| Step size = 0.741¢
| Step size = 0.741198¢
| Fifth = 947\1619(701.9148¢)
| Fifth = 947\1619 (701.915¢)
| Major 2nd = 275\1619 (203.8295¢)
| Major 2nd = 275\1619 (203.830¢)
| Semitones = 275:153
| Semitones = 153:122 (113.403¢ : 90.426¢)
}}
}}
1619edo divides the octave into parts of 741 millicents each. It is the 256th [[Prime EDO]].
'''1619edo''' divides the octave into parts of about 0.741 cents each.  


== Theory ==
== Theory ==
{{Harmonics in equal|1619|columns=10}}
1619edo is excellent in the 13-limit. It supports an extension of the [[Ragismic family|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.  
1619edo is excellent in the 13-limit. It supports an extension of the [[Ragismic family|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.
In general, 1619edo supports vidar, with the comma set 4225/4224, 4375/4374, and 6656/6655.


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 equivalent to 1619edo. When it comes to using 33/32 as the generator, 1619edo supports the temperament that tempers out 196625/196608, 200000/199927, 2912000/2910897, 3764768/3764475.
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 equivalent to 1619edo. When it comes to using 33/32 as the generator, 1619edo supports the temperament that tempers out 196625/196608, 200000/199927, 2912000/2910897, 3764768/3764475.
1619edo is the 256th [[Prime edo]].
=== Prime harmonics ===
{{Harmonics in equal|1619|columns=10}}


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |Subgroup
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal
! rowspan="2" | Optimal<br>8ve stretch (¢)
8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" |Tuning error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
|2.3
|{{monzo|-2566 1619}}
| {{monzo| -2566 1619 }}
|[{{val|1619 2566}}]
| [{{val| 1619 2566 }}]
|0.013
| 0.013
|0.013
| 0.013
|1.7
| 1.7
|-
|-
|2.3.5
| 2.3.5
|{{monzo|-69, 45, -1}}, {{monzo|-82, -1, 36}}
| {{monzo| -69 45 -1 }}, {{monzo| -82 -1 36 }}
|[{{val|1619 2566 3759}}]
| [{{val| 1619 2566 3759 }}]
|0.030
| 0.030
|0.026
| 0.026
|3.5
| 3.5
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, {{monzo|-6 3 9 -7}}, {{monzo|-67 14 6 11}}
| 4375/4374, {{monzo| -6 3 9 -7 }}, {{monzo| -67 14 6 11 }}
|[{{val|1619 2566 3759 4545}}]
| [{{val| 1619 2566 3759 4545 }}]
|0.030
| 0.030
|0.023
| 0.023
|3.1
| 3.1
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|117649/117612, 151263/151250, 759375/758912, [[117440512/117406179]]
| 117649/117612, 151263/151250, 759375/758912, [[117440512/117406179]]
|[{{val|1619 2566 3759 4545 5601}}]
| [{{val| 1619 2566 3759 4545 5601 }}]
|0.016
| 0.016
|0.034
| 0.034
|4.0
| 4.0
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|4225/4224, 43940/43923, 151263/151250, 91125/91091, 123201/123200
| 4225/4224, 43940/43923, 151263/151250, 91125/91091, 123201/123200
|[{{val|1619 2566 3759 4545 5601 5991}}]
| [{{val| 1619 2566 3759 4545 5601 5991 }}]
|0.013
| 0.013
|0.032
| 0.032
|4.2
| 4.2
|-
|-
|}
|}
[[Category:Ragismic family]]
 
[[Category:Equal divisions of the octave]]
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