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1619edo supports a very precise rank two temperament, {{nowrap|19 & 1619}}, which uses [[6/5]] as a generator and has a comma basis 4375/4374, 91125/91091, 196625/196608, and 54925000/54908469.   
1619edo supports a very precise rank two temperament, {{nowrap|19 & 1619}}, which uses [[6/5]] as a generator and has a comma basis 4375/4374, 91125/91091, 196625/196608, and 54925000/54908469.   


1619edo supports the keenanose temperament, which has comma basis 4225/4224, 4375/4374, 6656/6655, and 151263/151250. Keenanisma is the generator in the keenanose temperament, {{nowrap|270 & 1619}}, in which it highlights the relationship between 270 keenanismas and the octave. It also achieves this since {{nowrap|270 × 6 {{=}} 1620}}, and 1619 is 1 short of that and also excellent in the 13-limit.   
1619edo supports the keenanose temperament, which has comma basis 4225/4224, 4375/4374, 6656/6655, and 151263/151250. Keenanisma is the generator in the keenanose temperament, {{nowrap| 270 & 1619 }}, in which it highlights the relationship between 270 keenanismas and the octave. It also achieves this since {{nowrap| 270 × 6 {{=}} 1620 }}, and 1619 is 1 short of that and also excellent in the 13-limit.   


Another temperament which highlights the interval relationships in 1619edo is {{nowrap|45 & 1619}}, called ''decigrave'', since 10 steps make a 7/6, which is referred to as the grave minor third sometimes. It has a comma basis 4225/4224, 4375/4374, 6656/6655, {{monzo|23  5 13 -23  1 0}} in the 13-limit. Its generator is 36 steps, which represents 65/64 and 66/65 tempered together, and 2 of them make 33/32. 5 of them make [[27/25]], and 10 of them make 7/6.   
Another temperament which highlights the interval relationships in 1619edo is {{nowrap| 45 & 1619 }}, called ''decigrave'', since 10 steps make a 7/6, which is referred to as the grave minor third sometimes. It has a comma basis 4225/4224, 4375/4374, 6656/6655, {{monzo|23  5 13 -23  1 0}} in the 13-limit. Its generator is 36 steps, which represents 65/64 and 66/65 tempered together, and 2 of them make 33/32. 5 of them make [[27/25]], and 10 of them make 7/6.   


1619edo supports the {{nowrap|494 & 1619}} temperament called moulin, with the comma basis of 4225/4224, 4375/4374, 6656/6655, 91125/91091. The 25-tone scale of moulin is capable of supporting the 8:11:13 triad, as it takes less than 25 notes to map the 11th and 13th harmonics.   
1619edo supports the {{nowrap| 494 & 1619 }} temperament called moulin, with the comma basis of 4225/4224, 4375/4374, 6656/6655, 91125/91091. The 25-tone scale of moulin is capable of supporting the 8:11:13 triad, as it takes less than 25 notes to map the 11th and 13th harmonics.   


=== The Vidarines ===
=== The Vidarines ===
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|-
|-
! Temperament
! Temperament
! Generator<br />associated ratio
! Generator<br>associated ratio
! Completing comma
! Completing comma
|-
|-
| Keenanose ({{nowrap|270 &amp; 1619}})
| Keenanose ({{nowrap| 270 & 1619 }})
| 385/384
| 385/384
| 151263/151250
| 151263/151250
|-
|-
| Decigrave ({{nowrap|45 &amp; 1619}})
| Decigrave ({{nowrap| 45 & 1619 }})
| 66/65 ~ 65/64
| 66/65 ~ 65/64
| {{monzo|23  5 13 -23  1 0}}
| {{Monzo| 23 5 13 -23 1 0 }}
|-
|-
| Moulin ({{nowrap|494 &amp; 1619}})
| Moulin ({{nowrap| 494 & 1619 }})
| 13/11
| 13/11
| 91125/91091
| 91125/91091
|-
|-
| {{nowrap|46 &amp; 1619}}
| {{Nowrap| 46 & 1619 }}
| 3328/3087
| 3328/3087
| {{monzo| -18 9 -2 8 -3 -1 }}
| {{Monzo| -18 9 -2 8 -3 -1 }}
|-
|-
| {{nowrap|178 &amp; 1619}}
| {{Nowrap| 178 & 1619 }}
| 4429568/4084101
| 4429568/4084101
| {{monzo| -29 10 2 12 -3 -4 }}
| {{Monzo| -29 10 2 12 -3 -4 }}
|-
|-
| {{nowrap|224 &amp; 1619}}
| {{nowrap| 224 & 1619 }}
| 256/175
| 256/175
| 18753525/18743296
| 18753525/18743296
|-
|-
| {{nowrap|764 &amp; 1619}}
| {{nowrap| 764 & 1619 }}
| 12375/8918
| 12375/8918
| 52734375/52706752
| 52734375/52706752
|-
|-
| {{nowrap|901 &amp; 1619}}
| {{nowrap| 901 & 1619 }}
| 104/99
| 104/99
| 34875815625/34843787264
| 34875815625/34843787264
|}
|}
While [[abigail]] is a member of the vidarines, 1619edo does not support it because abigail is a period-2 temperament, and 1619 is an odd number.
While [[abigail]] is a member of the vidarines, 1619edo does not support it because abigail has a semi-octave period, and 1619 is an odd number.


=== Prime harmonics ===
=== Prime harmonics ===
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| perfect octave
| perfect octave
|}
|}
<nowiki />* Named in accordance to their most just 13-limit counterpart using the names accepted on the wiki.
<nowiki/>* Named in accordance to their most just 13-limit counterpart using the names accepted on the wiki.


== Regular temperament properties ==
== Regular temperament properties ==
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! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning error
|-
|-
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|-
|-
| 2.3
| 2.3
| {{monzo| -2566 1619 }}
| {{Monzo| -2566 1619 }}
| [{{val| 1619 2566 }}]
| {{Mapping| 1619 2566 }}
| +0.0127
| +0.0127
| 0.0127
| 0.0127
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|-
|-
| 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 }}]
| {{Mapping| 1619 2566 3759 }}
| +0.0299
| +0.0299
| 0.0265
| 0.0265
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| 2.3.5.7
| 2.3.5.7
| 4375/4374, 52734375/52706752, {{monzo| -67 14 6 11 }}
| 4375/4374, 52734375/52706752, {{monzo| -67 14 6 11 }}
| [{{val| 1619 2566 3759 4545 }}]
| {{Mapping| 1619 2566 3759 4545 }}
| +0.0295
| +0.0295
| 0.0229
| 0.0229
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| 2.3.5.7.11
| 2.3.5.7.11
| 4375/4374, 117649/117612, 759375/758912, {{monzo| 24 -6 0 1 -5 }}
| 4375/4374, 117649/117612, 759375/758912, {{monzo| 24 -6 0 1 -5 }}
| [{{val| 1619 2566 3759 4545 5601 }}]
| {{Mapping| 1619 2566 3759 4545 5601 }}
| +0.0159
| +0.0159
| 0.0341
| 0.0341
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| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 4225/4224, 4375/4374, 6656/6655, 78125/78078, 117649/117612
| 4225/4224, 4375/4374, 6656/6655, 78125/78078, 117649/117612
| [{{val| 1619 2566 3759 4545 5601 5991 }}]
| {{Mapping| 1619 2566 3759 4545 5601 5991 }}
| +0.0136
| +0.0136
| 0.0315
| 0.0315
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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
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| 435.083
| 435.083
| 9/7
| 9/7
| [[Supermajor]]
| [[Supermajor (temperament)|Supermajor]]
|-
|-
| 1
| 1
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| [[Counterschismic]]
| [[Counterschismic]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if  distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms|minimal form]] in parentheses if  distinct


== Music ==
== Music ==
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* "Le's Cancel Monday" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/5yxExt1gC5KA1grtcefU2m Spotify] | [https://francium223.bandcamp.com/track/les-cancel-monday Bandcamp] | [https://www.youtube.com/watch?v=TWAsePkJvtI YouTube]
* "Le's Cancel Monday" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/5yxExt1gC5KA1grtcefU2m Spotify] | [https://francium223.bandcamp.com/track/les-cancel-monday Bandcamp] | [https://www.youtube.com/watch?v=TWAsePkJvtI YouTube]
* "this you?" from ''Questions, Vol. 2'' (2025) – [https://open.spotify.com/track/3ZdhHP0wAyzg9aQkKwQIar Spotify] | [https://francium223.bandcamp.com/track/this-you Bandcamp] | [https://www.youtube.com/watch?v=28NveBGA3-U YouTube]
* "this you?" from ''Questions, Vol. 2'' (2025) – [https://open.spotify.com/track/3ZdhHP0wAyzg9aQkKwQIar Spotify] | [https://francium223.bandcamp.com/track/this-you Bandcamp] | [https://www.youtube.com/watch?v=28NveBGA3-U YouTube]
* "Derpy Cat" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/1j301ZrWIbkw1b8Ar5Ww5L Spotify] | [https://francium223.bandcamp.com/track/derpy-cat Bandcamp] | [https://www.youtube.com/watch?v=qjNJoR__pT4 YouTube]


[[Category:Quartismic]]
[[Category:Quartismic]]
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