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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1889}}  
{{ED intro}}  
== Theory ==
== Theory ==
1889edo is strong in the [[23-limit]], though [[1578edo|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament.  
1889edo is strong in the [[23-limit]], though [[1578edo|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament.  


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|1889|columns=11}}
{{Harmonics in equal|1889|columns=9}}
{{Harmonics in equal|1889|columns=9|start=10|title=Approximation of prime harmonics in 1889edo (continued)}}


=== Subsets and supersets ===
=== Subsets and supersets ===
1889edo is the 290th [[prime edo]].  
1889edo is the 290th [[prime edo]].  
== Intervals ==
{{Main|Table of 1889edo intervals}}


== 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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|2994 -1889}}
! rowspan="2" | [[Comma list]]
|{{mapping|1889 2994}}
! rowspan="2" | [[Mapping]]
| -0.0012
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| 2994 -1889 }}
| {{Mapping| 1889 2994 }}
| −0.0012
| 0.0012
| 0.0012
| 0.19
| 0.19
|-
|-
|2.3.5
| 2.3.5
|{{monzo|54 -37 2}}, {{monzo|-66 -36 53}}
| {{Monzo| 54 -37 2 }}, {{monzo| -66 -36 53 }}
|{{mapping|1889 2994 4386}}
| {{Mapping| 1889 2994 4386 }}
| +0.0104
| +0.0104
| 0.0163
| 0.0163
| 2.57
| 2.57
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 3955078125/3954653486, {{monzo|-57 16 10 3}}
| 4375/4374, {{monzo| -1 4 11 -1 }}, {{monzo| -57 16 10 3 }}
|{{mapping|1889 2994 4386 5303}}
| {{Mapping| 1889 2994 4386 5303 }}
| +0.0131
| +0.0131
| 0.0149
| 0.0149
| 2.35
| 2.35
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|4375/4374, 151263/151250, 820125/819896, 1879453125/1879048192
| 4375/4374, 151263/151250, 820125/819896, {{monzo| -28 7 7 -1 1 }}
|{{mapping|1889 2994 4386 5303 6535}}
| {{Mapping| 1889 2994 4386 5303 6535 }}
| +0.0055
| +0.0055
| 0.0201
| 0.0201
| 3.16
| 3.16
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|4375/4374, 4225/4224, 6656/6655, 4100625/4100096, 151263/151250
| 4225/4224, 4375/4374, 6656/6655, 151263/151250, 4100625/4100096
|{{mapping|1889 2994 4386 5303 6535 6990}}
| {{Mapping| 1889 2994 4386 5303 6535 6990 }}
| +0.0084
| +0.0084
| 0.0194
| 0.0194
| 3.05
| 3.05
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|4375/4374, 12376/12375, 4225/4224, 14400/14399, 14875/14872, 194481/194480
| 4225/4224, 4375/4374, 6656/6655, 12376/12375, 14875/14872, 194481/194480
|{{mapping|1889 2994 4386 5303 6535 6990 7721}}
| {{Mapping| 1889 2994 4386 5303 6535 6990 7721 }}
| +0.0120
| +0.0120
| 0.0200
| 0.0200
| 3.15
| 3.15
|-
|-
|2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
|4375/4374, 12376/12375, 5985/5984, 4225/4224, 14400/14399, 6175/6174, 61965/61952
| 4225/4224, 4375/4374, 5985/5984, 6175/6174, 6656/6655, 12376/12375, 61965/61952
|{{mapping|1889 2994 4386 5303 6535 6990 7721 8024}}
| {{Mapping| 1889 2994 4386 5303 6535 6990 7721 8024 }}
| +0.0167
| +0.0167
| 0.0226
| 0.0226
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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+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<br>(reduced)*
! Generator*
! Cents<br>(reduced)*
! Cents*
! Associated<br>Ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|392\1889
| 392\1889
|249.021
| 249.021
|{{monzo|-26 18 1}}
| {{Monzo| -26 18 1 }}
|[[Monzismic]]
| [[Monzismic]]
|-
|-
|1
| 1
|707\1889
| 707\1889
|449.127
| 449.127
|35/27
| 35/27
|[[Semidimi]]
| [[Semidimi]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct


== Music ==
== Music ==
; [[Francium]]
; [[Francium]]
* "Scoop" from ''Scoop'' (2024) – [https://open.spotify.com/track/7stqQkZKeaaonzwH2rnhzH Spotify] | [https://francium223.bandcamp.com/track/scoop Bandcamp] | [https://www.youtube.com/watch?v=387kUkmHIrk YouTube]
* "Scoop" from ''Scoop'' (2024) – [https://open.spotify.com/track/7stqQkZKeaaonzwH2rnhzH Spotify] | [https://francium223.bandcamp.com/track/scoop Bandcamp] | [https://www.youtube.com/watch?v=387kUkmHIrk YouTube]
* "The Technological Harbinger of Death" from ''Void'' (2025) – [https://open.spotify.com/track/3LDPz84VhVrTDgPLHQXWyJ YouTube] | [https://francium223.bandcamp.com/track/the-technological-harbinger-of-death Bandcamp] | [https://www.youtube.com/watch?v=CEeXQsHpCc8 YouTube]
* "Don't Worry" from ''Don't'' (2025) – [https://open.spotify.com/track/3Kd1Ql1nYOBMhFWi94ljEP Spotify] | [https://francium223.bandcamp.com/track/dont-worry Bandcamp] | [https://www.youtube.com/watch?v=8CCFVZkxIgk YouTube]


[[Category:Monzismic]]
[[Category:Monzismic]]
Retrieved from "https://en.xen.wiki/w/1889edo"