1889edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== 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= | {{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 == | |||
{| class="wikitable center-4 center-5 center-6" | |||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! 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 | |||
| 0.19 | |||
|- | |||
| 2.3.5 | |||
| {{Monzo| 54 -37 2 }}, {{monzo| -66 -36 53 }} | |||
| {{Mapping| 1889 2994 4386 }} | |||
| +0.0104 | |||
| 0.0163 | |||
| 2.57 | |||
|- | |||
| 2.3.5.7 | |||
| 4375/4374, {{monzo| -1 4 11 -1 }}, {{monzo| -57 16 10 3 }} | |||
| {{Mapping| 1889 2994 4386 5303 }} | |||
| +0.0131 | |||
| 0.0149 | |||
| 2.35 | |||
|- | |||
| 2.3.5.7.11 | |||
| 4375/4374, 151263/151250, 820125/819896, {{monzo| -28 7 7 -1 1 }} | |||
| {{Mapping| 1889 2994 4386 5303 6535 }} | |||
| +0.0055 | |||
| 0.0201 | |||
| 3.16 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 4225/4224, 4375/4374, 6656/6655, 151263/151250, 4100625/4100096 | |||
| {{Mapping| 1889 2994 4386 5303 6535 6990 }} | |||
| +0.0084 | |||
| 0.0194 | |||
| 3.05 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 4225/4224, 4375/4374, 6656/6655, 12376/12375, 14875/14872, 194481/194480 | |||
| {{Mapping| 1889 2994 4386 5303 6535 6990 7721 }} | |||
| +0.0120 | |||
| 0.0200 | |||
| 3.15 | |||
|- | |||
| 2.3.5.7.11.13.17.19 | |||
| 4225/4224, 4375/4374, 5985/5984, 6175/6174, 6656/6655, 12376/12375, 61965/61952 | |||
| {{Mapping| 1889 2994 4386 5303 6535 6990 7721 8024 }} | |||
| +0.0167 | |||
| 0.0226 | |||
| 3.56 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 392\1889 | |||
| 249.021 | |||
| {{Monzo| -26 18 1 }} | |||
| [[Monzismic]] | |||
|- | |||
| 1 | |||
| 707\1889 | |||
| 449.127 | |||
| 35/27 | |||
| [[Semidimi]] | |||
|} | |||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct | |||
== Music == | |||
; [[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] | |||
* "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]] | ||