1759edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|1759}} == Theory == 1759edo is consistent to the 23-odd-limit, tempering out 3025/3024, 2500/2499, 5985/5984, ..." |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1759edo is [[consistent]] to the [[23-odd-limit]], [[ | 1759edo is [[consistent]] to the [[23-odd-limit]], [[tempering out]] [[3025/3024]], [[2500/2499]], [[5985/5984]], [[4225/4224]], [[6175/6174]], 3520/3519, 14875/14872 and [[256000/255879]]. It [[support]]s [[etampesic]]. [[Essentially tempered chord]]s in 1759et include [[vicetertismic chords]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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== 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 | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
|- | ! colspan="2" | Tuning error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|2788 -1759}} | | {{monzo|2788 -1759}} | ||
| {{mapping|1759 2788}} | | {{mapping|1759 2788}} | ||
| | | −0.0110 | ||
| 0.0110 | | 0.0110 | ||
| 1.61 | | 1.61 | ||
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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* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| [[Vavoom]] | | [[Vavoom]] | ||
|} | |} | ||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Music == | |||
; [[Francium]] | |||
* "Regret" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/2pDNJUQzjQaPJcl1cwLJco Spotify] | [https://francium223.bandcamp.com/track/regret Bandcamp] | [https://www.youtube.com/watch?v=mB-qWsSfn3g YouTube] – in Etampesic, 1759edo tuning | |||
* ''1759'' (2025) – [https://open.spotify.com/album/3zA7ZVP09WlBw4WRjpjAZZ Spotify] | [https://francium223.bandcamp.com/album/1759 Bandcamp] | [https://www.youtube.com/playlist?list=PLLZE7hMjEXRYDHsUEkhpthaxFB4xoK9Tc YouTube] – 4-piece EP in 1759edo | |||
* "Chupacara Smith" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/4Wr1wq3jAAuUdlEqCtrXI1 Spotify] | [https://francium223.bandcamp.com/track/chupacara-smith Bandcamp] | [https://www.youtube.com/watch?v=diKcFA0m21A YouTube] − in Smithsonianic, 1759edo tuning | |||