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569edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|569}} == Theory == 569et is only consistent to the 5-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 33554432/33480783..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|569}}
{{ED intro}}


== Theory ==
== Theory ==
569et is only consistent to the [[5-odd-limit]]. Using the patent val, it tempers out 1220703125/1219784832, [[33554432/33480783]], [[65625/65536]] and 200120949/200000000 in the 7-limit; 95703125/95664294, 26214400/26198073, 1953125/1951488, 151263/151250, [[200704/200475]], 1879453125/1879048192, 422576/421875, 160083/160000, 16808715/16777216, 42592/42525 and 43923/43904 in the 11-limit.
569edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit. Using the [[patent val]], it [[tempering out|tempers out]] [[65625/65536]], 823543/820125, and [[33554432/33480783]] in the 7-limit; 42592/42525, 42875/42768, 43923/43904, and 151263/151250 in the 11-limit.


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
569edo is the 104th [[prime EDO]].
569edo is the 104th [[prime edo]].


== 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|902 -569}}
! rowspan="2" | [[Comma list]]
|{{mapping|569 902}}
! rowspan="2" | [[Mapping]]
| -0.1040
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 902 -569 }}
| {{mapping| 569 902 }}
| −0.1040
| 0.1040
| 0.1040
| 4.93
| 4.93
|-
|-
|2.3.5
| 2.3.5
|1600000/1594323, {{monzo|-94 -11 48}}
| 1600000/1594323, {{monzo| -94 -11 48 }}
|{{mapping|569 902 1321}}
| {{mapping| 569 902 1321 }}
| -0.0157
| −0.0157
| 0.1510
| 0.1510
| 7.16
| 7.16
|-
|-
|2.3.5.7
| 2.3.5.7
|823543/820125, 65625/65536, 1600000/1594323
| 65625/65536, 823543/820125, 1600000/1594323
|{{mapping|569 902 1321 1597}}
| {{mapping| 569 902 1321 1597 }}
| +0.0605
| +0.0605
| 0.1858
| 0.1858
| 8.81
| 8.81
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|42875/42768, 42592/42525, 160083/160000, 151263/151250
| 42592/42525, 42875/42768, 43923/43904, 151263/151250
|{{mapping|569 902 1321 1597 1968}}
| {{mapping| 569 902 1321 1597 1968 }}
| +0.0992
| +0.0992
| 0.1834
| 0.1834
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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>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|161\569
| 161\569
|339.54
| 339.54
|243/200
| 243/200
|[[Amity]]
| [[Paramity]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
== Music ==
; [[Francium]]
* "Cuckoo Pickpocket" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/6YZU6zGbFwGcEt5WDEzRFA Spotify] | [https://francium223.bandcamp.com/track/cuckoo-pickpocket Bandcamp] | [https://www.youtube.com/watch?v=DWNS4bGwFKg YouTube]
* "ME" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/6taed4kRYHcc2woLVzjNj7 Spotify] | [https://francium223.bandcamp.com/track/me Bandcamp] | [https://www.youtube.com/watch?v=OlvXsg9GJF8 YouTube]
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