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563edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|563}}
{{ED intro}}


== Theory ==
== Theory ==
563et is only consistent to the [[5-odd-limit]] and the [[harmonic]] [[3/1|3]] is about halfway its steps. It is suitable for the 2.9.7.11.19.23 [[subgroup]], tempering out [[1863/1862]], [[3971/3969]], 3449952/3447493, 7901568/7891499 and 4333568/4322241.
563edo is only [[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1|3]] is quite large. It is suitable for the 2.9.7.11.19.23 [[subgroup]], [[tempering out]] [[1863/1862]], [[3971/3969]], 3449952/3447493, 7901568/7891499 and 4333568/4322241.


=== Odd harmonics ===
=== Odd harmonics ===
Line 9: Line 9:


=== Subsets and supersets ===
=== Subsets and supersets ===
563edo is the 103rd [[prime edo]]. [[1126edo]], which doubles it, gives a good correction to the harmonic 3.
563edo is the 103rd [[prime edo]]. [[1689edo]], which triples it, gives a good correction to the harmonic 3.


== 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]] (%)
|-
|-
|2.9
! rowspan="2" | [[Subgroup]]
|{{monzo|1785 -563}}
! rowspan="2" | [[Comma list]]
|{{mapping|563 1785}}
! rowspan="2" | [[Mapping]]
| -0.1117
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.9
| {{monzo| 1785 -563 }}
| {{mapping| 563 1785 }}
| −0.1117
| 0.1117
| 0.1117
|5.24
| 5.24
|}
|}


=== 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
|263\563
| 263\563
|560.57
| 560.57
|864/625
| 864/625
|[[Whoosh]]
| [[Whoosh]]
|}
|}
<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 Woodpecker" from ''Cursed Cuckoo Creations'' (2024) &ndash; [https://open.spotify.com/track/2zHIlg1umqSkNrVke3YggJ Spotify] | [https://francium223.bandcamp.com/track/cuckoo-woodpecker Bandcamp] | [https://www.youtube.com/watch?v=7WwIpBsXP2A YouTube]
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