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]

Latest revision as of 13:06, 21 February 2025

← 562edo 563edo 564edo →
Prime factorization 563 (prime)
Step size 2.13144 ¢ 
Fifth 329\563 (701.243 ¢)
Semitones (A1:m2) 51:44 (108.7 ¢ : 93.78 ¢)
Dual sharp fifth 330\563 (703.375 ¢)
Dual flat fifth 329\563 (701.243 ¢)
Dual major 2nd 96\563 (204.618 ¢)
Consistency limit 5
Distinct consistency limit 5

563 equal divisions of the octave (abbreviated 563edo or 563ed2), also called 563-tone equal temperament (563tet) or 563 equal temperament (563et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 563 equal parts of about 2.13 ¢ each. Each step represents a frequency ratio of 21/563, or the 563rd root of 2.

Theory

563edo is only consistent to the 5-odd-limit and the error of harmonic 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

Approximation of odd harmonics in 563edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.712 -0.523 +0.979 +0.708 +0.725 -0.741 +0.896 -0.515 +0.888 +0.267 +0.500
Relative (%) -33.4 -24.6 +45.9 +33.2 +34.0 -34.8 +42.1 -24.2 +41.7 +12.5 +23.5
Steps
(reduced) 		892
(329) 		1307
(181) 		1581
(455) 		1785
(96) 		1948
(259) 		2083
(394) 		2200
(511) 		2301
(49) 		2392
(140) 		2473
(221) 		2547
(295)

Subsets and supersets

563edo is the 103rd prime edo. 1689edo, which triples it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.9 [1785 -563⟩ [⟨563 1785]] −0.1117 0.1117 5.24

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 263\563 560.57 864/625 Whoosh

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Music

Francium
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