1063edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1063}}
{{ED intro}}


== Theory ==
== Theory ==
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== Regular temperament properties ==
== Regular temperament properties ==
{{comma basis begin}}
{| 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
| 2.3
| {{monzo|1685 -1063}}
| {{monzo|1685 -1063}}
| {{mapping|1063 1685}}
| {{mapping|1063 1685}}
| -0.0658
| −0.0658
| 0.0658
| 0.0658
| 5.83
| 5.83
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| {{monzo|-20 -24 25}}, {{monzo|77 -31 -12}}
| {{monzo|-20 -24 25}}, {{monzo|77 -31 -12}}
| {{mapping|1063 1685 2468}}
| {{mapping|1063 1685 2468}}
| -0.0099
| −0.0099
| 0.0956
| 0.0956
| 8.47
| 8.47
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| 0.0937
| 0.0937
| 8.30
| 8.30
{{comma basis end}}
|}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{{rank-2 begin}}
{| 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
| 1
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| 6/5
| 6/5
| [[Counterhanson]]
| [[Counterhanson]]
{{rank-2 end}}
|}
{{orf}}
<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 ==
== Music ==
; [[Francium]]
; [[Francium]]
* "Interlude" from ''hope in dark times'' (2024) &ndash; [https://open.spotify.com/track/5jf2rJgqeFTYNmbZgopI3e Spotify] | [https://francium223.bandcamp.com/track/interlude Bandcamp] | [https://www.youtube.com/watch?v=oKVRo72Jhzg YouTube]
* "Interlude" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/5jf2rJgqeFTYNmbZgopI3e Spotify] | [https://francium223.bandcamp.com/track/interlude Bandcamp] | [https://www.youtube.com/watch?v=oKVRo72Jhzg YouTube]
* ''1063'' (2024) &ndash; [https://open.spotify.com/album/2J338pHEIYcB5GBDCCbChg Spotify] | [https://francium223.bandcamp.com/album/1063 Bandcamp] | [https://www.youtube.com/playlist?list=PLLZE7hMjEXRbvsZ972acZMd-RZ097Zb4a YouTube] &ndash; 5-piece EP in 1063edo
* ''1063'' (2024) &ndash; [https://open.spotify.com/album/2J338pHEIYcB5GBDCCbChg Spotify] | [https://francium223.bandcamp.com/album/1063 Bandcamp] | [https://www.youtube.com/playlist?list=PLLZE7hMjEXRbvsZ972acZMd-RZ097Zb4a YouTube] – 5-piece EP in 1063edo


[[Category:Listen]]
[[Category:Listen]]

Latest revision as of 13:31, 13 March 2026

← 1062edo 1063edo 1064edo →
Prime factorization 1063 (prime)
Step size 1.12888 ¢ 
Fifth 622\1063 (702.164 ¢)
Semitones (A1:m2) 102:79 (115.1 ¢ : 89.18 ¢)
Consistency limit 7
Distinct consistency limit 7

1063 equal divisions of the octave (abbreviated 1063edo or 1063ed2), also called 1063-tone equal temperament (1063tet) or 1063 equal temperament (1063et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1063 equal parts of about 1.13 ¢ each. Each step represents a frequency ratio of 21/1063, or the 1063rd root of 2.

Theory

1063et tempers out 2401/2400 in the 7-limit; 95703125/95664294, 26214400/26198073, 78675968/78594219, 1953125/1951488, 1879453125/1879048192, 3294225/3294172, 43923/43904, 102487/102400 and 781258401/781250000 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 1063edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.209 -0.237 -0.246 -0.424 +0.488 +0.030 +0.511 +0.512 -0.038 -0.351
Relative (%) +0.0 +18.5 -21.0 -21.8 -37.6 +43.3 +2.7 +45.3 +45.4 -3.4 -31.1
Steps
(reduced) 		1063
(0) 		1685
(622) 		2468
(342) 		2984
(858) 		3677
(488) 		3934
(745) 		4345
(93) 		4516
(264) 		4809
(557) 		5164
(912) 		5266
(1014)

Subsets and supersets

1063edo is the 179th prime EDO.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [1685 -1063⟩ [⟨1063 1685]] −0.0658 0.0658 5.83
2.3.5 [-20 -24 25⟩, [77 -31 -12⟩ [⟨1063 1685 2468]] −0.0099 0.0956 8.47
2.3.5.7 2401/2400, 3500000000/3486784401, 3367254360064/3363025078125 [⟨1063 1685 2468 2984]] +0.0144 0.0930 8.24
2.3.5.7.11 2401/2400, 19712/19683, 43923/43904, 1953125/1951488 [⟨1063 1685 2468 2984 3677]] +0.0361 0.0937 8.30

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 229\1063 258.514 [-32 13 5⟩ Lafa
1 280\1063 316.087 6/5 Counterhanson

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

Music

Francium
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