1063edo: Difference between revisions

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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|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|1685 -1063}}
! rowspan="2" | [[Comma list|Comma List]]
|{{mapping|1063 1685}}
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo|1685 -1063}}
| {{mapping|1063 1685}}
| -0.0658
| -0.0658
| 0.0658
| 0.0658
| 5.83
| 5.83
|-
|-
|2.3.5
| 2.3.5
|{{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
|-
|-
|2.3.5.7
| 2.3.5.7
|2401/2400, 3500000000/3486784401, 3367254360064/3363025078125
| 2401/2400, 3500000000/3486784401, 3367254360064/3363025078125
|{{mapping|1063 1685 2468 2984}}
| {{mapping|1063 1685 2468 2984}}
| +0.0144
| +0.0144
| 0.0930
| 0.0930
| 8.24
| 8.24
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|2401/2400, 19712/19683, 43923/43904, 1953125/1951488
| 2401/2400, 19712/19683, 43923/43904, 1953125/1951488
|{{mapping|1063 1685 2468 2984 3677}}
| {{mapping|1063 1685 2468 2984 3677}}
| +0.0361
| +0.0361
| 0.0937
| 0.0937
Line 53: Line 54:
=== 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
|229\1063
| 229\1063
|258.514
| 258.514
|{{monzo|-32 13 5}}
| {{monzo|-32 13 5}}
|[[Lafa]]
| [[Lafa]]
|-
|-
|1
| 1
|280\1063
| 280\1063
|316.087
| 316.087
|6/5
| 6/5
|[[Counterhanson]]
| [[Counterhanson]]
|}
|}
 
{{orf}}
<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 ==
== Music ==
; [[Francium]]
; [[Francium]]
* "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]
* "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]
* ''1063'' (2024) – [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
* ''1063'' (2024) – [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


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

Revision as of 01:15, 16 November 2024

← 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

Template:EDO intro

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

Template:Orf

Music

Francium
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