1000edo: Difference between revisions

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Eliora (talk | contribs)
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I am starting to like the bold introduction on 270edo's page so I edited it into 311edo, 1000edo, and I think every edo that is used as a step could have this written in an intro.
ArrowHead294 (talk | contribs)
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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! 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
| 2.3
| {{monzo| 317 -200 }}
| {{monzo| 317 -200 }}
| {{mapping| 1000 1585 }}
| {{mapping| 1000 1585 }}
| -0.0142
| &minus;0.0142
| 0.0142
| 0.0142
| 1.18
| 1.18
Line 36: Line 28:
| {{monzo| 38 -2 -15 }}, {{monzo| 55 -64 20 }}
| {{monzo| 38 -2 -15 }}, {{monzo| 55 -64 20 }}
| {{mapping| 1000 1585 2322 }}
| {{mapping| 1000 1585 2322 }}
| -0.0219
| &minus;0.0219
| 0.0159
| 0.0159
| 1.33
| 1.33
Line 60: Line 52:
| 0.0857
| 0.0857
| 7.14
| 7.14
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 85: Line 70:
|-
|-
| 4
| 4
| 317\1000<br>(67\1000)
| 317\1000<br />(67\1000)
| 380.400<br>(80.400)
| 380.400<br />(80.400)
| 5103/4096<br>(22/21)
| 5103/4096<br />(22/21)
| [[Quasithird]]
| [[Quasithird]]
|-
|-
| 10
| 10
| 263\1000<br>(37\1000)
| 263\1000<br />(37\1000)
| 315.600<br>(44.400)
| 315.600<br />(44.400)
| 6/5<br>(15/14)
| 6/5<br />(15/14)
| [[Deca]]
| [[Deca]]
|-
|-
|25
| 25
|301\1000<br>(21\1000)
| 301\1000<br />(21\1000)
|361.200<br>(25.200)
| 361.200<br />(25.200)
|[54 13 -32⟩<br>(?)
| [54 13 -32⟩<br />(?)
|[[Manganese]]
| [[Manganese]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Music ==
== Music ==
; [[Xotla]]
; [[Xotla]]
* "Moongazing" from ''Lessor Groove'' (2020) [https://xotla.bandcamp.com/track/moongazing-luna-25 Bandcamp] | [https://www.youtube.com/watch?v=EWuVnLOcaRg YouTube] – atmospheric-electro, luna[25] in 1000edo
* "Moongazing" from ''Lessor Groove'' (2020) [https://xotla.bandcamp.com/track/moongazing-luna-25 Bandcamp] | [https://www.youtube.com/watch?v=EWuVnLOcaRg YouTube] &ndash; atmospheric-electro, luna[25] in 1000edo


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

Revision as of 04:44, 16 November 2024

← 999edo 1000edo 1001edo →
Prime factorization 23 × 53
Step size 1.2 ¢ 
Fifth 585\1000 (702 ¢) (→ 117\200)
Semitones (A1:m2) 95:75 (114 ¢ : 90 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

1000edo's step size is called a millioctave when used as an interval size unit.

Theory

1000edo is related to 200edo, but the patent vals differ on the mapping for 5 and 7. In the 5-limit, it tempers out [38 -2 -15⟩ (luna comma) and [-17 62 -35⟩ (senior comma). In the 7-limit, it tempers out 4375/4374, 201768035/201326592, and 165288374272/164794921875, leading to the lunatic temperament and seniority temperament. It also tempers out 3025/3024, 9801/9800, and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, 4459/4455, and 10648/10647 in the 13-limit, leading to the deca temperament and donar temperament.

Prime harmonics

Approximation of prime harmonics in 1000edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.045 +0.086 -0.426 -0.518 -0.528 -0.555 +0.087 +0.526 +0.023 -0.236
Relative (%) +0.0 +3.7 +7.2 -35.5 -43.2 -44.0 -46.3 +7.2 +43.8 +1.9 -19.6
Steps
(reduced) 		1000
(0) 		1585
(585) 		2322
(322) 		2807
(807) 		3459
(459) 		3700
(700) 		4087
(87) 		4248
(248) 		4524
(524) 		4858
(858) 		4954
(954)

Subsets and supersets

Since 1000 factors into 23 × 53, 1000edo has subset edos 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, and 500.

2000edo, which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for harmonics 7, 11, 13, 17, and 23.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [317 -200⟩ | [⟨1000 1585]] | −0.0142 | 0.0142 | 1.18 |- | 2.3.5 | [38 -2 -15⟩, [55 -64 20⟩ | [⟨1000 1585 2322]] | −0.0219 | 0.0159 | 1.33 |- | 2.3.5.7 | 4375/4374, 201768035/201326592, [12 -3 -14 9⟩ | [⟨1000 1585 2322 2807]] | +0.0215 | 0.0764 | 6.37 |- | 2.3.5.7.11 | 3025/3024, 4375/4374, 391314/390625, [-32 13 1 2 1⟩ | [⟨1000 1585 2322 2807 3459]] | +0.0472 | 0.0854 | 7.12 |- | 2.3.5.7.11.13 | 1001/1000, 3025/3024, 4225/4224, 4375/4374, 708883245/708837376 | [⟨1000 1585 2322 2807 3459 3700]] | +0.0631 | 0.0857 | 7.14 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 161\1000 | 193.200 | 262144/234375 | Lunatic (7-limit) |- | 1 | 269\1000 | 322.800 | 3087/2560 | Seniority |- | 4 | 317\1000
(67\1000) | 380.400
(80.400) | 5103/4096
(22/21) | Quasithird |- | 10 | 263\1000
(37\1000) | 315.600
(44.400) | 6/5
(15/14) | Deca |- | 25 | 301\1000
(21\1000) | 361.200
(25.200) | [54 13 -32⟩
(?) | Manganese Template:Rank-2 end Template:Orf

Music

Xotla
  • "Moongazing" from Lessor Groove (2020) Bandcamp | YouTube – atmospheric-electro, luna[25] in 1000edo
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