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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1000}}
{{ED intro}}


1000edo is notable mostly because it is the equal division corresponding to millioctaves.
1000edo's step size is called a '''millioctave''' when used as an [[interval size unit]].


== Theory ==
== Theory ==
1000edo is related to 200edo, but the [[patent val]]s differ on the mapping for [[5/1|5]] and [[7/1|7]]. In the [[5-limit]], it tempers out {{monzo| 38 -2 -15 }} (luna comma) and {{monzo| -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.  
1000edo is related to [[200edo]], but the [[patent val]]s differ on the mapping for [[5/1|5]] and [[7/1|7]]. In the [[5-limit]], it [[tempering out|tempers out]] {{monzo| 38 -2 -15 }} ([[luna comma]]) and {{monzo| -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 ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
1000edo carries the interval size measure ''millioctave'' and has subset edos {{EDOs| 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500 }}.
Since 1000 factors into 2<sup>3</sup> × 5<sup>3</sup>, 1000edo has subset edos {{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, [[11/1|11]], [[13/1|13]], [[17/1|17]], and [[23/1|23]].
[[2000edo]], which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for harmonics 7, [[11/1|11]], [[13/1|13]], [[17/1|17]], and [[23/1|23]].
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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" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" | Tuning error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
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| {{monzo| 317 -200 }}
| {{monzo| 317 -200 }}
| {{mapping| 1000 1585 }}
| {{mapping| 1000 1585 }}
| -0.0142
| −0.0142
| 0.0142
| 0.0142
| 1.18
| 1.18
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| {{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
| −0.0219
| 0.0159
| 0.0159
| 1.33
| 1.33
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=== 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
|-
! Generator<br>(Reduced)
! Periods<br />per 8ve
! Cents<br>(Reduced)
! Generator*
! Associated<br>Ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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|-
|-
| 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
| 301\1000<br />(21\1000)
| 361.200<br />(25.200)
| [54 13 -32⟩<br />(?)
| [[Manganese]]
|}
|}
<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]]
* "Unsuspecting Tyrant Double Decker Beef Fort" from ''Unsuspecting Tyrant Double Decker Beef Fort'' (2026) – [https://open.spotify.com/track/0pblUR02SXzAHot04qdA10 Spotify] | [https://francium223.bandcamp.com/track/unsuspecting-tyrant-double-decker-beef-fort Bandcamp] | [https://www.youtube.com/watch?v=BrZ07LxWCvQ YouTube] – in Deca, 1000edo tuning
; [[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] – atmospheric-electro, in Luna[25], 1000edo tuning
 
[[Category:Listen]]
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