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The '''1000 edo''' divides the octave in 1000 equal parts of exactly 1.2 [[cent]]s, or 1 [[millioctave]] each. It is notable mostly because it is the equal division corresponding to millioctaves.
{{Infobox ET}}
{{ED intro}}


1000edo is related to 200edo, but the [[patent val]]s differ on the mapping for 5 and 7. In the [[5-limit]], it tempers out luna comma, 274877906944/274658203125 and senior comma, {{Monzo| -17 62 -35 }}. 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's step size is called a '''millioctave''' when used as an [[interval size unit]].


[[Category:Equal divisions of the octave]]
== Theory ==
[[Category: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 [[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 ===
{{Harmonics in equal|1000}}
 
=== Subsets and supersets ===
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]].
 
== Regular temperament properties ==
{| 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
| {{monzo| 317 -200 }}
| {{mapping| 1000 1585 }}
| −0.0142
| 0.0142
| 1.18
|-
| 2.3.5
| {{monzo| 38 -2 -15 }}, {{monzo| 55 -64 20 }}
| {{mapping| 1000 1585 2322 }}
| −0.0219
| 0.0159
| 1.33
|-
| 2.3.5.7
| 4375/4374, 201768035/201326592, {{monzo| 12 -3 -14 9 }}
| {{mapping| 1000 1585 2322 2807 }}
| +0.0215
| 0.0764
| 6.37
|-
| 2.3.5.7.11
| 3025/3024, 4375/4374, 391314/390625, {{monzo| -32 13 1 2 1 }}
| {{mapping| 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
| {{mapping| 1000 1585 2322 2807 3459 3700 }}
| +0.0631
| 0.0857
| 7.14
|}
 
=== Rank-2 temperaments ===
{| 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
| 161\1000
| 193.200
| 262144/234375
| [[Lunatic]] (7-limit)
|-
| 1
| 269\1000
| 322.800
| 3087/2560
| [[Seniority]]
|-
| 4
| 317\1000<br />(67\1000)
| 380.400<br />(80.400)
| 5103/4096<br />(22/21)
| [[Quasithird]]
|-
| 10
| 263\1000<br />(37\1000)
| 315.600<br />(44.400)
| 6/5<br />(15/14)
| [[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 ==
; [[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]]
* "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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