1000edo: Difference between revisions

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

== 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.

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 ===

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=== Subsets and supersets ===

Since 1000 factors into ~~{{factorization|1000}}~~, 1000edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, and 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]].

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| {{monzo| 317 -200 }}

| {{mapping| 1000 1585 }}

| ~~−0~~.0142

| −0.0142

| 0.0142

| 1.18

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| {{monzo| 38 -2 -15 }}, {{monzo| 55 -64 20 }}

| {{mapping| 1000 1585 2322 }}

| ~~−0~~.0219

| −0.0219

| 0.0159

| 1.33

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| [[Manganese]]

|}

<nowiki />* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if ~~it is~~ distinct

<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, ~~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]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1000}}
+{{ED intro}}
 edo's step size is called a '''millioctave''' when used as an [[interval size unit]].
 == Theory ==
-edo 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.
+edo 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 ===
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-Since 1000 factors into {{factorization|1000}}, 1000edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, and 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]].
@@ Line 30: / Line 30: @@
 | {{monzo| 317 -200 }}
 | {{mapping| 1000 1585 }}
-| &minus;0.0142
+| −0.0142
 | 0.0142
 | 1.18
@@ Line 37: / Line 37: @@
 | {{monzo| 38 -2 -15 }}, {{monzo| 55 -64 20 }}
 | {{mapping| 1000 1585 2322 }}
-| &minus;0.0219
+| −0.0219
 | 0.0159
 | 1.33
@@ Line 103: / Line 103: @@
 | [[Manganese]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<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] &ndash; 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]]