1000edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:31:36Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:31, 13 March 2026
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	\| [[Manganese]]		\| [[Manganese]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if 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 ==		== Music ==

Francium: /* Music */ +links

2026-02-26T11:44:04Z

Music: +links

← Older revision		Revision as of 11:44, 26 February 2026
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	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=BrZ07LxWCvQ ~~''Unsuspecting Tyrant Double Decker Beef Fort''~~] ~~(2025)~~ – in Deca, 1000edo tuning		* "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]]

Francium: /* Music */ +music

2025-11-15T12:42:52Z

Music: +music

← Older revision		Revision as of 12:42, 15 November 2025
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	== Music ==		== Music ==
			; [[Francium]]
			* [https://www.youtube.com/watch?v=BrZ07LxWCvQ ''Unsuspecting Tyrant Double Decker Beef Fort''] (2025) – 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]]		[[Category:Listen]]

ArrowHead294 at 16:37, 20 February 2025

2025-02-20T16:37:10Z

← Older revision		Revision as of 16:37, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1000~~}}		{{ED intro}}

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

FloraC: /* Theory */ cleanup

2025-01-17T16:41:26Z

Theory: cleanup

← Older revision		Revision as of 16:41, 17 January 2025
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	== 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 ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== 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]].		[[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]].

ArrowHead294 at 19:37, 15 January 2025

2025-01-15T19:37:24Z

← Older revision		Revision as of 19:37, 15 January 2025
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	== 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 [[~~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 [[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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	\| {{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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	\| [[Manganese]]		\| [[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 lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== 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] – atmospheric-electro, luna[25] in 1000edo

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

ArrowHead294: Partial undo

2024-11-16T12:25:27Z

Partial undo

← Older revision		Revision as of 12:25, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| 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		\| 2.3
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	\| 0.0857		\| 0.0857
	\| 7.14		\| 7.14
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| 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		\| 1
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	\| [54 13 -32⟩<br />(?)		\| [54 13 -32⟩<br />(?)
	\| [[Manganese]]		\| [[Manganese]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<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 ==

ArrowHead294 at 04:44, 16 November 2024

2024-11-16T04:44:50Z

← Older revision		Revision as of 04:44, 16 November 2024
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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		\| −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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	\| 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
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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		\| 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] – atmospheric-electro, luna[25] in 1000edo

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

Eliora: 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.

2024-09-04T00:58:54Z

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.

← Older revision		Revision as of 00:58, 4 September 2024
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	{{EDO intro\|1000}}		{{EDO intro\|1000}}

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

	== Theory ==		== Theory ==
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	~~1000edo carries the interval size measure ''millioctave''.~~ 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 {{factorization\|1000}}, 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]].

Francium: +categories

2024-02-13T18:22:14Z

+categories

← Older revision		Revision as of 18:22, 13 February 2024
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	; [[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, luna[25] in 1000edo

			[[Category:Listen]]