2000edo - 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"

2026-03-13T13:31:58Z

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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	\| [[Mercury]]		\| [[Mercury]]
	\|}		\|}
	<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 ==

ArrowHead294 at 14:13, 20 February 2025

2025-02-20T14:13:04Z

← Older revision		Revision as of 14:13, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2000~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:07, 15 January 2025

2025-01-15T16:07:34Z

← Older revision		Revision as of 16:07, 15 January 2025
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	\| [[Mercury]]		\| [[Mercury]]
	\|}		\|}
	<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 ==

ArrowHead294: Partial undo

2024-11-16T13:09:04Z

Partial undo

← Older revision		Revision as of 13:09, 16 November 2024
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	=== 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
	\|-		\|-
	\| 20		\| 20
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	\| 2275/1836<br />(?)		\| 2275/1836<br />(?)
	\| [[Mercury]]		\| [[Mercury]]
	~~{{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 02:15, 16 November 2024

2024-11-16T02:15:45Z

← Older revision		Revision as of 02:15, 16 November 2024
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	=== 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~~
	\|-		\|-
	\| 20		\| 20
	\| 287\2000<br>(87\2000)		\| 287\2000<br />(87\2000)
	\| 172.2<br>(52.2)		\| 172.2<br />(52.2)
	\| 169/153<br>(?)		\| 169/153<br />(?)
	\| [[Calcium]]		\| [[Calcium]]
	\|-		\|-
	\|25		\|25
	\|301\2000<br>(1\2000)		\|301\2000<br />(1\2000)
	\|180.6<br>(0.6)		\|180.6<br />(0.6)
	\|272/245<br>(?)		\|272/245<br />(?)
	\|[[Hemimanganese]]		\|[[Hemimanganese]]
	\|-		\|-
	\| 80		\| 80
	\| 619\2000<br>(19\2000)		\| 619\2000<br />(19\2000)
	\| 371.4<br>(11.4)		\| 371.4<br />(11.4)
	\| 2275/1836<br>(?)		\| 2275/1836<br />(?)
	\| [[Mercury]]		\| [[Mercury]]
	\|}		{{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 ==

	; [[Eliora]]		; [[Eliora]]

	* ''[https://www.youtube.com/watch?v=gM4dfrF5wPg Fugue, but Not (in A Mercury & Bidia)]'' (2024)		* ''[https://www.youtube.com/watch?v=gM4dfrF5wPg Fugue, but Not (in A Mercury & Bidia)]'' (2024)

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

Eliora at 20:15, 8 September 2024

2024-09-08T20:15:33Z

← Older revision		Revision as of 20:15, 8 September 2024
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	* ''[https://www.youtube.com/watch?v=gM4dfrF5wPg Fugue, but Not (in A Mercury & Bidia)]'' (2024)		* ''[https://www.youtube.com/watch?v=gM4dfrF5wPg Fugue, but Not (in A Mercury & Bidia)]'' (2024)

			[[Category:Listen]]

Eliora: Add music

2024-09-08T20:15:12Z

Add music

← Older revision		Revision as of 20:15, 8 September 2024
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	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			== Music ==

			; [[Eliora]]

			* ''[https://www.youtube.com/watch?v=gM4dfrF5wPg Fugue, but Not (in A Mercury & Bidia)]'' (2024)

FloraC: /* Theory */ no overlong tables

2024-02-07T08:41:03Z

Theory: no overlong tables

← Older revision		Revision as of 08:41, 7 February 2024
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|2000\|columns=16}}		{{Harmonics in equal\|2000\|columns=12}}
			{{Harmonics in equal\|2000\|start=13\|columns=12\|collapsed=1\|title=Approximation of prime harmonics in 2000edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

Godtone: /* Prime harmonics */ does well in the 53-limit (with a little inconsistency)

2024-02-06T23:40:08Z

Prime harmonics: does well in the 53-limit (with a little inconsistency)

← Older revision		Revision as of 23:40, 6 February 2024
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|2000\|columns=13}}		{{Harmonics in equal\|2000\|columns=16}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

FloraC: Adopt template: Factorization

2023-10-30T12:08:51Z

Adopt template: Factorization

← Older revision		Revision as of 12:08, 30 October 2023
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	== Theory ==		== Theory ==
	2000edo is ~~distinctly~~ [[consistent]] through the 29-odd-limit and a strong no-31's 41-limit system; the only smaller edo with a smaller [[29-limit]] [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being [[1578edo]]. The only ones superior to it in the [[23-limit]] are 1578 and [[1889edo]], and in the 19-limit, nothing smaller defeats it.		2000edo is [[consistency\|distinctly consistent]] through the [[29-odd-limit]] and a strong no-31's 41-limit system; the only smaller edo with a smaller [[29-limit]] [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being [[1578edo]]. The only ones superior to it in the [[23-limit]] are [[1578edo\|1578-]] and [[1889edo]], and in the 19-limit, nothing smaller defeats it.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	2000 = ~~2<sup>4</sup> × 5<sup>3</sup>~~, and its divisors are {{EDOs\| 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000 }}. From these, [[1000edo]] is notable because it carries the interval size measure [[millioctave]]. It is argued that cutting millioctaves in half makes for a better interval measuring system, in light of 2000edo's high consistency limit, which introduces just interval approximations not present in 1000edo. In addition, 2000edo inherits its fifth from [[200edo]], where it is semiconvergent.		2000 = {{factorization\|2000}}, and its nontrivial divisors are {{EDOs\| 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000 }}. From these, [[1000edo]] is notable because it carries the interval size measure [[millioctave]]. It is argued that cutting millioctaves in half makes for a better interval measuring system, in light of 2000edo's high consistency limit, which introduces just interval approximations not present in 1000edo. In addition, 2000edo inherits its fifth from [[200edo]], where it is semiconvergent.

	== Regular temperament properties ==		== Regular temperament properties ==
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	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-