3125edo - Revision history

FloraC at 11:02, 28 May 2026

2026-05-28T11:02:58Z

← Older revision		Revision as of 11:02, 28 May 2026
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	~~3125 =~~ {{~~factorization~~\|3125}}, and as such it is the 5th edo of the form ''n''<sup>''n''</sup>. It has subset edos {{EDOs\| 5, 25, 125, and 625 }}.		{{nowrap\| 3125 {{=}} 5<sup>5</sup> }}, and as such 3125edo is the 5th edo of the form ''n''<sup>''n''</sup>. It has subset edos {{EDOs\| 5, 25, 125, and 625 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Notability

2026-05-28T10:36:22Z

Notability

← Older revision		Revision as of 10:36, 28 May 2026
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	== Theory ==		== Theory ==
	3125et is notable for being an extremely strong [[7-limit]] system. It is also [[consistent]] through the [[15-odd-limit]], and except for [[17/11]] ~~and~~ [[19/17]] and their [[octave complement]]s, it is consistent to the [[35-odd-limit]].		3125et is notable for being an extremely strong [[7-limit]] system. It is also [[consistent]] through the [[15-odd-limit]], and except for [[17/11]], [[19/17]] and their [[octave complement]]s, it is consistent to the [[35-odd-limit]].

	A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the [[11-limit]], [[151263/151250]], 820125/819896, 21437500/21434787 and [[~~Quartisma~~\|117440512/117406179]] are tempered out—it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the [[13-limit]], [[6656/6655]], [[123201/123200]], [[140625/140608]] and 1399680/1399489 are all tempered out.		A basis for its 7-limit commas is [[78125000/78121827]], [[645700815/645657712]] and 281484423828125/281474976710656. In the [[11-limit]], [[151263/151250]], 820125/819896, 21437500/21434787 and [[quartisma\|117440512/117406179]] are tempered out—it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the [[13-limit]], [[6656/6655]], [[123201/123200]], [[140625/140608]] and 1399680/1399489 are all tempered out.

	~~In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called [[estates general]], described as {{nowrap\|1789 & 3125}}.~~

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Expand

2026-05-28T10:35:27Z

Expand

← Older revision		Revision as of 10:35, 28 May 2026
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	== Theory ==		== Theory ==
	~~3125edo~~ is [[~~consistency\|distinctly~~ consistent]] through the [[15-odd-limit]]~~. A basis for its 7-limit commas is 78125000/78121827~~, ~~645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787~~ and [[~~Quartisma\|117440512~~/~~117406179~~]] are tempered out—it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] ~~quartertones~~ and ~~one~~ [[~~7/6~~]] ~~subminor third. In~~ the 13-limit~~, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out~~.		3125et is notable for being an extremely strong [[7-limit]] system. It is also [[consistent]] through the [[15-odd-limit]], and except for [[17/11]] and [[19/17]] and their [[octave complement]]s, it is consistent to the [[35-odd-limit]].

	In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called [[estates general]], described as {{nowrap\|1789 &~~amp;~~ 3125}}.		A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the [[11-limit]], [[151263/151250]], 820125/819896, 21437500/21434787 and [[Quartisma\|117440512/117406179]] are tempered out—it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the [[13-limit]], [[6656/6655]], [[123201/123200]], [[140625/140608]] and 1399680/1399489 are all tempered out.

			In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called [[estates general]], described as {{nowrap\|1789 & 3125}}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|3125\|columns=11}}		{{Harmonics in equal\|3125\|columns=11}}
			{{Harmonics in equal\|3125\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 3125edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
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	== Regular temperament properties ==		== Regular temperament properties ==
	3125et is ~~notable for being an extremely strong 7-limit system, being~~ the first equal ~~division~~ past [[171edo]] with a lower [[~~Tenney-Euclidean~~ temperament measures #TE simple badness\|relative error]].		3125et is the first equal temperament past [[171edo\|171]] with a lower [[Tenney–Euclidean temperament measures #TE simple badness\|relative error]].

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
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	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Revopent]]		\| [[Revopent]]
	\|}		\|}
	<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		<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 ==

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"

2026-03-13T13:32:45Z

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 13:32, 13 March 2026
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	\| [[Revopent]]		\| [[Revopent]]
	\|}		\|}
	<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 14:36, 20 February 2025

2025-02-20T14:36:47Z

← Older revision		Revision as of 14:36, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|3125~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:58, 15 January 2025

2025-01-15T16:58:35Z

← Older revision		Revision as of 16:58, 15 January 2025
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	== Theory ==		== Theory ==
	3125edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma\|117440512/117406179]] are tempered ~~out – it~~ should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.		3125edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma\|117440512/117406179]] are tempered out—it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.

	In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called [[estates general]], described as 1789 & 3125.		In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called [[estates general]], described as {{nowrap\|1789 & 3125}}.

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| [[Revopent]]		\| [[Revopent]]
	\|}		\|}
	<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

2024-11-16T13:20:40Z

Partial undo

← Older revision		Revision as of 13:20, 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
	\|-		\|-
	\| 1		\| 1
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	\| 16807/12288		\| 16807/12288
	\| [[Revopent]]		\| [[Revopent]]
	~~{{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 01:33, 16 November 2024

2024-11-16T01:33:02Z

← Older revision		Revision as of 01:33, 16 November 2024
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center~~-~~all left-5"~~		{{rank-2 begin}}
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	~~! Associated<br>Ratio~~
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 16807/12288		\| 16807/12288
	\| [[Revopent]]		\| [[Revopent]]
	\|}		{{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: /* Theory */

2024-01-12T19:12:47Z

Theory

← Older revision		Revision as of 19:12, 12 January 2024
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	3125edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma\|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.		3125edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma\|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.

	In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.		In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called [[estates general]], described as 1789 & 3125.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Adopt template: Factorization

2023-10-30T09:53:55Z

Adopt template: Factorization

← Older revision		Revision as of 09:53, 30 October 2023
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	== Theory ==		== Theory ==
	3125edo is ~~distinctly~~ [[consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma\|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.		3125edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma\|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.

	In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.		In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	3125 = ~~5<sup>5</sup>~~ , and as such it is the 5th edo of the form ~~x^x~~. It has subset edos {{EDOs\|5, 25, 125, and 625}}.		3125 = {{factorization\|3125}}, and as such it is the 5th edo of the form ''n''<sup>''n''</sup>. It has subset edos {{EDOs\| 5, 25, 125, and 625 }}.

	== Regular temperament properties ==		== Regular temperament properties ==