Quintile family - Revision history

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:17:11Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:17, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Quintile family\| ]] <!-- main article -->		[[Category:Quintile family\| ]] <!-- main article -->
	[[Category:Quintile\| ]] <!-- key article -->		[[Category:Quintile\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

2025-06-24T00:31:15Z

Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:31, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Quintile family\| ]] <!-- main article -->		[[Category:Quintile family\| ]] <!-- main article -->
	[[Category:Quintile\| ]] <!-- key article -->		[[Category:Quintile\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 05:05, 12 June 2025

2025-06-12T05:05:09Z

← Older revision		Revision as of 05:05, 12 June 2025
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	: mapping generators: ~15/14, ~3		: mapping generators: ~15/14, ~3

	~~{{Multival\|legend=1\| -10 -50 -60 -56 -67 1 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:41:29Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:41, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''quintile family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[quintile comma]] ({{monzo\|legend=1\| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000).		The '''quintile family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[quintile comma]] ({{monzo\|legend=1\| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000).

BudjarnLambeth: {{Technical data page}}

2025-04-13T08:51:55Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 08:51, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''quintile family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[quintile comma]] ({{monzo\|legend=1\| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000).		The '''quintile family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[quintile comma]] ({{monzo\|legend=1\| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000).

FloraC: The 2\5 represents 320/243

2025-04-02T10:38:14Z

The 2\5 represents 320/243

← Older revision		Revision as of 10:38, 2 April 2025
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	== Quintile ==		== Quintile ==
	Quintile reaches the interval class of 5 by five perfect fifths (i.e. a major seventh) plus two periods of 1/5-octave. It is a member of the [[syntonic–diatonic equivalence continuum]] with {{nowrap\| ''n'' {{=}} 5 }}, so it equates a [[256/243\|Pythagorean limma]] with a stack of five [[81/80\|syntonic commas]].		Quintile reaches the interval class of 5 by five [[3/2\|perfect fifths]] (i.e. a major seventh) plus two periods of 1/5-octave; this two-period interval represents a grave fourth of [[320/243]], that is, a [[4/3\|perfect fourth]] minus a [[81/80\|syntonic comma]]. Quintile is a member of the [[syntonic–diatonic equivalence continuum]] with {{nowrap\| ''n'' {{=}} 5 }}, so it equates a [[256/243\|Pythagorean limma]] with a stack of five [[81/80\|syntonic commas]].

	The temperament was first introduced by [[Mike Battaglia]] in 2011 along with other temperaments in the continuum mentioned above<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99315.html#99323 Yahoo! Tuning Group \| ''Some new 5-limit microtemperaments'']</ref>. It did not get named until 2012, when [[Petr Pařízek]] called it ''pental''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104270.html Yahoo! Tuning Group \| ''2D temperaments, part II -- new 5-limit temperaments'']</ref>. In 2024, the community has decided to rename it for fear of confusion with the more common usage of the term ''pental'' to refer to the [[5-limit]].		The temperament was first introduced by [[Mike Battaglia]] in 2011 along with other temperaments in the continuum mentioned above<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99315.html#99323 Yahoo! Tuning Group \| ''Some new 5-limit microtemperaments'']</ref>. It did not get named until 2012, when [[Petr Pařízek]] called it ''pental''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104270.html Yahoo! Tuning Group \| ''2D temperaments, part II -- new 5-limit temperaments'']</ref>. In 2024, the community has decided to rename it for fear of confusion with the more common usage of the term ''pental'' to refer to the [[5-limit]].

FloraC: /* Quintile */

2025-02-19T13:10:57Z

Quintile

← Older revision		Revision as of 13:10, 19 February 2025
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	Quintile reaches the interval class of 5 by five perfect fifths (i.e. a major seventh) plus two periods of 1/5-octave. It is a member of the [[syntonic–diatonic equivalence continuum]] with {{nowrap\| ''n'' {{=}} 5 }}, so it equates a [[256/243\|Pythagorean limma]] with a stack of five [[81/80\|syntonic commas]].		Quintile reaches the interval class of 5 by five perfect fifths (i.e. a major seventh) plus two periods of 1/5-octave. It is a member of the [[syntonic–diatonic equivalence continuum]] with {{nowrap\| ''n'' {{=}} 5 }}, so it equates a [[256/243\|Pythagorean limma]] with a stack of five [[81/80\|syntonic commas]].

	The temperament was first introduced by [[Mike Battaglia]] in 2011 along with other temperaments in the continuum mentioned above<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99315.html#99323 Yahoo! Tuning Group \| ''Some new 5-limit microtemperaments'']</ref>. It did not get named until 2012, when [[Petr Pařízek]] called it ''pental''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104270.html Yahoo! Tuning Group \| ''2D temperaments, part II -- new 5-limit temperaments'']</ref>. In 2024, the community has decided to rename it for fear of confusion.		The temperament was first introduced by [[Mike Battaglia]] in 2011 along with other temperaments in the continuum mentioned above<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99315.html#99323 Yahoo! Tuning Group \| ''Some new 5-limit microtemperaments'']</ref>. It did not get named until 2012, when [[Petr Pařízek]] called it ''pental''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104270.html Yahoo! Tuning Group \| ''2D temperaments, part II -- new 5-limit temperaments'']</ref>. In 2024, the community has decided to rename it for fear of confusion with the more common usage of the term ''pental'' to refer to the [[5-limit]].

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

FloraC: Sorting

2025-02-19T12:27:46Z

Sorting

← Older revision		Revision as of 12:27, 19 February 2025
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	Badness (Smith): 0.047624		Badness (Smith): 0.047624

	==== ~~Hemiquint~~ ====		==== Hemiquintilis ====
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: 540/539, ~~1575/1573, 4096~~/~~4095~~, ~~8019~~/~~8000~~		Comma list: 351/350, 540/539, 676/675, 124215/123904

	Mapping: {{mapping\| 5 0 -28 18 -54 34 \| 0 2 10 -1 18 -13 }}		Mapping: {{mapping\| 5 0 -28 18 -54 34 \| 0 2 10 -1 18 13 }}

	Optimal tunings:		Optimal tunings:
	* CTE: ~147/128 = 240.0000, ~~~140~~/81 = 950.~~6607~~ (~~~144~~/~~143~~ = 9.~~3393~~)		* CTE: ~147/128 = 240.0000, ~26/15 = 950.6775 (~176/175 = 9.3225)
	* POTE: ~147/128 = 240.0000, ~~~140~~/81 = 950.~~6677~~ (~~~144~~/~~143~~ = 9.~~3323~~)		* POTE: ~147/128 = 240.0000, ~26/15 = 950.6593 (~176/175 = 9.3407)

	{{Optimal ET sequence\|legend=0\| ~~125~~, 130, ~~255~~, ~~385, 515~~ }}		{{Optimal ET sequence\|legend=0\| 125f, 130, 255f, 385f }}

	Badness (Smith): 0.~~041043~~		Badness (Smith): 0.033542

	==== ~~Hemiquintilis~~ ====		==== Hemiquint ====
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: ~~351~~/~~350~~, ~~540~~/~~539~~, ~~676~~/~~675~~, ~~124215~~/~~123904~~		Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000

	Mapping: {{mapping\| 5 0 -28 18 -54 34 \| 0 2 10 -1 18 13 }}		Mapping: {{mapping\| 5 0 -28 18 -54 34 \| 0 2 10 -1 18 -13 }}

	Optimal tunings:		Optimal tunings:
	* CTE: ~147/128 = 240.0000, ~140/81 = 950.~~6775~~ (~~~176~~/~~175~~ = 9.~~3225~~)		* CTE: ~147/128 = 240.0000, ~140/81 = 950.6607 (~144/143 = 9.3393)
	* POTE: ~147/128 = 240.0000, ~26/15 = 950.~~6593~~ (~~~176~~/~~175~~ = 9.~~3407~~)		* POTE: ~147/128 = 240.0000, ~140/81 = 950.6677 (~144/143 = 9.3323)

	{{Optimal ET sequence\|legend=0\| ~~125f~~, 130, ~~255f~~, ~~385f~~ }}		{{Optimal ET sequence\|legend=0\| 125, 130, 255, 385, 515 }}

	Badness (Smith): 0.~~033542~~		Badness (Smith): 0.041043

	== Decile ==		== Decile ==

FloraC: +CTE tunings. +error maps. Spell out the period in cents. Note the badness metric being used. Misc. cleanup

2025-02-19T12:26:49Z

+CTE tunings. +error maps. Spell out the period in cents. Note the badness metric being used. Misc. cleanup

Show changes

FloraC: FloraC moved page Pental family to Quintile family: Implement the community-anticipated rename

2025-02-19T12:02:39Z

FloraC moved page Pental family to Quintile family: Implement the community-anticipated rename

← Older revision	Revision as of 12:02, 19 February 2025
(No difference)