Quintile family - Revision history

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:33:34Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:33, 24 September 2026
Line 48:		Line 48:
	Comma list: 245/243, 385/384, 3087/3025		Comma list: 245/243, 385/384, 3087/3025

	~~Mapping:~~ {{~~mapping~~\| 5 0 -28 14 49 \| 0 1 5 0 -4 }}		{{Mapping\|legend=0\| 5 0 -28 14 49 \| 0 1 5 0 -4 }}

	Optimal tunings:		Optimal tunings:
Line 63:		Line 63:
	Comma list: 105/104, 144/143, 245/243, 3087/3025		Comma list: 105/104, 144/143, 245/243, 3087/3025

	~~Mapping:~~ {{~~mapping~~\| 5 0 -28 14 49 -29 \| 0 1 5 0 -4 6 }}		{{Mapping\|legend=0\| 5 0 -28 14 49 -29 \| 0 1 5 0 -4 6 }}

	Optimal tunings:		Optimal tunings:
Line 98:		Line 98:
	Comma list: 540/539, 8019/8000, 180224/180075		Comma list: 540/539, 8019/8000, 180224/180075

	~~Mapping:~~ {{~~mapping~~\| 5 0 -28 18 -54 \| 0 2 10 -1 18 }}		{{Mapping\|legend=0\| 5 0 -28 18 -54 \| 0 2 10 -1 18 }}

	Optimal tunings:		Optimal tunings:
Line 113:		Line 113:
	Comma list: 351/350, 540/539, 676/675, 124215/123904		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\|legend=0\| 5 0 -28 18 -54 34 \| 0 2 10 -1 18 13 }}

	Optimal tunings:		Optimal tunings:
Line 128:		Line 128:
	Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000		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\|legend=0\| 5 0 -28 18 -54 34 \| 0 2 10 -1 18 -13 }}

	Optimal tunings:		Optimal tunings:
Line 163:		Line 163:
	Comma list: 441/440, 8019/8000, 234375/234256		Comma list: 441/440, 8019/8000, 234375/234256

	~~Mapping:~~ {{~~mapping~~\| 10 0 -56 -67 -108 \| 0 1 5 6 9 }}		{{Mapping\|legend=0\| 10 0 -56 -67 -108 \| 0 1 5 6 9 }}

	Optimal tunings:		Optimal tunings:
Line 178:		Line 178:
	Comma list: 441/440, 729/728, 1001/1000, 4225/4224		Comma list: 441/440, 729/728, 1001/1000, 4225/4224

	~~Mapping:~~ {{~~mapping~~\| 10 0 -56 -67 -108 37 \| 0 1 5 6 9 0 }}		{{Mapping\|legend=0\| 10 0 -56 -67 -108 37 \| 0 1 5 6 9 0 }}

	Optimal tunings:		Optimal tunings:

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-09-04T06:42:32Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

FloraC: Units & misc. cleanup

2026-09-04T05:36:12Z

Units & misc. cleanup

Show changes

FloraC: Notes -> references; recategorize

2026-08-14T12:17:43Z

Notes -> references; recategorize

← Older revision		Revision as of 12:17, 14 August 2026
Line 191:		Line 191:
	Badness (Smith): 0.023948		Badness (Smith): 0.023948

	== ~~Notes~~ ==		== References ==

	~~[[Category:Temperament families]]~~
	[[Category:Quintile family\| ]] <!-- main article -->		[[Category:Quintile family\| ]] <!-- main article -->
	[[Category:Quintile\| ]] <!-- key article -->		[[Category:Quintile\| ]] <!-- key article -->
	[[Category:~~Rank~~ 2]]		[[Category:Temperament families]]
			[[Category:Catalogs of rank-2 temperaments]]

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
Line 194:		Line 194:

	[[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
Line 194:		Line 194:

	[[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
Line 150:		Line 150:

	: 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
Line 1:		Line 1:
	{{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
Line 1:		Line 1:
			{{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
Line 2:		Line 2:

	== 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]].