Perfect fifth - Revision history

FloraC: Merge

2026-03-30T12:18:24Z

Merge

@@ Line 1: / Line 1: @@
 {{Infobox interval region
 | Name = Perfect fifth
@@ Line 11: / Line 16: @@
 | Higher region = [[Minor&nbsp;sixth]]
 }}
-{{Wikipedia}}
+As a concrete [[interval region]], a perfect fifth is typically near 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale.
 This article covers intervals from 660 to 750{{c}}, but intervals between 650 and 660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.
 == In just intonation ==
@@ Line 114: / Line 172: @@
 * [[Mavila]], the temperament flattening 3/2 such that four 3/2s stack to [[6/5]]
 * Various historical [[well temperament]]s generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone
 {{Navbox intervals}}

FloraC: FloraC moved page Perfect fifth (interval region) to Perfect fifth: Merge

2026-03-30T12:12:52Z

FloraC moved page Perfect fifth (interval region) to Perfect fifth: Merge

← Older revision	Revision as of 12:12, 30 March 2026
(No difference)

FloraC: Page content split

2025-04-17T13:25:24Z

Page content split

← Older revision		Revision as of 13:25, 17 April 2025
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	~~{{About\|the [[interval region]]\|the just perfect fifth\|3/2}}~~
	{{Infobox interval region		{{Infobox interval region
	\| Name = Perfect fifth		\| Name = Perfect fifth
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	}}		}}
	{{Wikipedia}}		{{Wikipedia}}
	A '''perfect fifth''' ('''P5''') is an interval that spans four steps of the [[5L 2s\|diatonic]] scale with a perfect quality, i.e. the quality that exists in all but one modes. Depending on the specific tuning, it ranges from 686 to 720{{cent}} ([[7edo\|4\7]] to [[5edo\|3\5]]).		A '''perfect fifth''' ('''P5'''), as a concrete [[interval region]], is typically near 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale.

	~~In [[just intonation]]~~, ~~the just perfect fifth is [[3/2]]. Other intervals are also classified~~ as ~~perfect fifths, sometimes called '''wolf fifths''' or '''imperfect fifths''', if they are reasonably mapped to four steps of the diatonic scale and seven steps of the chromatic scale.~~

	As a concrete [[interval region]], it is typically near 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale.

	This article covers intervals from 660 to 750{{c}}, but intervals between 650 and 660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.		This article covers intervals from 660 to 750{{c}}, but intervals between 650 and 660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.

FloraC: FloraC moved page Perfect fifth to Perfect fifth (interval region): Page content split

2025-04-17T13:24:13Z

FloraC moved page Perfect fifth to Perfect fifth (interval region): Page content split

← Older revision	Revision as of 13:24, 17 April 2025
(No difference)

FloraC: -specific edosteps

2025-03-14T11:07:53Z

-specific edosteps

← Older revision		Revision as of 11:07, 14 March 2025
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	{{About\|the [[interval region]]\|the just perfect fifth\|3/2}}		{{About\|the [[interval region]]\|the just perfect fifth\|3/2}}
	{{Infobox interval region\|Name=Perfect fifth\|Cents lower=686\|Cents lower wide=650\|Cents upper=720\|Cents upper wide=750\|JI intervals=3/2\|MOSes=[[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]\|Complement=[[Perfect fourth]]\|Lower region=[[~~Semi-diminished~~ fifth]] <br> [[Tritone]]\|Higher region=[[Minor sixth]]}}{{Wikipedia}}		{{Infobox interval region
	A '''perfect fifth (P5)''' is an interval that spans four steps of the [[5L 2s\|diatonic]] scale with a perfect quality, i.e. the quality that exists in all but one modes. Depending on the specific tuning, it ranges from 686 to 720{{cent}} ([[7edo\|4\7]] to [[5edo\|3\5]]).		\| Name = Perfect fifth
			\| Cents lower = 686
			\| Cents lower wide = 650
			\| Cents upper = 720
			\| Cents upper wide = 750
			\| JI intervals = 3/2
			\| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]
			\| Complement = [[Perfect fourth]]
			\| Lower region = [[Semidiminished fifth]] <br> [[Tritone]]
			\| Higher region = [[Minor sixth]]
			}}
			{{Wikipedia}}
			A '''perfect fifth''' ('''P5''') is an interval that spans four steps of the [[5L 2s\|diatonic]] scale with a perfect quality, i.e. the quality that exists in all but one modes. Depending on the specific tuning, it ranges from 686 to 720{{cent}} ([[7edo\|4\7]] to [[5edo\|3\5]]).

	In [[just intonation]], the just perfect fifth is [[3/2]]. Other intervals are also classified as perfect fifths, sometimes called '''wolf fifths''' or '''imperfect fifths''', if they are reasonably mapped to ~~4\7 and [[24edo\|14\24]] (precisely~~ four steps of the diatonic scale and seven steps of the chromatic scale~~). The use of 24edo's 14\24 as the mapping criteria here rather than [[12edo]]'s 7\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]]~~.		In [[just intonation]], the just perfect fifth is [[3/2]]. Other intervals are also classified as perfect fifths, sometimes called '''wolf fifths''' or '''imperfect fifths''', if they are reasonably mapped to four steps of the diatonic scale and seven steps of the chromatic scale.

	As a concrete [[interval region]], it is typically near 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale.		As a concrete [[interval region]], it is typically near 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale.

VectorGraphics at 10:15, 14 March 2025

2025-03-14T10:15:21Z

← Older revision		Revision as of 10:15, 14 March 2025
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	{{About\|the [[interval region]]\|the just perfect fifth\|3/2}}		{{About\|the [[interval region]]\|the just perfect fifth\|3/2}}
	{{Wikipedia}}		{{Infobox interval region\|Name=Perfect fifth\|Cents lower=686\|Cents lower wide=650\|Cents upper=720\|Cents upper wide=750\|JI intervals=3/2\|MOSes=[[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]\|Complement=[[Perfect fourth]]\|Lower region=[[Semi-diminished fifth]] <br> [[Tritone]]\|Higher region=[[Minor sixth]]}}{{Wikipedia}}
	A '''perfect fifth (P5)''' is an interval that spans four steps of the [[5L 2s\|diatonic]] scale with a perfect quality, i.e. the quality that exists in all but one modes. Depending on the specific tuning, it ranges from 686 to 720{{cent}} ([[7edo\|4\7]] to [[5edo\|3\5]]).		A '''perfect fifth (P5)''' is an interval that spans four steps of the [[5L 2s\|diatonic]] scale with a perfect quality, i.e. the quality that exists in all but one modes. Depending on the specific tuning, it ranges from 686 to 720{{cent}} ([[7edo\|4\7]] to [[5edo\|3\5]]).

FloraC: The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition

2025-03-14T10:02:42Z

The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition

← Older revision		Revision as of 10:02, 14 March 2025
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	{{About\|the [[interval region]]\|the just perfect fifth\|3/2}}		{{About\|the [[interval region]]\|the just perfect fifth\|3/2}}
	{{Wikipedia}}		{{Wikipedia}}
	A '''perfect fifth (P5)'''~~, as a concrete~~ [[~~interval region~~]], ~~is typically near 700{{c}}~~ in ~~size~~, ~~distinct~~ from ~~semidiminished fifths of rougly 650~~{{c}}~~. A rough tuning range for the perfect fifth is about 670 to 730~~ [[~~cents~~]] ~~according~~ to [[~~Margo Schulter~~]]~~'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale~~.		A '''perfect fifth (P5)''' is an interval that spans four steps of the [[5L 2s\|diatonic]] scale with a perfect quality, i.e. the quality that exists in all but one modes. Depending on the specific tuning, it ranges from 686 to 720{{cent}} ([[7edo\|4\7]] to [[5edo\|3\5]]).

	In [[just intonation]], the just perfect fifth is [[3/2]]. Other intervals are also classified as perfect fifths, sometimes called '''wolf fifths''' or '''imperfect fifths''', if they are reasonably mapped to four steps of the diatonic scale and seven steps of the chromatic scale.		In [[just intonation]], the just perfect fifth is [[3/2]]. Other intervals are also classified as perfect fifths, sometimes called '''wolf fifths''' or '''imperfect fifths''', if they are reasonably mapped to 4\7 and [[24edo\|14\24]] (precisely four steps of the diatonic scale and seven steps of the chromatic scale). The use of 24edo's 14\24 as the mapping criteria here rather than [[12edo]]'s 7\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

	~~Functionally,~~ a ~~perfect fifth is an interval that spans four steps of the~~ [[~~5L 2s\|diatonic~~]] ~~scale with a perfect quality~~, ~~i.e. the quality that exists~~ in ~~all but one modes. Depending on the specific tuning~~, ~~it ranges~~ from ~~686 to 720~~{{~~cent~~}} ([[~~7edo\|4\7~~]] to [[~~5edo\|3\5~~]]).		As a concrete [[interval region]], it is typically near 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale.

	This article covers intervals from 660 to 750{{c}}, but intervals between 650 and 660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.		This article covers intervals from 660 to 750{{c}}, but intervals between 650 and 660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.

	== In just intonation ==		== In just intonation ==
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	* The 13-limit '''ultrafifth''' is a ratio of 20/13, and is about 746{{c}}, but it might be better analyzed as an [[minor sixth\|inframinor sixth]]. Despite that, it is also here for completeness.		* The 13-limit '''ultrafifth''' is a ratio of 20/13, and is about 746{{c}}, but it might be better analyzed as an [[minor sixth\|inframinor sixth]]. Despite that, it is also here for completeness.

	== In ~~EDOs~~ ==		== In edos ==
	The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[edo~~\|EDO~~]]s.		The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[edo]]s.

	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! ~~EDO~~		! Edo
	! 3/2		! 3/2
	! Other fifths		! Other fifths
Line 108:		Line 108:
	* Various historical [[well temperament]]s generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone		* Various historical [[well temperament]]s generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone

	== In ~~MOS~~ scales ==		== In mos scales ==
	Intervals between 654 and 750{{c}} generate the following [[mos~~\|MOS~~]] scales:		Intervals between 654 and 750{{c}} generate the following [[mos]] scales:

	These tables start from the last monolarge ~~MOS~~ generated by the interval range.		These tables start from the last monolarge mos generated by the interval range.

	Scales with more than 12 notes are not included.		Scales with more than 12 notes are not included.
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	\|-		\|-
	! Range		! Range
	! colspan="6" \| ~~MOS~~		! colspan="6" \| Mos
	\|-		\|-
	\| 720–750{{c}}		\| 720–750{{c}}

VectorGraphics at 07:03, 14 March 2025

2025-03-14T07:03:29Z

← Older revision		Revision as of 07:03, 14 March 2025
Line 1:		Line 1:
	{{About\|the [[interval region]]\|the just perfect fifth\|3/2}}		{{About\|the [[interval region]]\|the just perfect fifth\|3/2}}
	{{Wikipedia}}		{{Wikipedia}}
	A '''perfect fifth (P5)''' ~~is an interval that spans four steps of the~~ [[~~5L 2s\|diatonic~~]] ~~scale with a perfect quality~~, ~~i.e. the quality that exists~~ in ~~all but one modes. Depending on the specific tuning~~, ~~it ranges~~ from ~~686 to 720~~{{~~cent~~}} ([[~~7edo\|4\7~~]] to [[~~5edo\|3\5~~]]).		A '''perfect fifth (P5)''', as a concrete [[interval region]], is typically near 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale.

	In [[just intonation]], the just perfect fifth is [[3/2]]. Other intervals are also classified as perfect fifths, sometimes called '''wolf fifths''' or '''imperfect fifths''', if they are reasonably mapped to ~~4\7 and [[24edo\|14\24]] (precisely~~ four steps of the diatonic scale and seven steps of the chromatic scale~~). The use of 24edo's 14\24 as the mapping criteria here rather than [[12edo]]'s 7\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]]~~.		In [[just intonation]], the just perfect fifth is [[3/2]]. Other intervals are also classified as perfect fifths, sometimes called '''wolf fifths''' or '''imperfect fifths''', if they are reasonably mapped to four steps of the diatonic scale and seven steps of the chromatic scale.

	As a ~~concrete~~ [[~~interval region~~]], ~~it is typically near 700{{c}}~~ in ~~size~~, ~~distinct~~ from ~~semidiminished fifths of rougly 650~~{{c}}~~. A rough tuning range for the perfect fifth is about 670 to 730~~ [[~~cents~~]] ~~according~~ to [[~~Margo Schulter~~]]~~'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale~~.		Functionally, a perfect fifth is an interval that spans four steps of the [[5L 2s\|diatonic]] scale with a perfect quality, i.e. the quality that exists in all but one modes. Depending on the specific tuning, it ranges from 686 to 720{{cent}} ([[7edo\|4\7]] to [[5edo\|3\5]]).

	This article covers intervals from 660 to 750{{c}}, but intervals between 650 and 660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.		This article covers intervals from 660 to 750{{c}}, but intervals between 650 and 660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.

VectorGraphics at 02:48, 9 March 2025

2025-03-09T02:48:20Z

← Older revision		Revision as of 02:48, 9 March 2025
Line 7:		Line 7:
	As a concrete [[interval region]], it is typically near 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale.		As a concrete [[interval region]], it is typically near 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale.

	This article covers intervals from ~~650~~ to 750{{c}}~~, which is very wide~~, but ~~is done to avoid having~~ to ~~make articles for~~ the ~~tiny interval regions~~ that ~~would otherwise be required to cover the entire span of intervals~~.		This article covers intervals from 660 to 750{{c}}, but intervals between 650 and 660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.

	== In just intonation ==		== In just intonation ==

VectorGraphics: Capitalization of MOS and EDO

2025-03-05T20:37:44Z

Capitalization of MOS and EDO

← Older revision		Revision as of 20:37, 5 March 2025
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	* The 13-limit '''ultrafifth''' is a ratio of 20/13, and is about 746{{c}}, but it might be better analyzed as an [[minor sixth\|inframinor sixth]]. Despite that, it is also here for completeness.		* The 13-limit '''ultrafifth''' is a ratio of 20/13, and is about 746{{c}}, but it might be better analyzed as an [[minor sixth\|inframinor sixth]]. Despite that, it is also here for completeness.

	== In ~~edos~~ ==		== In EDOs ==
	The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[edo]]s.		The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[edo\|EDO]]s.

	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! ~~Edo~~		! EDO
	! 3/2		! 3/2
	! Other fifths		! Other fifths
Line 108:		Line 108:
	* Various historical [[well temperament]]s generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone		* Various historical [[well temperament]]s generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone

	== In ~~mos~~ scales ==		== In MOS scales ==
	Intervals between 654 and 750{{c}} generate the following [[mos]] scales:		Intervals between 654 and 750{{c}} generate the following [[mos\|MOS]] scales:

	These tables start from the last monolarge ~~mos~~ generated by the interval range.		These tables start from the last monolarge MOS generated by the interval range.

	Scales with more than 12 notes are not included.		Scales with more than 12 notes are not included.
Line 118:		Line 118:
	\|-		\|-
	! Range		! Range
	! colspan="6" \| ~~Mos~~		! colspan="6" \| MOS
	\|-		\|-
	\| 720–750{{c}}		\| 720–750{{c}}