Perfect fourth: Difference between revisions

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{{Infobox interval region|Name=Perfect fourth|Cents lower=480|Cents lower wide=450|Cents upper=514|Cents upper wide=550|JI intervals=4/3|MOSes=[[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]|Complement=[[Perfect fourth]]|Lower region=[[Major third]]|Higher region=[[Semi-augmented fourth]] <br> [[Tritone]]}}{{Wikipedia}}

{{Infobox interval region

A '''perfect fourth (P4)''' is an interval that spans three 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 480 to 514{{cent}} ([[5edo|2\5]] to [[7edo|3\7]]).

| Name = Perfect fourth

| Cents lower = 480

| Cents lower wide = 450

| Cents upper = 514

| Cents upper wide = 550

| JI intervals = 4/3

| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]

| Complement = [[Perfect fourth]]

| Lower region = [[Major third]]

| Higher region = [[Semi-augmented fourth]] <br> [[Tritone]]

}}

A '''perfect fourth''' ('''P4''') is an interval that spans three 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 480 to 514{{cent}} ([[5edo|2\5]] to [[7edo|3\7]]).

In [[just intonation]], the just perfect fourth is [[4/3]]. Other intervals are also classified as perfect fourths, sometimes called '''wolf fourths''' or '''imperfect fourths''', if they are reasonably mapped to ~~3\7 and [[24edo|10\24]] (precisely~~ three steps of the diatonic scale and five steps of the chromatic scale~~). The use of 24edo's 10\24 as the mapping criteria here rather than [[12edo]]'s 5\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]~~.

In [[just intonation]], the just perfect fourth is [[4/3]]. Other intervals are also classified as perfect fourths, sometimes called '''wolf fourths''' or '''imperfect fourths''', if they are reasonably mapped to three steps of the diatonic scale and five steps of the chromatic scale.

As a concrete [[interval region]], it is typically near 500{{c}} in size, distinct from the [[semiaugmented fourth]] of roughly 550{{c}}. A rough tuning range for the perfect fourth is about 470 to 530{{c}} according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 480 to 514{{c}}, which generates a diatonic scale.

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* Various historical [[well temperament]]s generated by tempered 4/3's or 3/2's, equivalent to 12edo as compton and meantone

== In ~~moment-of-symmetry~~ scales ==

== In mos scales ==

Intervals between 450 and 545 cents generate the following [[mos]] scales:

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 {{About|the [[interval region]]|the just perfect fourth|4/3}}
-{{Infobox interval region|Name=Perfect fourth|Cents lower=480|Cents lower wide=450|Cents upper=514|Cents upper wide=550|JI intervals=4/3|MOSes=[[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]|Complement=[[Perfect fourth]]|Lower region=[[Major&nbsp;third]]|Higher region=[[Semi-augmented&nbsp;fourth]] <br> [[Tritone]]}}{{Wikipedia}}
+{{Infobox interval region
-A '''perfect fourth (P4)''' is an interval that spans three 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 480 to 514{{cent}} ([[5edo|2\5]] to [[7edo|3\7]]).
+| Name = Perfect fourth
+| Cents lower = 480
+| Cents lower wide = 450
+| Cents upper = 514
+| Cents upper wide = 550
+| JI intervals = 4/3
+| MOSes = [[5L 2s]], [[2L 5s]], [[5L 3s]], [[7L 2s]], [[2L 7s]]
+| Complement = [[Perfect fourth]]
+| Lower region = [[Major&nbsp;third]]
+| Higher region = [[Semi-augmented&nbsp;fourth]] <br> [[Tritone]]
+}}
+{{Wikipedia}}
+A '''perfect fourth''' ('''P4''') is an interval that spans three 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 480 to 514{{cent}} ([[5edo|2\5]] to [[7edo|3\7]]).
-In [[just intonation]], the just perfect fourth is [[4/3]]. Other intervals are also classified as perfect fourths, sometimes called '''wolf fourths''' or '''imperfect fourths''', if they are reasonably mapped to 3\7 and [[24edo|10\24]] (precisely three steps of the diatonic scale and five steps of the chromatic scale). The use of 24edo's 10\24 as the mapping criteria here rather than [[12edo]]'s 5\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]].
+In [[just intonation]], the just perfect fourth is [[4/3]]. Other intervals are also classified as perfect fourths, sometimes called '''wolf fourths''' or '''imperfect fourths''', if they are reasonably mapped to three steps of the diatonic scale and five steps of the chromatic scale.
 As a concrete [[interval region]], it is typically near 500{{c}} in size, distinct from the [[semiaugmented fourth]] of roughly 550{{c}}. A rough tuning range for the perfect fourth is about 470 to 530{{c}} according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 480 to 514{{c}}, which generates a diatonic scale.
@@ Line 143: / Line 155: @@
 * Various historical [[well temperament]]s generated by tempered 4/3's or 3/2's, equivalent to 12edo as compton and meantone
-== In moment-of-symmetry scales ==
+== In mos scales ==
 Intervals between 450 and 545 cents generate the following [[mos]] scales: