Perfect fourth: Difference between revisions

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A '''perfect fourth (P4)''' is an interval that ~~is near 500~~ [[~~Cent~~|~~cents~~]] in ~~size~~, ~~distinct~~ from ~~augmented~~ fourths (a ~~type of~~ [[~~tritone~~]], ~~about 600~~ cents). A rough tuning range for the perfect fourth is about ~~450~~ to ~~550~~ [[~~cents~~]]~~, though this is extremely wide; some might prefer to restrict it to around 470-530 cents~~. Another common range is the ~~even~~ stricter ~~diatonic~~ range, from 480 to ~514 cents, which ~~corresponds to [[diatonic perfect fourth]]s that can be used to generate~~ a ~~[[5L 2s|~~diatonic scale]].

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]]s ([[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]].

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

== In just intonation ==

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|}

== In ~~EDOs~~ ==

== In edos ==

The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[~~EDOs~~]].

The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[edos]].

{| class="wikitable"

|+

!~~EDO~~

!Edo

!4/3

!Other fourths

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 {{About|the [[interval region]]|the just perfect fourth|4/3}}
-A '''perfect fourth (P4)''' is an interval that is near 500 [[Cent|cents]] in size, distinct from augmented fourths (a type of [[tritone]], about 600 cents). A rough tuning range for the perfect fourth is about 450 to 550 [[cents]], though this is extremely wide; some might prefer to restrict it to around 470-530 cents. Another common range is the even stricter diatonic range, from 480 to ~514 cents, which corresponds to [[diatonic perfect fourth]]s that can be used to generate a [[5L 2s|diatonic scale]].
+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]]s ([[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]].
+As a concrete [[interval region]], it is typically near 500 cents in size, distinct from the [[semiaugmented fourth]] of roughly 550 cents. A rough tuning range for the perfect fourth is about 470 to 530 cents according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 480 to 514 cents, which generates a diatonic scale.
 == In just intonation ==
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 |}
-== In EDOs ==
+== In edos ==
-The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[EDOs]].
+The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[edos]].
 {| class="wikitable"
 |+
-!EDO
+!Edo
 !4/3
 !Other fourths