User:Fredg999/Sandbox: Difference between revisions

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== Perfect fourth ==

In Western music theory, a '''perfect fourth''' is an [[interval]] with a [[frequency ratio]] equal or approximately equal to [[4/3]] (≈498{{c}}). It is a strongly [[consonant]] interval, hence its [[interval quality]] "perfect". A perfect fourth always spans four degrees of a [[diatonic]] scale (e.g. C-F spanning C-D-E-F), hence its [[interval number]] "fourth". In particular, a perfect fourth spans two whole tones (e.g. C-D-E) and one diatonic semitone (e.g. E-F).

An ''imperfect fourth'' also spans four degrees, but with a different combination of steps. In particular, the augmented fourth spans three whole tones, hence its other name "[[tritone]]". Other fourths may occur in altered diatonic scales, such as the diminished fourth in the harmonic minor scale (e.g. B-E{{flat}}).

A ''wolf fourth'' (or ''imperfect fourth'', in a second sense) is an interval that attempts to close a [[circle of fourths]], but that fails to approximate a frequency ratio of 4/3. For example, in [[quarter-comma meantone]] temperament, an augmented third (e.g. A{{flat}}-C{{sharp}}) can be used to close the 12-tone circle of fourths, but it falls approximately 36{{c}} flat of a just perfect fourth.

In microtonal music, an interval may be considered a perfect fourth even if it exhibits only one of the two defining features of a perfect fourth:

* As intervals in an [[interval region]], perfect fourths only need to have a size close to ≈498{{c}}, no matter the underlying scale or other harmonic context. According to [[Margo Schulter]]'s ''[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]'', perfect fourths typically range from approximately 470{{c}} to 530{{c}}. Intervals that are too sharp or too flat to qualify as perfect fourths are often called [[superfourth]]s and [[subfourth]]s respectively.

* As intervals in a diatonic [[MOS scale]], perfect fourths only need to span two large steps and one small step. This approach allows for sizes ranging from [[7edo|4\7]] (≈686{{c}}) to [[5edo|3\5]] (720{{c}}). Intervals inflected by a [[quartertone]] alteration up or down from a perfect fourth are often called [[semi-augmented fourth]]s and [[semi-diminished fourth]]s respectively.

== Temperament databox ==

Using [[User:FloraC/Temperament data]].

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+== Perfect fourth ==
+{{Wikipedia|Perfect fourth}}
+{{About|the [[interval category]]|the just perfect fourth|4/3}}
+In Western music theory, a '''perfect fourth''' is an [[interval]] with a [[frequency ratio]] equal or approximately equal to [[4/3]] (≈498{{c}}). It is a strongly [[consonant]] interval, hence its [[interval quality]] "perfect". A perfect fourth always spans four degrees of a [[diatonic]] scale (e.g. C-F spanning C-D-E-F), hence its [[interval number]] "fourth". In particular, a perfect fourth spans two whole tones (e.g. C-D-E) and one diatonic semitone (e.g. E-F).
+An ''imperfect fourth'' also spans four degrees, but with a different combination of steps. In particular, the augmented fourth spans three whole tones, hence its other name "[[tritone]]". Other fourths may occur in altered diatonic scales, such as the diminished fourth in the harmonic minor scale (e.g. B-E{{flat}}).
+A ''wolf fourth'' (or ''imperfect fourth'', in a second sense) is an interval that attempts to close a [[circle of fourths]], but that fails to approximate a frequency ratio of 4/3. For example, in [[quarter-comma meantone]] temperament, an augmented third (e.g. A{{flat}}-C{{sharp}}) can be used to close the 12-tone circle of fourths, but it falls approximately 36{{c}} flat of a just perfect fourth.
+In microtonal music, an interval may be considered a perfect fourth even if it exhibits only one of the two defining features of a perfect fourth:
+* As intervals in an [[interval region]], perfect fourths only need to have a size close to ≈498{{c}}, no matter the underlying scale or other harmonic context. According to [[Margo Schulter]]'s ''[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]'', perfect fourths typically range from approximately 470{{c}} to 530{{c}}. Intervals that are too sharp or too flat to qualify as perfect fourths are often called [[superfourth]]s and [[subfourth]]s respectively.
+* As intervals in a diatonic [[MOS scale]], perfect fourths only need to span two large steps and one small step. This approach allows for sizes ranging from [[7edo|4\7]] (≈686{{c}}) to [[5edo|3\5]] (720{{c}}). Intervals inflected by a [[quartertone]] alteration up or down from a perfect fourth are often called [[semi-augmented fourth]]s and [[semi-diminished fourth]]s respectively.
 == Temperament databox ==
 Using [[User:FloraC/Temperament data]].