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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=== Summary of proposed changes (2025-02-17 update) ===

; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).

; Merge ''General Theory'' and ''Mathematical Theory'' into ''~~Overview~~'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory"~~; it could just as well be~~ "~~Overview of xenharmonic theory~~"~~, too~~.

; Merge ''General Theory'' and ''Mathematical Theory'' into ''Theory overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory" (while "Theory overview" would be the shorthand for the sidebar).

; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.

; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here, especially since we have the [[Links]] page. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.

; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.

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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]].
@@ Line 86: / Line 99: @@
 === Summary of proposed changes (2025-02-17 update) ===
 ; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).
-; Merge ''General Theory'' and ''Mathematical Theory'' into ''Overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory"; it could just as well be "Overview of xenharmonic theory", too.
+; Merge ''General Theory'' and ''Mathematical Theory'' into ''Theory overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory" (while "Theory overview" would be the shorthand for the sidebar).
-; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.
+; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here, especially since we have the [[Links]] page. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.
 ; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.