Interval quality: Difference between revisions

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The '''~~interval~~ quality''' of an [[interval]] ~~within a~~ [[~~scale~~]] ~~describes the relative size of the interval~~ compared to ~~the other~~ intervals ~~of the same [[interval class]]~~.

The '''quality''' of an [[interval]] describes its relative [[Interval size measure|size]] compared to similar intervals. Commonly used qualities include ''major'', ''minor'', ''perfect'', ''augmented'', and ''diminished''.

In the [[~~5L 2s|diatonic~~]] ~~scale,~~ which is an [[MOS scale]], there are two interval qualities for each interval class, except the unison. The unison is always qualified as ''perfect'', the fifth and the fourth can be ''perfect'' or ''imperfect'', while ~~other intervals are qualified as~~ ''~~major~~'' or ''~~minor''. This set~~ of ~~interval qualities can be generalized to all MOS scales by replacing~~ the ~~fifth by~~ the ~~interval class of the generator~~.

The '''relative quality''' of an interval is defined with relation to the [[scale]] in which it is used in context, while its '''absolute quality''' is defined with relation to a fixed scale independent of the context in which it is used, usually the [[5L 2s|diatonic]] scale.

{{todo|expand|inline=1|comment=~~Distinguish between two conflicting uses: "relative quality" (within a scale) and~~ "absolute quality" (similar to interval regions).}}

The concept of quality can also be expanded to chords. Chord qualities are related to the qualities of the component intervals that define the chord.

== Relative interval quality ==

In any scale, each [[interval class]] consists of the set of all intervals that span a given number of [[step]]s. For example, all intervals that span two steps of a scale are ''thirds'' or ''2-steps'' (the latter form being often used to avoid confusion with absolute interval quality). Scales with a higher density of notes compared to the diatonic scale typically have smaller thirds and vice versa; as a result, the thirds may fall outside of the usual range for diatonic thirds (i.e. between 240{{cent}} and 480{{cent}}).

In an [[equal tuning|equal scale]], each interval class contains a single perfect interval; in other words, each interval is perfect. Therefore, both intervals 5\[[8edo|8]] and 5\[[13edo|13]] are perfect sixths (or perfect 5-steps) within their respective [[edo]] taken as a scale, even though they have significantly different sizes.

In [[moment of symmetry]] (MOS) scales, each interval class contains two intervals except for the unison class, which only contains the unison class. The two interval classes that correspond to the [[Modal UDP notation#Generalizing to arbitrary MOS scales: bright and dark generators (chroma-positive and chroma-negative)||bright and dark generators]] contain only perfect intervals except for one, which corresponds to the "wolf" interval, which is qualified as either ''augmented'' or ''diminished'' depending on its size relative to the perfect generator, or sometimes ''imperfect'' when considering the general case. The other interval classes contain major and minor intervals.

Scales with higher [[interval variety]] require additional qualities. Although there are no standard labels yet, several widespread terms lend themselves well in this context, such as ''neutral'' which can be added to the major/minor pair for variety-3 interval classes.

The [[harmonic series]] taken a scale theoretically contains infinitely many interval qualities for each interval class. For that reason, relative quality is rarely used in that context and other tools are used to describe the variety of intervals found in [[just intonation]] taken as a whole, such as absolute interval quality.

== Absolute interval quality ==

{{todo|expand|inline=1|comment=Expand "absolute quality" (similar to interval regions).}}

== See also ==

* [[Interval variety]]

[[Category:Interval]]

[[Category:Scale]]

~~[[Category:Interval]]~~

[[Category:Stub]]

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-The '''interval quality''' of an [[interval]] within a [[scale]] describes the relative size of the interval compared to the other intervals of the same [[interval class]].
+The '''quality''' of an [[interval]] describes its relative [[Interval size measure|size]] compared to similar intervals. Commonly used qualities include ''major'', ''minor'', ''perfect'', ''augmented'', and ''diminished''.
-In the [[5L 2s|diatonic]] scale, which is an [[MOS scale]], there are two interval qualities for each interval class, except the unison. The unison is always qualified as ''perfect'', the fifth and the fourth can be ''perfect'' or ''imperfect'', while other intervals are qualified as ''major'' or ''minor''. This set of interval qualities can be generalized to all MOS scales by replacing the fifth by the interval class of the generator.
+The '''relative quality''' of an interval is defined with relation to the [[scale]] in which it is used in context, while its '''absolute quality''' is defined with relation to a fixed scale independent of the context in which it is used, usually the [[5L 2s|diatonic]] scale.
-{{todo|expand|inline=1|comment=Distinguish between two conflicting uses: "relative quality" (within a scale) and "absolute quality" (similar to interval regions).}}
+The concept of quality can also be expanded to chords. Chord qualities are related to the qualities of the component intervals that define the chord.
+== Relative interval quality ==
+In any scale, each [[interval class]] consists of the set of all intervals that span a given number of [[step]]s. For example, all intervals that span two steps of a scale are ''thirds'' or ''2-steps'' (the latter form being often used to avoid confusion with absolute interval quality). Scales with a higher density of notes compared to the diatonic scale typically have smaller thirds and vice versa; as a result, the thirds may fall outside of the usual range for diatonic thirds (i.e. between 240{{cent}} and 480{{cent}}).
+In an [[equal tuning|equal scale]], each interval class contains a single perfect interval; in other words, each interval is perfect. Therefore, both intervals 5\[[8edo|8]] and 5\[[13edo|13]] are perfect sixths (or perfect 5-steps) within their respective [[edo]] taken as a scale, even though they have significantly different sizes.
+In [[moment of symmetry]] (MOS) scales, each interval class contains two intervals except for the unison class, which only contains the unison class. The two interval classes that correspond to the [[Modal UDP notation#Generalizing to arbitrary MOS scales: bright and dark generators (chroma-positive and chroma-negative)||bright and dark generators]] contain only perfect intervals except for one, which corresponds to the "wolf" interval, which is qualified as either ''augmented'' or ''diminished'' depending on its size relative to the perfect generator, or sometimes ''imperfect'' when considering the general case. The other interval classes contain major and minor intervals.
+Scales with higher [[interval variety]] require additional qualities. Although there are no standard labels yet, several widespread terms lend themselves well in this context, such as ''neutral'' which can be added to the major/minor pair for variety-3 interval classes.
+The [[harmonic series]] taken a scale theoretically contains infinitely many interval qualities for each interval class. For that reason, relative quality is rarely used in that context and other tools are used to describe the variety of intervals found in [[just intonation]] taken as a whole, such as absolute interval quality.
+== Absolute interval quality ==
+{{todo|expand|inline=1|comment=Expand "absolute quality" (similar to interval regions).}}
 == See also ==
 * [[Interval variety]]
+[[Category:Interval]]
 [[Category:Scale]]
-[[Category:Interval]]
 [[Category:Stub]]