Interval quality: Difference between revisions

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== 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 typically have smaller 2-steps; as a result, in a scale with more or fewer notes per octave than the diatonic scale, the 2-steps may fall outside of the usual range for diatonic thirds (i.e. between 240{{cent}} and 480{{cent}}).

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 and to make interval arithmetic more intuitive for unfamiliar scales). Scales with a higher density of notes typically have smaller 2-steps; as a result, in a scale with more or fewer notes per octave than the diatonic scale, the 2-steps 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 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 5-steps (or perfect sixths) 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.

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 == 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 typically have smaller 2-steps; as a result, in a scale with more or fewer notes per octave than the diatonic scale, the 2-steps may fall outside of the usual range for diatonic thirds (i.e. between 240{{cent}} and 480{{cent}}).
+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 and to make interval arithmetic more intuitive for unfamiliar scales). Scales with a higher density of notes typically have smaller 2-steps; as a result, in a scale with more or fewer notes per octave than the diatonic scale, the 2-steps 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 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 5-steps (or perfect sixths) 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.