Interval quality: Difference between revisions

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== Relative interval quality ==

Given a scale, a ''relative interval quality'' is a specific interval size that occurs in a given [[interval class]] of the scale. An interval class is the set of all intervals in the scale 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 is often used to avoid confusion with absolute interval quality and to make interval arithmetic in unfamiliar scales easier.) 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}}).

Given a scale, a ''relative interval quality'' is a specific interval size that occurs in a given [[interval class]] of the scale. An interval class is the set of all intervals in the scale 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 is often used to avoid confusion with absolute interval quality and to make interval arithmetic in unfamiliar scales easier.) 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, 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 exactly one interval; in other words, every 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.

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 == Relative interval quality ==
-Given a scale, a ''relative interval quality'' is a specific interval size that occurs in a given  [[interval class]] of the scale. An interval class is the set of all intervals in the scale 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 is often used to avoid confusion with absolute interval quality and to make interval arithmetic in unfamiliar scales easier.) 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}}).
+Given a scale, a ''relative interval quality'' is a specific interval size that occurs in a given  [[interval class]] of the scale. An interval class is the set of all intervals in the scale 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 is often used to avoid confusion with absolute interval quality and to make interval arithmetic in unfamiliar scales easier.) 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, 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 exactly one interval; in other words, every 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.