Interval class: Difference between revisions

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~~{{Wikipedia~~|Generic and specific intervals}}

'''Interval class''' is used in the following ways:

# First, common in academic [[Wikipedia: Set theory (music)|set theory]], defines it as the [[Octave #Octave equivalence|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.

# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''~~. The newer term '''''ordinal category''''' has also been used for this second sense~~. For example, the interval class~~, or ordinal category,~~ of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.

# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. For example, the interval class of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.

== See also ==

* [[Pitch class]]

* [[Interval size measure]]

* [[Interval region]]

* [[Functional systems]]

[[Category:Interval]]

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-{{Wikipedia}}
+{{Wikipedia|Interval class|Generic and specific intervals}}
-{{Wikipedia|Generic and specific intervals}}
 '''Interval class''' is used in the following ways:
 # First, common in academic [[Wikipedia: Set theory (music)|set theory]], defines it as the [[Octave #Octave equivalence|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.
-# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''.  The newer term '''''ordinal category''''' has also been used for this second sense. For example, the interval class, or ordinal category, of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.
+# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. For example, the interval class of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.
 == See also ==
+* [[Pitch class]]
 * [[Interval size measure]]
 * [[Interval region]]
+* [[Functional systems]]
 [[Category:Interval]]