Interval class: Difference between revisions

Line 2:

'''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 than the second definition.

# 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 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}.

@@ Line 2: / Line 2: @@
 {{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 than the second definition.
+# 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 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}.