Interval class: Difference between revisions

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'''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 two grounds: it is not a class in the vocabulary of mathematics, and it is less useful than the second definition.

The second definition, used for example by [[Scala]], defines the interval class as the "generic interval" to which the specific intervals at a certain number of scale steps apart belong. The newer term '''''ordinal category''''' has also been used for this second sense. An ordinal category of a scale is simply the set of all ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''.

The second definition, used for example by [[Scala]], defines the interval class as the "generic interval" to which the specific intervals at a certain number of scale steps apart belong. The newer term '''''ordinal category''''' has also been used for this second sense. An ordinal category of a scale is simply the set of all ''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 ==

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 '''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 two grounds: it is not a class in the vocabulary of mathematics, and it is less useful than the second definition.
-The second definition, used for example by [[Scala]], defines the interval class as the "generic interval" to which the specific intervals at a certain number of scale steps apart belong. The newer term '''''ordinal category''''' has also been used for this second sense. An ordinal category of a scale is simply the set of all ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''.
+The second definition, used for example by [[Scala]], defines the interval class as the "generic interval" to which the specific intervals at a certain number of scale steps apart belong. The newer term '''''ordinal category''''' has also been used for this second sense. An ordinal category of a scale is simply the set of all ''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 ==