Interval class: Difference between revisions
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The term "class" has varying definitions in math; the term often refers to equivalence classes, which does fit the musical set theory definition. |
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{{Wikipedia|Generic and specific intervals}} | {{Wikipedia|Generic and specific intervals}} | ||
'''Interval class''' is used in the following ways: | '''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 | # 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. | ||
# 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}. | # 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}. | ||
Revision as of 00:36, 25 August 2023
Interval class is used in the following ways:
- First, common in academic set theory, defines it as the 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.
- 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}.