Interval class: Difference between revisions
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{{Wikipedia| | {{Wikipedia}} | ||
{{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 two grounds: it is not a class in the vocabulary of mathematics, and 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 two grounds: it is not a class in the vocabulary of mathematics, and it is less useful than the second definition. | ||
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== See also == | == See also == | ||
* [[Interval size measure]] | * [[Interval size measure]] | ||
* [[Interval | * [[Interval region]] | ||
[[Category:Interval]] | [[Category:Interval]] | ||
Revision as of 00:49, 24 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 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, 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}.