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. | '''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''. For example, the interval class 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 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 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 == | == See also == | ||
Revision as of 21:14, 28 May 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 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 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}.