# Interval class

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English Wikipedia has an article on:

English Wikipedia has an article on:

**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 and less generalizable than the second definition.
- The second definition, used for example by Scala, defines the
*interval class*, or the, as the set of all specific intervals (interval qualities) 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**generic interval***k*-step intervals, or*k*-steps, for a specific fixed integer*k*. The newer termhas 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}.**ordinal category**