Interval class

In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'" (Rahn 1980, 29; Whittall 2008, 273–74), is the shortest distance in pitch class space between two unordered pitch classes.

(To hear a MIDI realization, click the following: 106 KBⓘ In the example above, all four labeled pitch-pairs, or dyads, share a common "intervallic color."

In atonal theory, this similarity is denoted by interval class—ic 5, in this case.

The unordered pitch class interval i(a, b) may be defined as where i⟨a, b⟩ is an ordered pitch-class interval (Rahn 1980, 28).

While notating unordered intervals with parentheses, as in the example directly above, is perhaps the standard, some theorists, including Robert Morris,[1] prefer to use braces, as in i{a, b}.