Interval class

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Interval class Play.

In

modulo
12. The largest interval class is 6 since any greater interval n may be reduced to 12 − n.

Use of interval classes

The concept of interval class accounts for

inversional equivalency
. Consider, for instance, the following passage:

Octatonic motif

(To hear a MIDI realization, click the following: 106 KB

In the example above, all four labeled pitch-pairs, or

atonal theory, this similarity is denoted by interval class—ic 5, in this case. Tonal
theory, however, classifies the four intervals differently: interval 1 as perfect fifth; 2, perfect twelfth; 3, diminished sixth; and 4, perfect fourth.

Notation of interval classes

The unordered pitch class interval i(ab) may be defined as

where iab 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{ab}. Both notations are considered acceptable.

Table of interval class equivalencies

Interval Class Table
ic included intervals tonal counterparts extended intervals
0 0 unison and octave diminished 2nd and augmented 7th
1 1 and 11 minor 2nd and major 7th augmented unison and diminished octave
2 2 and 10 major 2nd and minor 7th diminished 3rd and augmented 6th
3 3 and 9 minor 3rd and major 6th augmented 2nd and diminished 7th
4 4 and 8 major 3rd and minor 6th diminished 4th and augmented 5th
5 5 and 7 perfect 4th and perfect 5th augmented 3rd and diminished 6th
6 6 augmented 4th and diminished 5th

See also

References

Sources

  • Morris, Robert (1991). Class Notes for Atonal Music Theory. Hanover, NH: Frog Peak Music.
  • Rahn, John (1980). Basic Atonal Theory. .
  • Whittall, Arnold (2008). The Cambridge Introduction to Serialism. New York: Cambridge University Press. (pbk).

Further reading