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Set (music)

"Set class" redirects here. For the concept in set theory, see Class (set theory).
Six-element set of rhythmic values used in Variazioni canoniche by Luigi Nono[1]

A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.[2]

Prime form of five pitch class set from Igor Stravinsky's In memoriam Dylan Thomas[3]
Set 3-1 has three possible rotations/inversions, the normal form of which is the smallest pie or most compact form

A set by itself does not necessarily possess any additional structure, such as an ordering or permutation. Nevertheless, it is often musically important to consider sets that are equipped with an order relation (called segments); in such contexts, bare sets are often referred to as "unordered", for the sake of emphasis.[4]

Two-element sets are called dyads, three-element sets trichords (occasionally "triads", though this is easily confused with the traditional meaning of the word triad). Sets of higher cardinalities are called tetrachords (or tetrads), pentachords (or pentads), hexachords (or hexads), heptachords (heptads or, sometimes, mixing Latin and Greek roots, "septachords"),[5] octachords (octads), nonachords (nonads), decachords (decads), undecachords, and, finally, the dodecachord.

A time-point set is a duration set where the distance in time units between attack points, or time-points, is the distance in semitones between pitch classes.[6]

  1. ^ Whittall, Arnold (2008). The Cambridge Introduction to Serialism, p.165. New York: Cambridge University Press. ISBN 978-0-521-68200-8 (pbk).
  2. ^ Wittlich, Gary (1975). "Sets and Ordering Procedures in Twentieth-Century Music", Aspects of Twentieth-Century Music, p.475. Wittlich, Gary (ed.). Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0-13-049346-5.
  3. ^ Whittall (2008), p.127.
  4. ^ Morris, Robert (1987). Composition With Pitch-Classes: A Theory of Compositional Design, p.27. Yale University Press. ISBN 0-300-03684-1.
  5. ^ E.g., Rahn (1980), 140.
  6. ^ Wittlich (1975), p.476.

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