Set (music)

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In musical set theory, a set is a collection of discrete entities, for example pitch sets, duration sets, and timbre sets (DeLone et. al., 1975, p.475). A set form is the arrangement of an ordered set: the prime form (original order), inverse (upside down), retrograde (backwards), and retrograde inverse (backwards and upside down) (ibid).

A derived set is one which is generated or derived from consistent operations on a subset, for example Webern's Concerto, Op.24, in which the last three sets are derived from the first (ibid, p.474):

B Bb D Eb G F# G# E F C C# A

Represented numerically:

0 11 3 4  8 7  9  5 6 1 2  10

The first set being:

0 11 3 4

The second being the first transposed up eight semitones:

  0 11 3 4
+ 8 8  8 8
  --------
= 8 7  9 5

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 (ibid, p.476).