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