PERMUTATION (MUSIC)

In music a 'permutation' of a set is a transformation of its ''prime form'' by applying zero or more of certain ''operations'', specifically transposition, inversion, and 'retrograde'.
The ''permutations'' resulting from applying the ''inversion'' or ''retrograde'' operations are categorized as the prime form's ''inversions'' and ''retrogrades'', respectively. Likewise, applying both ''inversion'' and ''retrograde'' to a prime form produces its ''retrograde-inversions'', which are considered a distinct type of permutation.
Here is an example of permutation usage in the tone row (or twelve tone series) from Anton Webern's ''Concerto'':
B, Bb, D, Eb, G, F#, G#, E, F, C, C#, A
If the first three notes are regarded as the "original" cell, then the next three are its retrograde inversion (backwards and upside down), the next three are retrograde (backwards), and the last three are its inversion (upside down).
In the twelve tone technique, a tone row has a maximum of 48 permutations, including its ''prime form''. However, not all prime series have so many variations because the tranposed and inverse transformations of a tone row may be identical to each other, a phenomenon known as invariance.
More generally, a musical ''permutation'' is any reordering of the prime form of an ordered set of pitch classes (DeLone et al. (Eds.), 1975, chap. 6). In that regard, a musical ''permutation'' is a combinatorial permutation from mathematics as it applies to music.

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See also

Reference

See also

★ Counterpoint

★ Multiplication (music)

★ Musical set theory

★ Permutation

Reference

★ DeLone et al. (Eds.) (1975). Aspects of Twentieth-Century Music. Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0-13-049346-5, Ch. 6.