Permutation (music)
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In musical set theory, a permutation of a musical 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. In the twelve tone technique, a tone row or twelve tone series 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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Reference
- DeLone et. al. (Eds.) (1975). Aspects of Twentieth-Century Music. Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0130493465, Ch. 6.Template:Music-theory-stub