In music and the terminology of the twelve tone technique a permutation is one of the many forms a tone row or twelve tone series. That is, prime form and any transposition, inversion, retrograde or retrograde-inversion , a total of 48 permutations. However, not all prime series will yield so many variations because tranposed and/or inverse transformations may be identical to each other, this being known as invariance. More generally permutation is any reordering of the original or prime form of an ordered set of pitch classes (DeLone et. al. (Eds.), 1975, chap. 6). In other words, the concept of permutation in music is the same as that of permutation in combinatorial mathematics except that the latter is applied not only to music but to other things as well. Reordering may be called an operation or transformation.
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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.