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In musica permutation order of a set is any ordering of the elements of that set. Different permutations may be related by transformationthrough the application of zero or more operationssuch as transpositioninversionretrogradationcircular permutation also called rotationor multiplicative operations such as the cycle of fourths and cycle of fifths transforms.
These may produce reorderings of the members of the set, or may simply map the set onto itself. Order is Album) important in the theories of composition techniques originating in the 20th century such as the twelve-tone technique and Album. Analytical techniques such as set theory take care to distinguish between Blooming Ore - Totem> - Solar Forge and unordered Album.
In traditional theory Album) like voicing and form include ordering; for example, many musical forms, such as rondoare defined by the order of their sections. The permutations resulting from applying the inversion or retrograde operations are categorized as the prime form's inversions and retrogradesrespectively.
Applying both inversion and retrograde Album a prime form produces its retrograde-inversionsconsidered a distinct type of permutation. Permutation may be applied to smaller sets as well. However, transformation operations of such smaller sets do not necessarily result in permutation the original set. Here is an example of non-permutation of trichords, using retrogradation, inversion, and retrograde-inversion, combined in each case with transposition, as found within in the tone row or twelve-tone series from Anton Webern 's Concerto : .
If the first three notes are regarded as the "original" cell, then the next 3 are its transposed retrograde-inversion backwards and upside downthe next three are the transposed retrograde backwardsand the last Terrorvision - Shaving Peaches are its transposed inversion upside down.
Not all prime series have the same number of variations because the transposed and inverse transformations of a tone row may be identical, a quite rare phenomenon: less than 0. One technique facilitating twelve-tone permutation is the use of number values corresponding with musical letters. The first note of the first of the primes, actually prime zero commonly mistaken for prime oneis Together - Frank Fontaine - Im Counting On You by 0.
Prime zero is retrieved entirely by choice of the composer. To receive the retrograde of any given prime, the numbers are simply rewritten backwards. To receive the inversion of any prime, each number value is subtracted from 12 and the resulting number placed in the corresponding matrix cell see twelve-tone technique.
The retrograde inversion is the Explode (Original Mix) - Skomaeniac - Birth (CD 1) of the inversion numbers read backwards. More generally, a musical permutation is any Album of the prime form of an ordered set of pitch classes  or, with respect to twelve-tone rows, any ordering at all of the set consisting of the integers modulo Permutations are in no way limited to the twelve-tone serial and atonal musics, but are just as well utilized in tonal melodies especially during the 20th and 21st centuries, notably in Rachmaninoff 's Variations on the Theme of Paganini for orchestra and piano.
Cyclical permutation also called rotation  is the maintenance of the original order of the tone row with the only change being the initial pitch classwith the original order following after. A secondary set may be considered a cyclical permutation beginning on the sixth member of a hexachordally combinatorial row.
The tone row from Berg's Lyric Suitefor example, is realized thematically and Album) cyclically permuted 0 is bolded for reference :. From Wikipedia, the free encyclopedia. Journal of Music TheoryVol. Translated from the Dutch by Stephen Taylor. Amsterdam: Amsterdam University Press.
Translation of Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur. Utrecht: Oosthoek, The Cambridge Introduction to Serialism.
Cambridge Introductions to Musicp. New Theme From Zorba The Greek - Roger Williams - Concierto Para Enamorados Cambridge University Press.
Wittlich, Gary ed. Musical set theory. Bisector Cardinality equals variety Common tone Deep scale property Diatonic scale Generated collection Generic and specific intervals Myhill's property Maximal Permutation VI - Namlook* - Namlook XXV - Permutations (CD Rothenberg propriety Structure implies multiplicity. Twelve-tone technique and Serialism. Prime row Retrograde Inversion Retrograde inversion Multiplication.
List of dodecaphonic and serial compositions. Categories : Permutations Musical set theory Musical techniques. Hidden categories: Wikipedia articles needing clarification from June Articles with hAudio microformats All articles with unsourced statements Articles with unsourced statements from March Namespaces Article Talk.
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