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In music using the twelve tone technique invariance describes the portions of rows which have been so designed that they remain invariant under the allowable transformations (inversion, retrograde, retrograde-inversion, multiplication). George Perle describes their use as "pivots" or non- tonal ways of emphasizing certain pitches. Invariant rows are also combinatorial. Musical terminology

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Topics: Invariance (music), Invariance Of Domain...

Invariance of domainInvariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space R n''. It states: :If U is an open subset of R n and f : U → R n is an injective continuous map, then V f ''U is open and f is a homeomorphism between U and V

Invariance (music)In music using the twelve tone technique invariance describes the portions of rows which have been so designed that they remain invariant under the allowable transformations (inversion, retrograde, retrograde-inversion, multiplication). George Perle descr

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