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Generalized Musical Intervals and Transformations$
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David Lewin

Print publication date: 2007

Print ISBN-13: 9780195317138

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780195317138.001.0001

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Generalized Set Theory (2): The Injection Function

Generalized Set Theory (2): The Injection Function

(p.123) 6 Generalized Set Theory (2): The Injection Function
Generalized Musical Intervals and Transformations

David Lewin

Oxford University Press

This chapter continues the study of set theory, generalizing the work of Chapter 5 even further. The basic construction is now the Injection Function: given a space S, finite subsets X and Y of S, and a transformation f mapping S into itself, INJ(X, Y) (f) counts how many members of X are mapped by f into members of Y. This number is meaningful even when S does not have a Generalized Interval System structure, and even when the transformation f is not so well behaved as are transpositions, inversions, and the like. Passages from Schoenberg and from Babbitt are studied by way of illustration.

Keywords:   music theory, musical spaces, Injection Function, Schoenberg, Babbitt, Generalized Interval System

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