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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 Interval Systems (2): Formal Features

Generalized Interval Systems (2): Formal Features

(p.31) 3 Generalized Interval Systems (2): Formal Features
Generalized Musical Intervals and Transformations

David Lewin

Oxford University Press

This chapter concerns itself with further formal properties of the Generalized Interval System (GIS) model. In this model, the points of the space may be labeled by their intervals from one referential point; this has advantages and disadvantages. New GIS structures may be constructed from old in various ways. A passage from Webern is examined in connection with a combined pitch-and-rhythm GIS constructed in one such way. Generalized analogs of transposition and inversion operations are explored. So are “interval-preserving operations”; these coincide with transpositions in some GIS models but not in others, specifically not in GISs that are “non-commutative”.

Keywords:   Generalized Interval System, musical space, Webern, pitch, rhythm, transposition, inversion

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