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Replicative network structures : theoretical definitions and analytical applications Lind, Stephanie Kathleen

Abstract

Among the techniques associated with the theory of musical transformations, network analysis stands out because of its broad applicability, demonstrated by the diverse examples presented in David Lewin’s seminal work Musical Form and Transformation and related articles by Lewin, Klumpenhouwer, Gollin, and others. While transformational theory can encompass a wide variety of analytical structures, objects, and transformations, two particular types of network postulated by Lewin are often featured: the product network and the network-of-networks. These structures both incorporate repetition, but in different ways. This document will propose one possible definition for product networks and networks-of-networks that is consistent with Lewin’s theories as presented in Generalized Musical Intervals and Transformations. This definition will clarify how each of these two network formats may be generated from the same sub-graphs, which in turn will clarify the advantages and disadvantages of each structure for musical analysis, specifically demonstrating how analytical goals shape the choice of network representation. The analyses of Chapters 3 and 4 examine works by contemporary Canadian composers that have not been the subject of any published analyses. Chapter 3 presents short examples from the works of contemporary Québécois composers, demonstrating the utility of these networks for depicting connections within brief passages that feature short, repeated motives. Chapter 4 presents an analysis of R. Murray Schafer’s Seventh String Quartet, demonstrating how these structures can be used to link small-scale events with longer prolongations and motivic development throughout a movement. Chapter 5 demonstrates through a wider repertoire how analytical goals shape the choice of network representation, touching on such factors as continuity, motivic return, and implied collections.

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