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Replicative Network Structures: Theoretical Definitions and Analytical Applications REPLICATIVE NETWORK STRUCTURES: THEORETICAL DEFINITIONS AND ANALYTICAL APPLICATIONS by STEPHANIE KATHLEEN LIND B. Mus., Wilfrid Laurier University, 2000 M. A., The University of British Columbia, 2003 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF: DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Music) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) July 2008 © Stephanie Kathleen Lind, 2008 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 ii 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. iii Table of Contents Abstract .............................................................................................................................. ii Table of Contents ............................................................................................................. iv List of Figures .................................................................................................................... v Acknowledgements ........................................................................................................viii Chapter 1 : Introduction ................................................................................................... 1 Chapter 2 : Theoretical Definitions................................................................................ 29 Section 1: Defining Product Graphs and Networks................................................. 30 Section 2: Networks-of-Networks ........................................................................... 47 Section 3: Other Replicative Structures................................................................... 59 Section 4: Relating Replicative Networks ............................................................... 61 Chapter 3 : Analyses of Contemporary Québécois Works............................................. 65 Chapter 4 : An Analysis of Schafer’s Seventh String Quartet ..................................... 100 Chapter 5 : Analytical Goals and a Broader Range of Analyses.................................. 146 Chapter 6 : Conclusion................................................................................................. 185 Limitations .............................................................................................................. 185 Differences between Networks-of-Networks and Product Networks..................... 186 Hierarchy................................................................................................................. 188 Network Structure and Analytical Meaning ........................................................... 189 Expectation and Network Structure........................................................................ 190 Scale and Choice of Networks................................................................................ 192 Issues for Future Research...................................................................................... 192 Bibliography .................................................................................................................. 197 iv List of Figures Figure 1.1 : Pépin, Monade VI – Réseaux , Cahier 7, fourth system .................................. 2 Figure 1.2 : A network and other related formal structures ............................................... 4 Figure 1.3 : Networks depicting the music of Pépin, Monade VI – Réseaux , Cahier 7, fourth system........................................................................................... 5 Figure 1.4 : Analyses from Lewin, GMIT , section 9.5.5 ................................................... 7 Figure 1.5 : Gilles Tremblay, Phases , I 4 relations in measures 1-4................................. 14 Figure 1.6 : An analysis of inversionally-based pitch-class relationships in Tremblay, Phases , mm. 1-3 .................................................................................. 14 Figure 1.7 : A large-scale network of Klumpenhouwer networks................................... 17 Figure 1.8 : An example of Lewin's contextual transformation "K" ............................... 19 Figure 1.9 : Figures from Lewin's “Transformational Considerations in Schoenberg’s Opus 23, Number 3” ...................................................................... 20 Figure 1.10 : A network, corresponding to Lewin’s analytical commentary, which incorporates the graph of his Figure 9.1..................................................... 21 Figure 1.11 : Reinterpreting Lewin's Figure 9.2 .............................................................. 22 Figure 1.12 : Lewin's Figures 9.10 and 9.11.................................................................... 24 Figure 1.13 : An analysis of Stockhausen's Klavierstück III , from Lewin’s Musical Form and Transformation ....................................................................... 25 Figure 1.14 : A complete product network-of-networks based on Figure 1.13............... 26 Figure 2.1 : A network of mode-step transformations involving the pitch classes of the C-Major mode............................................................................................. 47 Figure 2.2 : Nested network and graph structures ........................................................... 48 Figure 2.3 : CONTENTSMAP and TRANSIT mappings within the network-of-networks NON................................................................................... 56 Figure 2.4 : The derivation of a sequential graph ............................................................ 60 v Figure 3.1 : Pépin, Monade VI – Réseaux , Cahier 7, fourth system ................................ 66 Figure 3.2 : Network representations of the motive boxed in Figure 3.1 ........................ 67 Figure 3.3 : Pépin, Monade VI – Réseaux , Cahier 7, 12th-14th systems......................... 70 Figure 3.4 : A network for the transpositionally-generated phrases of Figure 3.3 .......... 71 Figure 3.5 : Hétu, Prélude , measures 16-20 .................................................................... 72 Figure 3.6 : Hétu, Prélude , similar network structures between representations of the augmented triad and instances of the main motivic group ......................... 73 Figure 3.7 : Hétu, Prélude , measures 25-28 .................................................................... 74 Figure 3.8 : Hétu, Prélude , similar network structures between representations of the augmented triad and instances of the main motivic group in measures 25-28 ..................................................................................................... 74 Figure 3.9 : Hétu, Toccata , op. 1, measures 1-18 ............................................................ 76 Figure 3.10 : Sequences and near-sequences in measures 1-18 of Hétu’s Toccata , op. 1........................................................................................................ 77 Figure 3.11 : Interpreting pitch classes in measures 9-10 of Hétu, Toccata , op. 1, right hand.................................................................................................... 79 Figure 3.12 : Hétu, Sonate pour Piano , first movement, measures 1-6........................... 80 Figure 3.13 : Analytical networks for Hétu, Sonate pour piano , first movement, mm. 1-6................................................................................................................. 80 Figure 3.14 : Hétu, Sonate pour Piano , first movement, measures 17-19....................... 83 Figure 3.15 : Transformations involved in SC 0167........................................................ 84 Figure 3.16 : Transformations between tetrachords in measures 17-19 of Hétu's Sonate pour piano , first movement......................................................................
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