Dissertation Index
Author: Argentino, Joe R Title: Transformations and Hexatonic Tonnetz Spaces in Late Works of Schoenberg Institution: The University of Western Ontario Begun: September 2004 Completed: February 2010 Abstract: Schoenberg’s Modern Psalm Opus 50c, is a combinatorial work based on a 6-20[014589] hexachord. Each of set class 6-20’s trichordal generators contains at least one instance of interval class 4, and thus these trichordal subsets can symmetrically divide the aggregate by interval cycle 4, or the single interval class of the 3-12 trichord. The significance of the 3-12 trichord extends from guiding hexachordal regions and formal design, to representing Schoenberg’s God. This dissertation explores the cyclic properties of the 6-20 hexachord and its trichordal subsets, and constructs cyclic Tonnetz spaces that reproduce a modified version of Richard Cohn’s hyper-hexatonic system. Using redefined versions of the neo-Riemannian operators R, P, and L, and my newly formed operator S, I generate each hexatonic system purely as set-class consistent cycles of 3-3, 3-4 or 3-11 trichords. Armed with these cycles, this study analyzes the systematic exhaustion of particular forms of a set-class, and how the small- and large-scale cycles guide the form in Modern Psalm. Throughout Modern Psalm, Schoenberg uses cyclic large-scale transformational 6-35 collections supported by alternating and complementary invariant hexatonic cycles. The invariance within the hexatonic cycles leads to two additional transformations, entitled SWAP and SDR; these transformations eloquently reveal not only how hexachords are related to one another, but more importantly, why they are related to one another. This study also establishes that A Survivor from Warsaw can be regarded as the precursor to Schoenberg’s Modern Psalm. It is in A Survivor from Warsaw that Schoenberg initiates large-scale T4-related regions, small-scale transformational 6-35 cycles, the musical representation of God with pcs {048}, and tripartite structures in the text. The omnipresence of tripartite structures permeates A Survivor from Warsaw, and modified versions of these tripartite and symmetrical structures occur throughout Modern Psalm. The symmetry that governs the musical form and the textual form contributes to a meshing of formal organization that is vital for comprehensibility and unity. The theoretical constructs that I have derived from my analysis of Modern Psalm and A Survivor form Warsaw may be used as a prism through which to view other serial and non-serial works based on the 6-20 hexachord. Keywords: transformation, neo-Riemannian, 6-20 hexachord, hyper-hexatonic system, Schoenberg, Modern Psalm op. 50c, A Survivor from Warsaw, cycles, Tonnetz. TOC: ABSTRACT....................................................................................................... iii ACKNOWLEDGMENTS...................................................................................... v LIST OF EXAMPLES........................................................................................... ix CHAPTER 1: TONNETZE, HEXATONIC SYSTEMS, AND DODECAPHONIC APPLICATIONS............................................................................ 1 Neo-Riemannian Theory, Cohn, Siciliano, and Dodecaphony .................. 2 Richard Cohn: Hyper-Hexatonic System and Parsimonious Voice Leading.................................................................................................. 5 Toggling Cycles and Hexatonic Systems.................................................. 16 New Definitions: R, P, L, and Newly Formed S, and 3-3, 3-4, and 3-11 Cycles..................................................................................................... 21 Conclusion ............................................................................................. 27 CHAPTER 2: TONNETZ SPACES AND HEXATONIC CYCLES............................ 28 The 6-20 Hexachord, its Subsets, and their Tonnetz Spaces................ 28 Tonnetz8 Axis Cycles........................................................................... 31 Length-12 *Tonnetz Axis Cycles: (T1) and (T5)............................... 32 Length-4 Tonnetz Axis Cycles....................................................... 38 Length-3 Tonnetz Axis Cycles....................................................... 39 Tonnetz Axis Cycles and their Collective PC Collections........................ 41 Tonnetz Alley Cycles............................................................................... 45 Invariant Hexatonic Alley Cycle............................................................... 46 Analysis: “Nacht” from Pierrot Lunaire, op. 21..................................... 49 Hexatonic Systems, Tonnetz Cycles, and Modern Psalm....................... 51 Conclusion............................................................................................... 56 CHAPTER 3: A SURVIVOR FROM WARSAW AND TRIPARTITE CYCLES.......................................................................................... 57 Schoenberg’s Text for A Survivor from Warsaw....................................... 60 Tripartite Text Structures........................................................................ 63 Row Charts, Theoretical Background, and Cycles of A Survivor From Warsaw................................................................................................... 67 Hexachords Based on T4-Invariant Cycles.............................................. 70 Practical Instances of Small-Scale T4-Invariant Cycles...................... 74 Small-scale T1-Cycles............................................................................ 79 Hexachords based on a T4-Cycle of I-Combinatorial Regions................ 87 Integration of Text, Cycles, and Overall Form of A Survivor from Warsaw................................................................................................... 91 Conclusion.............................................................................................. 99 CHAPTER 4: MODERN PSALM: TEXT, FORM, AND THE TRANSFORMATIONAL 6-35 CYCLE.............................................. 101 Introduction............................................................................................ 102 The Texts of Modern Psalm..................................................................... 104 Der Erste Psalm and Tripartite Structures................................................ 108 Modern Psalm’s Prime Row and Matrix.................................................... 113 Cyclic Aspects of Schoenberg’s Die Wunder-Reihe............................... 116 Modern Psalm and the Transformational 6-35 Cycle............................... 128 Conclusion.............................................................................................. 135 CHAPTER 5: TRANSFORMATIONS SWAP AND SDR........................................... 137 Some Schoenbergian Rows that Contain 6-20 Hexachords and Their General and Particular Features...................................................... 138 Modern Psalm and Transformational Models: SWAP, RSWAP, SDR, and RSDR........................................................................................ 146 SWAP and SDR Analysis of Modern Psalm............................................. 155 Conclusion.............................................................................................. 159 CHAPTER 6: HEXATONIC CYCLES, TRANSFORMATIONS, AND FUTURE PATHS............................................................................................ 161 Summary................................................................................................ 161 What Next? Other Possible Areas of Investigation.................................... 168 BIBLIOGRAPHY............................................................................................... 171 APPENDIX....................................................................................................... 177 CURRICULUM VITAE........................................................................................ 184 Contact: Joe Argentino 66 Fairmount Avenue Hamilton, Ontario L8P 3Z5 905 522 9283 argentg@mcmaster.ca |