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

Date Listed: 08/26/2010


     Return to dissertations