Dissertation Index

Author: Thiebaut, Ines

Title: Symmetry and Interval Cycles in the Quartettos of Mario Davidovsky

Institution: CUNY Graduate Center

Begun: September 2010

Completed: September 2016


The music of Mario Davidovsky has seldom been analyzed past the timbral implications of his electroacoustic pieces and gestural aspects of his phrasing, and there has been virtually no attention paid to its pitch organization, despite the composer’s longstanding interest in writing for acoustic instruments. In this dissertation, I demonstrate how two main consistent resources for the organization of pitch govern the musical continuity and formal structure of his music, what I’ve called symmetry potentiality—actuality, and interval cycle potentiality-actuality processes. The interval cycle potentiality-actuality process refers to the various interval cycles that self-perpetuate, completing aggregates. This self-perpetuation means that incomplete cycles will consistently be understood as longing for the pitch that will fulfill the cycle’s potentiality for completion. The symmetrical potentiality-actuality process refers to asymmetrical collections that will consistently long for the pitch that will fulfill their symmetrical potentiality, also completing aggregates in the process.

Both of these processes will be explored thoroughly in the context of Davidovsky’s Quartettos No.1—No.4 in Chapter Two (symmetrical processes) and Chapter Three (interval cycle processes). Chapter Two will also include a study of particular asymmetrical collections with interesting degrees of near-symmetry. The degree of near-symmetry measures, so to speak, the effort required of an asymmetrical collection to become symmetrical by moving one of its voices parsimoniously within its own cardinality n (e.g., asymmetrical tetrachord becoming a symmetrical tetrachord), or that of becoming symmetrical within the cardinality n+1 by introducing a particular pitch (e.g., asymmetrical tetrachord becoming a symmetrical pentachord). The degree of near-symmetry, in essence, allows us to determine how strong is the collection’s potentiality for symmetry—a valuable property when studying Davidovsky’s music.

Keywords: Davidovsky, symmetry, cycles, voice-leading, process, continuity, interval, potentiality, actuality


1. Davidovsky’s Organicism And Musical Continuity
1.1 The Polyphony-Of-Space Metaphor: Davidovsky’s Organicism
1.2 A Brief Note on Davidovsky’s Quartettos
1.3 Davidovsky’s Potentiality–Actuality Processes
1.4 Davidovsky’s Aggregate
1.5 Representing the Polyphony-Of-Space Metaphor: Methodology
2. Symmetrical Potentiality–Actuality Processes in Quartettos No.2 and No.4
2.1 Quartetto No.4
2.2 Near-Symmetry: A Brief Study Of The Symmetrical Telos
2.3 Quartetto No.2
2.4 A Brief Conclusion
3. Interval Cycle Potentiality–Actuality Processes in Quartettos (No.1) and No.3
3.1 Quartetto (No.1)
3.2 Quartetto No.3


Inés Thiebaut
Visiting Assistant Professor, Music Theory
University of Utah
(801) 581-7369

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