Author: Kurth, Richard B.
Title: Mosaic Isomorphism and Mosaic Polyphony: Balance and Imbalance in Schoenberg's Twelve-tone Rhetoric
Institution: Harvard University
Begun: May 1990
Completed: April 1993
Formal features of phrases in Schoenberg's twelve-tone music are studied using techniques elaborated from work on mosaics by Martino, Mead, and Morris and Alegant. First the concept of "mosaic isomorphism" is developed to provide a contextually sensitive determination of the constituent building blocks which make up serial phrases involving several row-forms. Then the allied notion of "mosaic polyphony" is used to explore the specific rhythmic settings of the mosaic-subsets, as well as their formal and rhetorical properties, in a detailed hearing of the music's foreground.
The method reveals specific features of construction and "developing variation" in the music. The mosaic polyphony projects symmetry or formal balance among certain mosaic-subsets, and detects deviations from such balances among others. Symmetries arising in various dimensions--register, rhythm, meter, timbre, and so forth--are set in conflict, balanced one against another. The mosaic polyphony displays how these interacting balances shape phrases, and give the music its dynamic fluidity.
Extensive analyses focus on the Suite for Piano Op.25, Moses und Aron, the Fourth Quartet Op.37, and the String Trio Op.45. Mosaic isomorphisms and mosaic polyphony are used analytically in a number of ways: some analyses examine features of individual phrases; others explore formal connections between several phrases. The chosen works, representing various media, also scan chronological developments in Schoenberg's twelve-tone compositional rhetoric.
Some abstract theoretical properties of mosaic isomorphisms are examined, and tools are developed for comparing different mosaic isomorphisms. The principal arguments are set in the context of Schoenberg's own writings and analyses. A pair of appendices studies certain properties of invariant pitch class partitions.
Keywords: Schoenberg, analysis, phrase formation, rhythm, developing variation, symmetry, formal balance, mosaics, partitions, order numbers, invariance
Chapter 1. First Considerations: Phrase Formation and Balance
in Schoenberg's Twelve-Tone Rhetoric.
Chapter 2. Three Analyses from the Prelude to the Suite for Piano Op.25.
Chapter 3. Formalizing Mosaic Isomorphisms (1): Partitions, Rows, and
Chapter 4. Formalizing Mosaic Isomorphisms (2): Comparing Mosaic
Chapter 5. Local and Distant Formal Connections in the First Movement of
the Fourth Quartet Op.37.
Chapter 6. Mosaic Isomorphisms, Music, Drama, and Rhetoric in Three
Passages from Moses und Aron.
Chapter 7. Projecting Formal Balance in the String Trio Op.45: Mosaic
Isomorphisms on Combinatorial Hexachords.
Chapter 8. Mosaic Polyphonies in Counterpoint: Implicit Mosaic
Isomorphisms and Musical Continuity.
Figures for Chapters 1 through 8.
Appendix A: Invariant Pitch Class Partitions: General Requirements.
Appendix B: Invariant Dyadic Partitions listed by Equivalence Class.
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