Dissertation Index

Author: Bisciglia, Sebastiano

Title: On Row-Class Equivalence Classes

Institution: Eastman School of Music, University of Rochester

Begun: July 2010

Completed: April 2013


This dissertation adds a statistical layer to twelve-tone analysis, and in so doing, broadens the purview from the row class of an individual composition to a larger context of collections of row classes that share features relevant to a composition at hand. Twelve-tone analysis traditionally details the members of a row class that appear within a composition and suggests ways to interpret coherence in the combination and succession of row forms. The present study builds upon this approach by evaluating row-form selection in a context that classifies row properties within all row classes. The dissertation creates this context by asking: how many twelve-tone row classes possess the features emphasized in an analysis? Answering the question identifies norms within the collection of twelve-tone row classes; degrees of normativity are expressed via the normalcy / distinctiveness rating, a useful measure for the types of compositional relationships found in row-based works. The dissertation argues that these norms offer one avenue for contextualizing twelve-tone analyses and thereby provide additional opportunities for interpretation.

Chapter 1 reviews the relevant scholarship on twelve-tone theory and analysis. It focuses, first, on the origins and development of “classical” twelve-tone analysis and, second, the tradition of enumerating twelve-tone rows with certain features. Chapter 2 presents a methodology for enumerating the twelve-tone row classes that possess particular features, creates equivalence classes within the collection of twelve-tone row classes, and formalizes the normalcy / distinctiveness rating. Chapters 3 and 4 explore the interpretive potential of enumerations for twelve-tone analysis. Chapter 3 illustrates the theory with analytical vignettes of Arnold Schoenberg’s Violin Concerto op. 36/I and Variations for Orchestra, op. 31, and Anton Webern’s Concerto for Nine Instruments, op. 24/I. Chapter 4 focuses exclusively on Webern’s Variations for Orchestra, op. 30. In each discussion, both the potential and composed-out features of the row-class are evaluated within the context of the piece and with reference to larger statistical norms

Keywords: Schoenberg, Webern, statistics on row properties, twelve-tone analysis


Chapter 1: Compositional Possibilities and Row Structure in Twelve-Tone Theory and Analysis
Chapter 2: Property-Based Row-Class Equivalence Relations and Equivalence Classes

Chapter 3: Three Analytical Vignettes
Chapter 4: Compositional Progression and Row-Class Equivalence Classes in Webern’s Variations for Orchestra, Op. 30
Appendix 1
Appendix 2


sebastian [dot] bisciglia [at] gmail [dot] com

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