Music Theory Online

A Journal of Criticism, Commentary, Research, and Scholarship


Volume 7, Number 1, January 2001
Copyright � 2001 Society for Music Theory

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New Dissertations


Gollin, Edward H. "Representations of Space and Conceptions of Distance in Transformational Music Theories." Harvard University, 2000.

AUTHOR: Gollin, Edward H.
TITLE: Representations of Space and Conceptions of Distance in Transformational Music Theories
INSTITUTION: Harvard University
BEGUN: September, 1997
COMPLETED: June, 2000

ABSTRACT: The dissertation examines metaphors of space and distance in transformational music theories, formalizing the notion of a music-transformational space. A music-transformational space is a particular arrangement of musical elements whose structure is determined by a family of normative relations or transformations acting on those elements. Such spaces may take the form of maps or networks of musical elements or they may be expressed through the symbolic language used to represent transformations: normative relations are expressed by unitary symbols whereas more complex relations�those relating distant elements in a space�are expressed as combinations of the space�s normative relations. A music- transformational space, for example, underlies the familiar symbology of twelve-tone operations, in which unitary operations such as R and I are considered normative while the relation RI is understood to be composite or derivative. The dissertation explores how music-transformationl spaces and the transformational pathways therein reflect the distinct ways of experiencing a given transformation in particular musical contexts. The dissertation also uses music-transformational spaces as tools for historical interpretation, examining how explicit graphic and symbolic accounts of musical relationships in compositional and theoretical treatises of the eighteenth through twentieth centuries reflect the often implicit theoretical priorities of their creators. Particularly central are the writings of Hugo Riemann for whom the notion of space was fundamental to ideas of harmonic relatedness and progression. The work concludes by illustrating applications of spatial models in the analysis of musical works in both harmonic and non-harmonic structural domains.

KEYWORDS: Riemann, neo-Riemannian, transformation, group theory, graph theory, combinatorial, Heinichen, Schubert, Prokofiev


0. Introduction
1. Some Examples of Spaces and Problems of Distance
1.1. Some Serial Spaces
1.2. Intervals and Tone Spaces
1.3. Some Hexatonic Spaces
2. The Mathematics of Spaces and Pathways
2.1. Words, Group Presentations and Graphs
2.2. Pathways, Equivalence and Transformation Classes
2.3. Conceptions of Distance: Representative Words and Characteristic Path Length
3. Some Eighteenth Century Spaces
3.1. The Mediant Circle: Werckmeister�s Paradoxal Discourse
3.2. Heinichen�s Musicalische Circul
3.3. David Kellner�s Musicalische Circul
3.4. Vial�s Arbre Genealogique de l�Harmonie
4. Tone Spaces and Pathways in the Nineteenth Century: The Theories of Hugo Riemann Part I
4.1. The Development of the Table of Relations: Oettingen and the Acoustical Perspective
4.2. Riemann�s Changing Perspective: Toward the Table as Map
4.3. Tonbestimmung and the Combinatorial Conception of Interval
4.4. A Historical Curiosity: Euler�s Speculum Musicum
4.5. Ottokar Hostinsky�s Tonschema
5. Triadic and Key Space in the Nineteenth Century: the Theories of Hugo Riemann Part II
5.1. Riemann�s System of Harmonieschritte
5.2. Space, Enharmonicism and Aesthetics in Riemann�s Harmonic Theories
6. Music-Transformational Spaces in Neo-Riemannian Theories
6.1. Parsimonious Generators, Cohn Functions and Tonnetz Duals
6.2. The Harmonic Spaces of Brian Hyer and David Kopp
7. Some Analytical Applications of Music-Transformational Spaces
7.1. Text and Space in Three Schubert Lieder
7.2. Automorphisms and Some Non-Traditional Harmonic Spaces
7.3. Distance, Pathway and Analysis in Some Permutation Spaces
Appendix A. Basic Definitions and Concepts: Functions, Operations, Transformations and Groups

Department of Music
Harvard University
Cambridge, MA 02138

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Gosman, Alan R. "Compositional Approaches to Canons from Ockeghem to Brahms." Harvard University, 2000.

AUTHOR: Gosman, Alan R.
TITLE: Compositional Approaches to Canons from Ockeghem to Brahms
INSTITUTION: Harvard University
BEGUN: April, 1997
COMPLETED: August, 2000

ABSTRACT: This dissertation examines methods of large-scale organization within a span of European canonic writing extending from Ockeghem through Brahms. The organizational methods discussed serve a wide variety of ends, from assuring that consonances and chords sound between parts, to providing musical demonstrations of contrapuntal and harmonic theoretical systems. The first part of the dissertation focuses on patterns involving intervals between notes in the dux; the second part focuses on intervallic patterns involving both dux and comes voices.

Chapter One examines four Renaissance canons. The analyses show that there are strong patterns involving intervals between dux notes separated by the time interval of the canon. These dux patterns free the composer to focus on large-scale melodic considerations, rather than constantly verifying that a melodic choice is harmonically viable. Chapter Two considers how the canonic notes separated by the time interval of the canon can be organized in support of contrasting music-theoretical explanations. Two canons by Zarlino, found as the culminating compositional examples in Part III of the Istitutioni harmoniche, are compared with two canons by Rameau, found as the culminating examples in Book III of the Trait� de l�harmonie. The differences between the pieces are considered in the context of the ways each composer organizes his treatise as a whole and his ideas about harmony in particular.

Chapter Three shows a number of Baroque and Classical canons that depend on very similar patterns of intervals between dux notes. These dux patterns limit the harmonic progressions from which a composer may choose. Chapter Four considers canons whose dux notes are best understood as being organized by harmonic, rather than intervallic patterns. Burmeister�s account of how to compose this type of piece by what he calls a harmoniola is discussed. This chapter also extends the harmoniola�s function from that of a compositional tool to that of an analytical tool.

Part Two of the dissertation finds multiple examples of what I call "canonic threads"�patterns made of alternating dux and comes TIC notes at the time interval of the canon. The concept of canonic threads is developed using as focus pieces Bach�s Goldberg Variations, and Brahms�s Variations on a theme by Schumann, Op. 9. Threads are shown to be a powerful method of integrating a theme�s harmonic and phrase-structural constraints into a variation with strict canonic form.

KEYWORDS: canon, counterpoint, Ockeghem, Zarlino, Rameau, Bach, Brahms

Part I - Dux Patterns
1. Stacked Canons
2. Rameau and Zarlino: Polemics in the Trait� de l�harmonie
3. Dux Patterns and Harmonic Progressions
4. The Harmoniola

Part II - Canonic Threads
5. Canonic Threads: Formal Features
6. Repeated-Note Threads
7. Stepwise Threads
8. Threads at Intervals Larger than a Second
9. Arpeggiated Threads

Alan Gosman
Music Dept.
Harvard University
Cambridge, MA 02138
(617) 495-2791

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Kosovsky, Robert. "Bernard Herrmann's Radio Music for the Columbia Workshop." Graduate Center, the City University of New York, 2000.

AUTHOR: Kosovsky, Robert
TITLE: Bernard Herrmann's Radio Music for the Columbia Workshop
INSTITUTION: Graduate Center, the City University of New York
COMPLETED: September 2000

ABSTRACT: The radio music of Bernard Herrmann (1911-1975) is an area of his output that has escaped serious scrutiny and study. This dissertation examines the composer's development as discerned through his compositions intended to accompany radio dramas, bringing attention not only to his craft but also to the very neglected field of radio music. The Columbia Workshop (beginning in 1936) was the first regular series for which he consistently composed new music. As its music director, Herrmann was able to formulate, develop, and refine his compositional responses to narrative situations. His music for the Columbia Workshop therefore forms a logical unit for study.

A brief survey of the state of music on radio reveals that composers made adjustments in orchestration and musical style due to the needs of broadcasting. These alterations lead to the creation of an idiomatic use of music on the radio. The origins and significance of the Columbia Workshop are discussed, focusing on the experimental and adventurous nature of the program. Begun by producer/director Irving Reis (who had begun work as an engineer), the Workshop sought to explore and find innovative ways of using the radio and putting these innovations to work for dramatic narrative.

Herrmann's familiarity with theatre and his compositions for ballet sequences in Broadway plays prepared him for composing music for the radio. His first works for the medium, a genre he called "Melodrams," consisted of poetry recitations to musical scores. This provided a foundation for his introduction to the Columbia Workshop, which began with dramatizations of poetry. His initial efforts for the Workshop revealed certain issues that would remain significant throughout his career on radio as well as in his later work for film and television. These issues involved borrowing and reuse of previously composed music, the influence of narrative sound effects on music, the problem of underscoring dialogue, the creation of a musical continuum parallel to the dramatic narrative, and the creation of structural organization. Various excerpts of incidental music from plays composed during the period 1937-39 are discussed, concluding with an examination of Herrmann's collaborations with author Norman Corwin, in particular the latter's play Untitled.

The history of Herrmann's development as a composer is but one part of a larger history of radio music that has yet to be written. This dissertation may serve as the foundation for such a history.

KEYWORDS: radio music, radio drama, American music

Chapter 1 : Introduction
Chapter 2: Biographical Background on Bernard Herrmann
Chapter 3: The Columbia Workshop
Chapter 4: Music on the Radio in the 1930s
Chapter 5 : The Melodrams
Chapter 6 : Early Dramas
Chapter 7 : Columbia Workshop Plays 1937-39
Chapter 8 : The Corwin-Herrmann Collaboration
Chapter 9 : Conclusion

Robert Kosovsky
121 Bennett Ave., Apt. 25-A
New York, NY 10033
(212) 795-3843

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prepared by
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Updated 14 November, 2002