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Volume 5, Number 4 September 1999
Copyright � 1999 Society for Music Theory
Brown, Stephen C. "Dual Interval Space in Twentieth-Century Music." Yale University, 1999.
AUTHOR: Brown, Stephen C.
TITLE: "Dual Interval Space in Twentieth-Century Music"
INSTITUTION: Yale University
BEGUN: September 1994
COMPLETED: May 1999
ABSTRACT:
This study proposes a model of pitch-class space called "dual interval
space." A dual interval space (or "DIS") is a two-dimensional
array of pitch classes, in which each dimension corresponds to a unique
(non-zero) interval class. Given some pitch-class collection, the members of
that collection can be visualized as residing in various locations of a DIS.
These locations can then be translated within the space or flipped about some
axis. The flipping operations in particular offer new ways to relate
set-classes, even set-classes of different cardinalities. Aside from its
theoretical interest, the concept of dual interval space is suggestive for the
analysis of certain twentieth-century pieces. Moreover, it can apply to music
displaying a wide range of styles and techniques, including pitch-centric,
freely atonal, and serial music.
Chapter 1 introduces the concept and develops the idea of operations in a DIS, exploring their effects on pitch-classes and pitch-class sets. It closes by relating some ideas from graph theory to the concept of dual interval space. Chapter 2 discusses precedents for dual interval space and traces connections with more recent developments in music theory. Chapter 3 shows how the concept can provide the basis for the detailed study of a single body of music, specifically, that of late Shostakovich. Finally, Chapter 4 demonstrates the broader applicability of the concept, using it to analyze pieces by Ruggles, Schoenberg, and Webern.
KEYWORDS: atonal theory, post-tonal theory, graph theory, transpositional combination, Klumpenhouwer networks, Shostakovich, Ruggles, Schoenberg, Webern
TOC:
Chapter 1 Theory and Methodology
Chapter 2 Other Music Theories: Precedents and Intersections
Chapter 3 Ic1/Ic5 Space in the Music of Shostakovich
Chapter 4 Dual Interval Space in Other Music
CONTACT:
Stephen C. Brown
15 North Cedar Street
Oberlin, OH 44074
440-775-0249 (home)
440-775-8239 (office)
<stephen.brown@oberlin.edu>
Cox, Arnie W. "The Metaphoric Logic of Musical Motion and Space." University of Oregon, 1999.
AUTHOR: Cox, Arnie W.
TITLE: "The Metaphoric Logic of Musical Motion and Space."
INSTITUTION: University of Oregon
BEGUN: June, 1995
COMPLETED: June, 1999
ABSTRACT:
Music discourse relies on concepts of musical motion and space despite the fact
that tones do not actually move in the ways that we describe. This study employs
Lakoff and Johnson's theory of metaphor to analyze the logic behind these basic
concepts, and it grounds the musical meanings afforded by these concepts in
phenomenology, embodied cognition, and the logic of metaphoric thought. Concepts
of motion and space are shown to emerge in the imagination of embodied listeners
as we map experience in the domain of actual motion onto the domain of musical
experience.
Chapter 1 offers an account of verticality in terms of a blend of ten sources, seven of which depend on the conceptual metaphor "More Is Higher." Chapter 2 presents the 'mimetic hypothesis', which argues that we understand music in terms of our own experience of making vocal sounds and via tacit imitation of the sounds and gestures of performers. Chapter 3 examines the role of metaphor in Kaluli and Ancient Greek music theories and finds verticality integral there as well. The analysis of Greek theories also reveals the pervasiveness of the metaphor "More Is Higher" and demonstrates, among other things, that verticality in the West predates its representation in staff notation. Chapter 4 extends Lakoff and Johnson's analysis of our temporal metaphors and shows musical motion and space to be special cases of temporal motion and space. The identical dynamics of anticipation, presence, and memory in the domains of music and actual motion motivate us to map spatial relations onto the relations of tones.
By setting out the details of the cross-domain mappings we can account for both the logic and the paradox of musical motion and space. By grounding musical meaning in embodied cognition, this study also establishes the basis of an affective theory of meaning.
KEYWORDS:
Metaphor, verticality, motion, time, space, Greek theory, perception, cognition,
philosophy
TOC:
Chapter 1: 'High' and 'Low'
Chapter 2: The Mimetic Hypothesis and Embodied Music Cognition
Chapter 3: Conceptions of Pitch in Kaluli and Ancient Greek Music
Chapter 4: Temporal Motion and Musical Motion
CONTACT:
Arnie Cox
Visiting Assistant Professor
Oberlin College Conservatory of Music
77 W. College St.
Oberlin, OH 44074
Office 440-775-8945
Home 440-775-3174
Fax 440-775-6972
<Arnie.Cox@oberlin.edu>
Derkert, Jacob. "Tonalitet och harmonisk artikulation i Claude Debussys verk. Om reception, harmonikteori och analys." University of Stockholm, 1998.
AUTHOR: Derkert, Jacob
TITLE: "Tonalitet och harmonisk artikulation i Claude Debussys verk.
Om reception, armonikteori och analys."
INSTITUTION: University of Stockholm
COMPLETED: October, 1998
ABSTRACT:
This dissertation is a study of ways to analyze some harmonic features of the
music of Claude Debussy. It begins with a critical survey of the discussion of
tonality and dissolution of tonality in Debussy's works, as it manifested itself
in contemporary French criticism and in the German-speaking countries after
World War I. It tries to clarify the notion of "tonality" involved in
this discussion. It comes to a critical conclusion concerning the
characterization of Debussy's music as embodying dissolution of tonality, which
is found to be either rather trivial or speculative, i.e. unproven and difficult
to test. A conceptual clarification is suggested, which gives a slightly
different, at once more general and more precise, meaning to the trivial version
of the discussed characterization.
Next we turn to a discussion of the use of different scale-forms found in Debussy's music. We show that, in spite of the absence of tonality at the chord level, and in spite of the presence of a wide variety of different scale-forms, a scale-based conception of keys can be used to analyze at least some works of Debussy as embodying an articulation of keys. We then turn to ways to analyze the scale-form variation in itself. Lastly, we note that key-articulation in Debussy's music is due to two factors: transposition and scale-form variation. We present a simple method to single out the contributions of these two factors.
TOC:
Kapitel I Det problem som avhandlas
Kapitel II Om musikteori och musikanalys
Kapitel III Debussy som impressionist
Ursprunget till en g�ngse karakt�ristik: Hur Debussys behandling av harmonik
och tonalitet diskuterades i den samtida kritiken
Kapitel IV Studiet av tonalitetsuppl�sning i Debussys musik med utg�ngspunkt i
traditionell musikteori
Del 1: Om tonalitetsbegreppet
Kapitel V Studiet av tonalitetsuppl�sning i Debussys musik med utg�ngspunkt i
traditionell musikteori
Del 2: Om debussyreceptionen [sic! A small letter at the beginning of the last
word!]
Kapitel VI Andra ansatser i analysen av Debussys harmonik
Kapitel VII Ett formalt tonalitetsbegrepp
Kapitel VIII Tonalitet i Debussys musik?
Kapitel IX Tonartsartikulation i Debussys musik?
Kapitel X Analys baserad p� tonf�rr�ds intervallinneh�ll och dess
till�mpbarhet p� Debussys musik
Kapitel XI Tonartsartikulationens tv� orsaker: Formvariation och transposition
Kapitel XII Slutsatser
Summary in English
CONTACT:
Jacob Derkert
Musikvetenskapliga institutionen
Stockholms universitet
Valhallavagen 103-109
S-115 31 Stockholm
Sweden
fax: +46 8 163 281
<jacob.derkert@telia.com>
Steffen, Ralph Martin. "Metalogik: The Music Theory of Walter Harburger." University of California, Santa Barbara, 1999.
AUTHOR: Steffen, Ralph Martin
TITLE: "Metalogik: The Music Theory of Walter Harburger"
INSTITUTION: University of California, Santa Barbara
BEGUN: September, 1996
COMPLETED: June, 1999
ABSTRACT:
This dissertation investigates the music theory, called the "metalogic,"
of the German writer and composer Walter Harburger (1888-1967). The metalogic
offers an alternative interpretation of rhythm and harmony in tonal music.
Rooted in the familiar German theoretical tradition of Moritz Hauptmann and Hugo
Riemann, it differs by embracing the rebellious spirit of the post-World War I
era. The new approach to logic proposed by Edmund Husserl and his school of
phenomenology is apparent in Harburger's writing, as well as the influence of
new trends in mathematics and physics. Based on his idea of a logic unigue to
music, Harburger reconceptualizes the primal elements of rhythm, melody, and
harmony in familiar common-practice musical constructions. His unique
mathematics, the "metalogic calculus," allows him to attain this goal.
In Harburger's theory, all musical structures, from the lowest level such as beats and scale degrees, to complex structures such as motives and harmonies, relate to one another through hierarchical levels of unity. In order to perceive structures on different levels, such as a single beat vs. a grouping of beats into duple or triple meters, the mind must "cross over" from one level of consciousness to another. In his metalogic equations, which resemble algebraic equations, Harburger aims to express the transformations that occur between adjacent levels of consciousness.
Die Metalogik, published in 1919, is the source for Harburer's theory. The dissertation features original translations from this book, as well as from other published and unpublished primary sources, the latter studied at the Bayerische Staatsbibliothek in Munich, Germany.
Chapters 1 and 2 survey Harburger's life in Munich and the nineteenth- and twentieth-century philosophical and scientific developments that influenced his thought. Chapters 3 and 4 investigate the metalogic in detail and Harburger's application of mathematics to music. Chapters 5 and 6 present his theories of rhythm and harmony. A concluding chapter shows how Harburger's mathematical approach foreshadows recent work in tonal music theory, especially the neo-Riemannian theories of David Lewin and Richard Cohn.
KEYWORDS:
phenomenology, mathematics, musical logic, tonal theory, rhythm, perception,
Hauptmann, Riemann
TOC:
Chapter 1: Harburger's Life, Work, and Critical Recognition
Chapter 2: Harburger's Philosophy and Influences
Chapter 3: _Metalogik_
Chapter 4: Harburger's Mathematical Conception of Music
Chapter 5: The Rhythmic Theory
Chapter 6: The Harmonic Theory
Chapter 7: Conclusion
Bibliography
CONTACT:
Ralph Martin Steffen
P.O. Box 14103
Santa Barbara, CA 93107
805-683-5664
<stfn@umail.ucsb.edu>
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14 November 2002