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Tonality and Transformation, by Steven Rings. Oxford Studies in Music Theory
Tonality and Transformation, by Steven Rings. Oxford Studies in Music Theory. Richard Cohn, series editor. New York: Oxford University Press, 2011. xiv + 243 pp. ISBN 978-0-19-538427-7. $35 (Hardback).1 Reviewed by William O’Hara Harvard University teven Rings’ Tonality and Transformation is only one entry in a deluge of recent volumes1 in the Oxford Studies in Music Theory series,2 but its extension of the transformational ideas pioneered by S scholars like David Lewin, Brian Hyer, and Richard Cohn into the domain of tonal music sets it apart as a significant milestone in contemporary music theory. Through the “technologies” of transformational theory, Rings articulates his nuanced perspective on tonal hearing by mixing in generous helpings of Husserlian philosophy and mathematical graph theory, and situating the result in a broad historical context. The text is also sprinkled throughout with illuminating methodological comments, which weave a parallel narrative of analytical pluralism by bringing transformational ideas into contact with other modes of analysis (primarily Schenkerian theory) and arguing that they can complement rather than compete with one another. Rings manages to achieve all this in 222 concise pages that will prove both accessible to students and satisfying for experts, making the book simultaneously a substantial theoretical contribution, a valuable exposition of existing transformational ideas, and an exhilarating case study for creative, interdisciplinary music theorizing. [2] Tonality and Transformation is divided into two parts. The first three chapters constitute the theory proper—a reimagining of tonal music theory from the ground up, via the theoretical technologies mentioned above. The final 70 pages consist of four analytical essays, which begin to put Rings’ ideas into practice. -
A Theory of Spatial Acquisition in Twelve-Tone Serial Music
A Theory of Spatial Acquisition in Twelve-Tone Serial Music Ph.D. Dissertation submitted to the University of Cincinnati College-Conservatory of Music in partial fulfillment of the requirements for the degree of Ph.D. in Music Theory by Michael Kelly 1615 Elkton Pl. Cincinnati, OH 45224 [email protected] B.M. in Music Education, the University of Cincinnati College-Conservatory of Music B.M. in Composition, the University of Cincinnati College-Conservatory of Music M.M. in Music Theory, the University of Cincinnati College-Conservatory of Music Committee: Dr. Miguel Roig-Francoli, Dr. David Carson Berry, Dr. Steven Cahn Abstract This study introduces the concept of spatial acquisition and demonstrates its applicability to the analysis of twelve-tone music. This concept was inspired by Krzysztof Penderecki’s dis- tinctly spatial approach to twelve-tone composition in his Passion According to St. Luke. In the most basic terms, the theory of spatial acquisition is based on an understanding of the cycle of twelve pitch classes as contiguous units rather than discrete points. Utilizing this theory, one can track the gradual acquisition of pitch-class space by a twelve-tone row as each of its member pitch classes appears in succession, noting the patterns that the pitch classes exhibit in the pro- cess in terms of directionality, the creation and filling in of gaps, and the like. The first part of this study is an explanation of spatial acquisition theory, while the se- cond part comprises analyses covering portions of seven varied twelve-tone works. The result of these analyses is a deeper understanding of each twelve-tone row’s composition and how each row’s spatial characteristics are manifested on the musical surface. -
Conductus and Modal Rhythm
Conductus and Modal Rhythm BY ERNEST H. SANDERS T HAS BEEN MORE THAN EIGHTY YEARS since Friedrich Ludwig (1872-193o), arguably the greatest of the seminal figures in twenti- eth-century musicology, began to publish his studies of medieval music. His single-handed occupation of the field, his absolute sover- eignty over the entire repertoire and all issues of scholarly significance arising from it, and his enormous, inescapably determinative influ- ence on the thinking of his successors, most of whom had studied with him, explain the epithet der Grossehe was given on at least one occasion.' Almost his entire professional energies were devoted to the music of the twelfth and, particularly, the thirteenth centuries, as well as to the polyphony of the fourteenth century, which he began to explore in depth in the 1920s. His stringent devotion to the facts and to conclusions supported by them was a trait singled out by several commentators.2 Ludwig's insistence on scholarly rigor, however, cannot be said to account completely for his Modaltheorie,which appeared to posit the applicability of modal rhythm to all music of the Notre Dame period-except organal style-and of the pre-Garlandian (or pre- Franconian) thirteenth century, including particularly the musical settings of poetry. Much of the pre-Garlandian ligature notation in thirteenth-century sources of melismatic polyphonic compositions of the first half of that century (clausulae, organa for more than two voices) and of melismatic portions of certain genres, such as the caudae of conducti,3 signifies modal rhythms, and the appropriatenessof the modal system cannot be disputed in this context. -
Chromatic Sequences
CHAPTER 30 Melodic and Harmonic Symmetry Combine: Chromatic Sequences Distinctions Between Diatonic and Chromatic Sequences Sequences are paradoxical musical processes. At the surface level they provide rapid harmonic rhythm, yet at a deeper level they function to suspend tonal motion and prolong an underlying harmony. Tonal sequences move up and down the diatonic scale using scale degrees as stepping-stones. In this chapter, we will explore the consequences of transferring the sequential motions you learned in Chapter 17 from the asymmetry of the diatonic scale to the symmetrical tonal patterns of the nineteenth century. You will likely notice many similarities of behavior between these new chromatic sequences and the old diatonic ones, but there are differences as well. For instance, the stepping-stones for chromatic sequences are no longer the major and minor scales. Furthermore, the chord qualities of each individual harmony inside a chromatic sequence tend to exhibit more homogeneity. Whereas in the past you may have expected major, minor, and diminished chords to alternate inside a diatonic sequence, in the chromatic realm it is not uncommon for all the chords in a sequence to manifest the same quality. EXAMPLE 30.1 Comparison of Diatonic and Chromatic Forms of the D3 ("Pachelbel") Sequence A. 624 CHAPTER 30 MELODIC AND HARMONIC SYMMETRY COMBINE 625 B. Consider Example 30.1A, which contains the D3 ( -4/ +2)-or "descending 5-6"-sequence. The sequence is strongly goal directed (progressing to ii) and diatonic (its harmonies are diatonic to G major). Chord qualities and distances are not consistent, since they conform to the asymmetry of G major. -
Fourier Phase and Pitch-Class Sum
Fourier Phase and Pitch-Class Sum Dmitri Tymoczko1 and Jason Yust2(B) Author Proof 1 Princeton University, Princeton, NJ 08544, USA [email protected] 2 Boston University, Boston, MA 02215, USA [email protected] AQ1 Abstract. Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest. Keywords: Voice leading Fourier transform Tonal harmony Musical scales Chord geometry· · · · 1Introduction Early twenty-first century music theory explored a two-pronged generalization of traditional set theory. One prong situated sets and set-classes in continuous, non-Euclidean spaces whose paths represented voice leadings, or ways of mov- ing notes from one chord to another [4,13,16]. This endowed set theory with a contrapuntal aspect it had previously lacked, embedding its discrete entities in arobustlygeometricalcontext.AnotherpronginvolvedtheFouriertransform as applied to pitch-class distributions: this provided alternative coordinates for describing chords and set classes, coordinates that made manifest their harmonic content [1,3,8,10,19–21]. Harmonies could now be described in terms of their resemblance to various equal divisions of the octave, paradigmatic objects such as the augmented triad or diminished seventh chord. These coordinates also had a geometrical aspect, similar to yet distinct from voice-leading geometry. In this paper, we describe a new convergence between these two approaches. Specifically, we show that there exists a class of simple circular voice-leading spaces corresponding, in the case of n-note nearly even chords, to the nth Fourier “phase spaces.” An isomorphism of points exists for all chords regardless of struc- ture; when chords divide the octave evenly, we can extend the isomorphism to paths, which can then be interpreted as voice leadings. -
An Introductory Survey on the Development of Australian Art Song with a Catalog and Bibliography of Selected Works from the 19Th Through 21St Centuries
AN INTRODUCTORY SURVEY ON THE DEVELOPMENT OF AUSTRALIAN ART SONG WITH A CATALOG AND BIBLIOGRAPHY OF SELECTED WORKS FROM THE 19TH THROUGH 21ST CENTURIES BY JOHN C. HOWELL Submitted to the faculty of the Jacobs School of Music in partial fulfillment of the requirements for the degree, Doctor of Music Indiana University May, 2014 Accepted by the faculty of the Jacobs School of Music, Indiana University, in partial fulfillment of the requirements for the degree Doctor of Music. __________________________________________ Mary Ann Hart, Research Director and Chairperson ________________________________________ Gary Arvin ________________________________________ Costanza Cuccaro ________________________________________ Brent Gault ii ACKNOWLEDGMENTS I am indebted to so many wonderful individuals for their encouragement and direction throughout the course of this project. The support and generosity I have received along the way is truly overwhelming. It is with my sincerest gratitude that I extend my thanks to my friends and colleagues in Australia and America. The Australian-American Fulbright Commission in Canberra, ACT, Australia, gave me the means for which I could undertake research, and my appreciation goes to the staff, specifically Lyndell Wilson, Program Manager 2005-2013, and Mark Darby, Executive Director 2000-2009. The staff at the Sydney Conservatorium, University of Sydney, welcomed me enthusiastically, and I am extremely grateful to Neil McEwan, Director of Choral Ensembles, and David Miller, Senior Lecturer and Chair of Piano Accompaniment Unit, for your selfless time, valuable insight, and encouragement. It was a privilege to make music together, and you showed me how to be a true Aussie. The staff at the Australian Music Centre, specifically Judith Foster and John Davis, graciously let me set up camp in their library, and I am extremely thankful for their kindness and assistance throughout the years. -
Generalized Tonnetze and Zeitnetz, and the Topology of Music Concepts
June 25, 2019 Journal of Mathematics and Music tonnetzTopologyRev Submitted exclusively to the Journal of Mathematics and Music Last compiled on June 25, 2019 Generalized Tonnetze and Zeitnetz, and the Topology of Music Concepts Jason Yust∗ School of Music, Boston University () The music-theoretic idea of a Tonnetz can be generalized at different levels: as a network of chords relating by maximal intersection, a simplicial complex in which vertices represent notes and simplices represent chords, and as a triangulation of a manifold or other geomet- rical space. The geometrical construct is of particular interest, in that allows us to represent inherently topological aspects to important musical concepts. Two kinds of music-theoretical geometry have been proposed that can house Tonnetze: geometrical duals of voice-leading spaces, and Fourier phase spaces. Fourier phase spaces are particularly appropriate for Ton- netze in that their objects are pitch-class distributions (real-valued weightings of the twelve pitch classes) and proximity in these space relates to shared pitch-class content. They admit of a particularly general method of constructing a geometrical Tonnetz that allows for interval and chord duplications in a toroidal geometry. The present article examines how these du- plications can relate to important musical concepts such as key or pitch-height, and details a method of removing such redundancies and the resulting changes to the homology the space. The method also transfers to the rhythmic domain, defining Zeitnetze for cyclic rhythms. A number of possible Tonnetze are illustrated: on triads, seventh chords, ninth-chords, scalar tetrachords, scales, etc., as well as Zeitnetze on a common types of cyclic rhythms or time- lines. -
The Aquitanian Sacred Repertoire in Its Cultural Context
THE AQUITANIAN SACRED REPERTOIRE IN ITS CULTURAL CONTEXT: AN EXAMINATION OF PETRI CLA VIGER! KARl, IN HOC ANNI CIRCULO, AND CANTUMIRO SUMMA LAUDE by ANDREA ROSE RECEK A THESIS Presented to the School ofMusic and Dance and the Graduate School ofthe University of Oregon in partial fulfillment ofthe requirements for the degree of Master of Arts September 2008 11 "The Aquitanian Sacred Repertoire in Its Cultural Context: An Examination ofPetri clavigeri kari, In hoc anni circulo, and Cantu miro summa laude," a thesis prepared by Andrea Rose Recek in partial fulfillment ofthe requirements for the Master ofArts degree in the School ofMusic and Dance. This thesis has been approved and accepted by: Dr. Lori Kruckenberg, Chair ofth xamining Committee Committee in Charge: Dr. Lori Kruckenberg, Chair Dr. Marc Vanscheeuwijck Dr. Marian Smith Accepted by: Dean ofthe Graduate School 111 © 2008 Andrea Rose Recek IV An Abstract ofthe Thesis of Andrea Rose Recek for the degree of Master ofArts in the School ofMusic and Dance to be taken September 2008 Title: THE AQUITANIAN SACRED REPERTOIRE IN ITS CULTURAL CONTEXT: AN EXAMINATION OF PETRI CLA VIGER! KARl, INHOC ANNI CIRCULO, AND CANTU MIRa SUMMA LAUDE Approved: ~~ _ Lori Kruckenberg Medieval Aquitaine was a vibrant region in terms of its politics, religion, and culture, and these interrelated aspects oflife created a fertile environment for musical production. A rich manuscript tradition has facilitated numerous studies ofAquitanian sacred music, but to date most previous research has focused on one particular facet of the repertoire, often in isolation from its cultural context. This study seeks to view Aquitanian musical culture through several intersecting sacred and secular concerns and to relate the various musical traditions to the region's broader societal forces. -
Composing Each Time Robert Morris
Composing Each Time Robert Morris Introduction Each time I finish a piece, there is little time to rest or reflect; something else demands my attention, and I attend to it. Of course, finishing a piece is not really abrupt; after the first draft, there is revision, computer engraving, and editing. During these tasks, new ideas and conceptions begin to enter consciousness so the experience of writing a particular piece fades even before all the work is done. Later, when I return to a work—to coach a performance or lecture on it—I try to reconstruct the process of composition and return to the way it felt to write it, but much of the passion and clarity that brought the work into being is lost. With some thought of addressing this problem I decided immediately after completing my piano piece Each Time to write about it while the experience of its composition was still fresh in my memory. In this way, I hope to express as vividly as possible what I try to put into a piece and how and why—something which might be useful to future performers or listeners. In some respects, Each Time is not very different from my other piano pieces; however, I wanted to express in music some new insights I had into the phenomenology of time derived from Buddhist philosophy. Rather than spelling this out now, I’ll just say that I composed the piece so it might suggest to an attentive listener that impermanence is at the root of experience and that time is both flowing and discontinuous at once. -
2-Voice Chorale Species Counterpoint Christopher Bailey
2-Voice Chorale Species Counterpoint Christopher Bailey Preamble In order to make the leap from composing in a 4-part chorale style to composing in a free- texture style, we will first re-think the process of composing chorales in a more contrapuntal manner. To this end, we will compose exercises in 2-voice (soprano and bass) Chorale Species Counterpoint. Species counterpoint is a way of studying counterpoint formulated by J.J. Fux (1660-1741) after the music of Palestrina and the Renaissance masters. Exercises in species were undertaken by many of the great composers--including Mozart, Beethoven, Brahms, Schubert, and so forth. The basic idea is that one starts with simple, consonant, note-against-note counterpoint, and gradually attempts more and more elaborate exercises, involving more rhythmic complexity and dissonance, in constrained compositional situations. We will be learning a modified (simpler and freer) version of this, to fit in with the study of 4-part voice-leading and chorales, and tonal music in general. For each exercise, we will assume, at first, that one is given either a bass line, or a soprano line. Given either line, our first task is to compose the other line as a smooth counterpoint against the given line. With the possible exception of the cadence, we will not think about harmony and harmonic progression at all during this part of the process. We will think about line, and the intervals formed by the 2 voices. After the lines are composed in this way, only then do we go back and consider questions of harmony, and add the 2 inner voices to create a 4-voice chorale texture. -
Prolongation, Expanding Variation, and Pitch Hierarchy: a Study of Fred Lerdahl’S Waves and Coffin Hollow
PROLONGATION, EXPANDING VARIATION, AND PITCH HIERARCHY: A STUDY OF FRED LERDAHL’S WAVES AND COFFIN HOLLOW J. Corey Knoll A Thesis Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of MASTER OF MUSIC December 2006 Committee: Nora Engebretsen, Advisor Mikel Kuehn, Advisor William Lake Marilyn Shrude ii ABSTRACT Mikel Kuehn, Co-Advisor Nora Engebretsen, Co-Advisor This thesis consists of two independent yet interrelated portions. The theory portion explores connections between Fred Lerdahl’s theoretical and compositional output by examining his work Waves in relation to his theoretical writings, primarily A Generative Theory of Tonal Music and “Tonal Pitch Space.” The theories together form a generative theory of tonal music that strives to create a musical grammar. “Tonal Pitch Space” defines a hierarchy among pitches and chords within and across tonal regions. Lerdahl uses these ideas in Waves, which is in the key of D minor. All other pitch classes, and likewise all other chords and tonal regions, are elaborations of the tonic D. The initial D tonic statement, called a flag motive because it heralds each variation, is the fundamental construct in Waves. Just as all other pitches elaborate D, all other motives in Waves are elaborations of the flag motive. Thus rich hierarchies are established. Lerdahl also incorporates ideas from GTTM into his compositional process. GTTM focuses on four categories of event hierarchies: grouping and metrical structures and time-span and prolongational reductions. These four hierarchies and a set of stability conditions all interact with one another to form a comprehensive musical grammar. -
Robert Walser Published Titles My Music by Susan D
Running With the Devil : Power, Gender, title: and Madness in Heavy Metal Music Music/culture author: Walser, Robert. publisher: Wesleyan University Press isbn10 | asin: 0819562602 print isbn13: 9780819562609 ebook isbn13: 9780585372914 language: English Heavy metal (Music)--History and subject criticism. publication date: 1993 lcc: ML3534.W29 1993eb ddc: 781.66 Heavy metal (Music)--History and subject: criticism. Page i Running with the Devil Page ii MUSIC / CULTURE A series from Wesleyan University Press Edited by George Lipsitz, Susan McClary, and Robert Walser Published titles My Music by Susan D. Crafts, Daniel Cavicchi, Charles Keil, and the Music in Daily Life Project Running with the Devil: Power, Gender, and Madness in Heavy Metal Music by Robert Walser Subcultural Sounds: Micromusics of the West by Mark Slobin Page iii Running with the Devil Power, Gender, and Madness in Heavy Metal Music Robert Walser Page iv WESLEYAN UNIVERSITY PRESS Published by University Press of New England, Hanover, NH 03755 © 1993 by Robert Walser All rights reserved Printed in the United States of America 5 4 3 2 1 CIP data appear at the end of the book Acknowledgments for song lyrics quoted: "Electric Eye": Words and music by Glenn Tipton, Rob Halford, and K. K. Downing, © 1982 EMI APRIL MUSIC, INC. / CREWGLEN LTD. / EBONYTREE LTD. / GEARGATE LTD. All rights controlled and administered by EMI APRIL MUSIC, INC. International copyright secured. All rights reserved. Used by permission. "Suicide Solution": Words and music by John Osbourne, Robert Daisley, and Randy Rhoads, TRO© Copyright 1981 Essex Music International, Inc. and Kord Music Publishers, New York, N.Y.