In This Article American Music Theory, 1955-2010

  • Introduction
  • Schenkerian Theory and Analysis
  • Twelve-Tone Theory
  • Transformational Theory
  • Performance
  • Phenomenological Approaches
  • Approaches from Literary Theories
  • Popular Music
  • Non-Western Approaches
  • Multimedia Studies
  • Timbre
  • Cognition

Music American Music Theory, 1955-2010
by
David Forrest, Severine Neff, John Reef
  • LAST MODIFIED: 29 June 2011
  • DOI: 10.1093/obo/9780199757824-0073

Introduction

Since ancient Greece, the discipline of music theory has offered explanations for the nature of musical phenomena and the fundamental principles governing their use. As early as the Middle Ages, musicians utilized such explanations to analyze specific musical compositions. However, analysis as a subdiscipline of theory burgeoned only centuries later in 19th-century Europe. At that time, conservatory musicians, most often composers, taught theory as compositional craft—counterpoint, harmony, and form. In the mid-1950s, American composer-theorists began reformulating the conceptual basis of the 19th-century European tradition by proposing new explanatory models of musical structure influenced by the developments in contemporary science, philosophy, and linguistics. Their investigations resulted in their advocacy of a music-theoretical discipline centered at universities and composed of professional theorists or composer-theorists who had mastered an essential tripartite core of knowledge: Schenkerian theory and analysis, history of theory, and the pioneering subfields addressing post-tonal music, twelve-tone theory, and set theory. From the 1980s to the present, new paradigms and approaches including the topics of challenges from the New Musicology and music criticism, musical meaning (encompassing approaches from nonanalytic philosophy and semiotic approaches), phenomenological approaches, approaches from literary theory, popular music studies, non-Western approaches, multimedia studies, timbre, cognition, and social issues such as gender, queer, and disability studies, have further expanded the nature and scope of the discipline. Together these rich and varied fields of music-theoretical inquiry offer a scholarly literature unprecedented in Western musical thought.

General Overviews

In his essay “Behind the Beyond: A Response to Edward Cone,” David Lewin, the leading American music theorist of the last generation, distinguishes between the field of music theory and the subfield of music analysis. Music theory, he states, studies generalized musical systems from which composers derive their materials; music analysis engages the structural individuality of compositions. The general overviews in this section include a historical conspectus of the fields of music theory and analysis as well as surveys of recent developments. Traditional Texts seek to specify the scope of theoretical investigations and their methodologies. Analytic Methodologies view the different ways that American theory has illuminated particular musical works and repertories. Bibliographies offer useful tools to locate analytic literature. The Cambridge History of Western Music Theory is the first and only English-language text to attempt to give an overview of the disciplines of Western music theory and analysis from ancient Greece to the present (see Christensen 2002). Bent 1987 is the first of a series of texts in English to offer an analogous historical overview of the subfield of music analysis. The brief dictionary entry Forte 1974 is crucial for this bibliography in that it provides a short history of 20th-century music theory and analysis with an emphasis on American theory.

  • Bent, Ian. Analysis. With a glossary by William Drabkin. New York: Norton, 1987.

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    Presents a survey of the history of musical analysis, with large sections devoted to analysis before 1900 and analysis in the 20th century. A third section is organized by methodologies and musical parameters (“Fundamental Structure,” “Formal Analysis,” “Phrase-Structure Analysis,” etc.). Contains a thorough glossary supplemented by many musical examples.

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    • Christensen, Thomas, ed. The Cambridge History of Western Music Theory. Cambridge, UK: Cambridge University Press, 2002.

      DOI: 10.1017/CHOL9780521623711E-mail Citation »

      Thirty-one chapters by thirty-two contributing authors, which treat historical eras as well as methodological traditions.

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      • Forte, Allen. “Theory.” In Dictionary of Contemporary Music. Edited by John Vinton, 741–753. New York: E. F. Dutton, 1974.

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        An overview of music theory from 1900 to 1974 described in terms of the following categories: “New Theories of Tonal Music,” “Theoretical Aspects of Nontraditional Music,” “New Pitch Systems,” “Number and Proportion,” “Explanation of Newer Music,” “12-Tone Theory” (e.g., Babbitt), “Models: Information Theory,” “Linguistic and Logical Approaches,” and “Computational Research.” Contains an extended bibliography.

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        Traditional Texts

        By employing the philosophical tenets of logical positivism and the rigors of scientific thinking, the composer-theorist Milton Babbitt conceived the theory of twelve-tone music—the first formalized explanation of post-tonal music in America (see Babbitt 1965). By contrast, Allen Forte’s classic text The Structure of Atonal Music (Forte 1973, cited under Set Theory) formalized a theory for atonal music called pitch-class set theory. Both Babbitt and Forte understood the tonal theory of the Austrian theorist Heinrich Schenker as the primary basis for the study for tonal music. Babbitt’s student Benjamin Boretz produced an important doctoral dissertation (supervised by Babbitt and composer James K. Randall): Boretz 1995. Working with Babbitt’s seminal ideas on the twelve-tone system, Schenkerian analysis, and analytic philosophy, Boretz presented order- and content-based systems of pitch, the structural interrelations of which were interpreted through the analytic theories of philosopher Nelson Goodman. Boretz, however, was also critical of Babbitt for his lack of interest in the musical experience. Babbitt 2003 offers a later formulation of Babbitt’s thoughts on the relationships of contemporary music and music theory to the intellectual life of his time and criticizes some prevalent misconceptions about contemporary music. Brown and Dempster 1989 compares criticism of the scientific thought of Babbitt and Boretz with piece-specific analytic approaches. The colloquy between Edward T. Cone and David Lewin concerns the purpose of analysis as conceived in the early 1960s, the era during which American theorists were reformulating the values of the European music-theoretical tradition and conceiving new fields for study (see Cone 1967 and Lewin 1969). For more recent alternatives to the ideologies detailed here, which emphasize the possibilities of newer fields of inquiry and disciplinary restructuring, see New Paradigms and Approaches and the subsequent subject categories.

        • Babbitt, Milton. “The Structure and Function of Musical Theory.” College Music Symposium 5 (1965): 49–60.

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          Argues that music theory should be defined as a set of axioms explicating observable facts about music. Suggests that a scientific approach to music theory is indispensable. Equates history of theory to a second-tier discipline like history of science. Fosters the crucial role of the composer-theorist in music theory.

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          • Babbitt, Milton. “Contemporary Music Composition and Musical Theory as Contemporary Intellectual History.” In The Collected Essays of Milton Babbitt. By Milton Babbitt, 270–307. Princeton, NJ: Princeton University Press, 2003.

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            Describes the poor representation of contemporary music and music theory in contemporary (1972) intellectual work. A brief analysis demonstrates interactions of formal and interpreted theories, and the resultant constraints upon the statements that can be made about music. Includes a reading list.

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            • Boretz, Benjamin. Meta-Variations: Studies in the Foundations of Musical Thought. Red Hook, NY: Open Space, 1995.

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              Presents a theory that aims to uncover cognitive, rational bases of thinking about music. Proposes axiomatically defined music systems to analyze works in novel ways (e.g., the twelve-tone analysis of Wagner’s Prelude to Tristan and Isolde). Originally published in 1970–1973 as six installments in Perspectives of New Music: an introductory essay, “Sketch of a Musical System,” “The Construction of Musical Syntax” I and II, and “Analytic Fallout” I and II.

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              • Brown, Matthew, and Douglas J. Dempster. “The Scientific Image of Music Theory.” Journal of Music Theory 33.1 (1989): 65–106.

                DOI: 10.2307/843666E-mail Citation »

                Characterizes an opposition between scientific music theory (the search for general laws of music, exemplified by Boretz 1995) and analysis (the search for the uniqueness of pieces of music). Argues that criticisms against the former are overstated and advocates their refinement.

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                • Cone, Edward T. “Beyond Analysis.” Perspectives of New Music 6.1 (1967): 33–51.

                  DOI: 10.2307/832404E-mail Citation »

                  Asserts that structurally equivalent and equally satisfying analyses can be prepared for the inversions and retrogrades of twelve-tone pieces. Differentiates, therefore, between concrete values, which are the bases for absolute decisions made by the composer, and those which may extend beyond structure and hence be “beyond analysis.”

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                  • Lewin, David. “Behind the Beyond: A Response to Edward T. Cone.” Perspectives of New Music 7.2 (1969): 59–69.

                    DOI: 10.2307/832293E-mail Citation »

                    A response to Cone 1967. Differentiates among theory (which studies the structures of “sound-universes”), analysis (which targets informed listening of pieces), and criticism (which pertains to the analyst’s likes and dislikes). Concludes with a discussion of the nature of composition and its relation to analysis.

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                    • Rahn, John. “Aspects of Musical Explanation.” Perspectives of New Music 17.2 (1979): 204–224.

                      DOI: 10.2307/832840E-mail Citation »

                      Describes four different dimensions on which musical explanations may be situated, defined by the following four opposites: analog versus digital, in-time versus time-out, top-down or concept-driven versus bottom-up or data-driven, and theory of experience versus theory of pieces. Presents examples from theoretical and analytic literature to illustrate various negotiations of these dimensions.

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                      Analytic Methodologies

                      Dunsby and Whittall 1988 offers sample analyses illustrating the classic methodologies: Schenkerian analysis, set theory, and twelve-tone theory. The edited collection Stein 2005 contains sample analyses of concert music as well as of popular music. The essays in Tenzer 2006 focus on the meaning of analysis in an ethnomusicological and theoretical context. Schuijer 2008 and Cohn 1998 offer methodological overviews as well as academic contextualization of set theory and transformational theory, respectively.

                      • Cohn, Richard. “Introduction to Neo-Riemannian Theory: A Survey and Historical Perspective.” Journal of Music Theory 42.2 (1998): 167–180.

                        DOI: 10.2307/843871E-mail Citation »

                        Basic principles of neo-Riemannian theory and basic analytic techniques. Situates neo-Riemannian analysis in relation to other analytic methodologies including transformational theory, tonal theory, set theory, and the historical writings of Hugo Riemann.

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                        • Dunsby, Jonathan, and Arnold Whittall. Music Analysis in Theory and Practice. London: Faber, 1988.

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                          Divided into sections on tonal and post-tonal analysis, each of which features chapters on their methodologies (Schenkerian analysis, set theory, twelve-tone music harmony and voice leading in post-tonal music, etc.). Offers historical contexts for many of the methods described. Contains an epilogue on musical semiotics.

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                          • Schuijer, Michiel. Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts. Rochester, NY: University of Rochester Press, 2008.

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                            An intellectual history of the development of set theory. Discusses the evolution of the following concepts: equivalence, inclusion, similarity, operations.

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                            • Stein, Deborah, ed. Engaging Music: Essays in Musical Analysis. New York: Oxford University Press, 2005.

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                              Collection of essays designed for pedagogical use. Covers analytic topics including rhythm, meter, phrase, pitch, form, and ambiguity, and includes sample analyses of texted and instrumental music. Includes contributions (some previously published) by Charles Burkhart, Allen Forte, David Lewin, Carl Schachter, Joseph Straus, and others.

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                              • Tenzer, Michael, ed. Analytical Studies in World Music. New York: Oxford University Press, 2006.

                                DOI: 10.1093/acprof:oso/9780195177893.001.0001E-mail Citation »

                                Collection of essays on music analysis that encompasses music from around the world (including flamenco and gamelan music as well as Western classical music). Contains essays by Peter Manuel, Robin Moore and Elizabeth Sayre, Robert D. Morris, and others. Includes a compact disc.

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                                Bibliographies

                                The concern with analytic theory fostered the appearance of bibliographic texts that catalog essays devoted to particular works. Diamond 1991 is an annotated English-language bibliography of analytic writings on European and American art music. The commentary takes into account the technical level of study required to comprehend cited analyses. Hoek and Wenk 2007, also focusing on European and American art music, catalogues analytic literature in English, French, German, and Italian.

                                • Diamond, Harold J. Music Analyses: An Annotated Guide to the Literature. New York: Schirmer, 1991.

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                                  Refers to works from the Middle Ages to the 20th century, arranged alphabetically by composer.

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                                  • Hoek, D. J., and Arthur Wenk. Analyses of Nineteenth- and Twentieth-Century Music, 1940–2000. Lanham, MD: Scarecrow, 2007.

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                                    Bibliography of articles, dissertations, etc., offering analyses of specific 19th- and 20th-century works, arranged alphabetically by composer.

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                                    Pedagogy

                                    Americans have written the seminal pedagogical texts for Schenkerian theory. These textbook volumes include the Salzer and Schachter 1969 counterpoint text, which the authors regard as a study on its own, but which nevertheless is essential to Schenkerian analysis; Aldwell, et al. 2010, on harmony and voice-leading; the Cadwallader and Gagné 2007 course in Schenkerian analysis; and analogously, American theorists have authored the initial pedagogical texts on post-tonal theory, including the popular book Straus 2005 (see Textbooks for the previous four citations). Other pedagogical literature deals with musicianship and issues in aural skills, some of which includes methods that utilize recent technologies including the iPod and the laptop. Among sources of general concern to theory pedagogy, Schachter 1977 warns that increased specialization in the field of music theory has threatened the quality of theory training. Current American literature such as Rogers 2004, White and Lake 2002, and Zbikowski and Long 1994 discusses educational psychology and active learning strategies from the scholarship of teaching and learning (SoTL). Along with Rogers 2004, a special issue of Indiana Theory Review (Wallarab 1993) assesses the current role of pedagogy within the field of music theory as a whole. Jones and Burgee 2008 examine pre-college predictors of success in introductory music theory and aural skills classes. See Lindley 1982 (cited under History) for the teaching of graduate-level courses in the history of theory, in which the subfield’s vast literature is organized into syllabi for several graduate seminars.

                                    • Jones, M. Rusty, and Martin Bergee. “Elements Associated with Success in the First-Year Music Theory and Aural-Skills Curriculum.” Journal of Music Theory Pedagogy 22 (2008): 93–116.

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                                      Compares student success in first-year theory and aural skills with nine pre-college factors. Success in music theory strongly correlated to high school class rank and ACT math score. Success in aural skills correlated to diagnostic exam performance, ACT composite score, high school class rank, and instrumental experience.

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                                      • Rogers, Michael. Teaching Approaches to Music Theory: An Overview of Pedagogical Philosophies. 2d ed. Carbondale: Southern Illinois University Press, 2004.

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                                        Describes both philosophical and practical approaches to aural skills training and written theory instruction. Includes a commentary on the state of music theory pedagogy as a research field; discusses appropriate use of textbooks and technology as well as curricular decisions. Includes research from music theory as well as from the growing field of the scholarship of teaching and learning (SoTL). Substantial bibliography included.

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                                        • Schachter, Carl E. “Diversity and the Decline of Literacy in Music Theory.” College Music Symposium 17.1 (1977): 150–153.

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                                          A state-of-affairs discussion that cites how diversity and specialization in music theory threaten the quality of pedagogy.

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                                          • Wallarab, Clair L., ed. Indiana Theory Review 14.2 (1993).

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                                            Special issue devoted to music theory pedagogy.

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                                            • White, John D., and William Lake. Guidelines for College Teaching of Music Theory. 2d ed. Lanham, MD: Scarecrow, 2002.

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                                              Philosophical approach based on Piaget’s learning theory with practical application to the first two years of a music theory curriculum. Second edition includes “Technology for Teaching and Learning” by William Lake.

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                                              • Zbikowski, Lawrence M., and Charles K. Long. “Cooperative Learning in the Music Theory Classroom.” Journal of Music Theory Pedagogy 8 (1994): 135–158.

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                                                Discussion of the structure and implementation of small group projects. Four sample lessons take a cooperative approach to fundamentals, harmony, aural skills, and extended projects.

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                                                Textbooks

                                                The textbooks annotated here reflect the teaching needs of the categories of study listed in this bibliography. The combination of Aldwell, et al. 2010 on harmony and voice leading with Salzer and Schachter 1969 constitutes the core preparation for the study of Schenkerian Theory and Analysis in Cadwallader and Gagné 2007. Westergaard 1975 also relies on Schenkerian principles, but also adopts a scientific approach to theory. Schubert and Neidhöfer 2006 utilizes concepts found in Renaissance and Baroque theoretical treatises, thus enhancing students’ knowledge of the history of theory. Straus 2005 is the preferred text for teaching twelve-tone theory and set theory.

                                                • Aldwell, Edward, Carl Schachter, and Allen Cadwallader. Harmony and Voice Leading. 4th ed. New York: Schirmer, 2010.

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                                                  The classic pedagogical text acting as a precursor to the study of Schenkerian theory and analysis.

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                                                  • Cadwallader, Allen, and David Gagné. Tonal Analysis: A Schenkerian Approach. 2d ed. New York: Oxford University Press, 2007.

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                                                    The main pedagogical text for Schenkerian theory and analysis.

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                                                    • Salzer, Felix, and Carl Schachter. Counterpoint in Composition. New York: McGraw-Hill, 1969.

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                                                      The major modern text for training in the Fuxian method of species counterpoint.

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                                                      • Schubert, Peter, and Christoph Neidhöfer. Baroque Counterpoint. Upper Saddle River, NJ: Prentice-Hall, 2006.

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                                                        Introduces 18th-century counterpoint from a harmonic, rather than linear, point of view. Includes extensive quotations from Baroque-era authors. Distinguishes between “strict” and “free” styles of composition.

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                                                        • Straus, Joseph N. Introduction to Post-Tonal Theory. 3d ed. Upper Saddle River, NJ: Prentice Hall, 2005.

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                                                          Concise and clear introduction to the various elements of post-tonal music analysis, rich with musical and abstract examples. Each chapter features analysis exercises and an annotated bibliography.

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                                                          • Westergaard, Peter. An Introduction to Tonal Theory. New York: Norton, 1975.

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                                                            Undergraduate textbook that acknowledges the historic theories of Bernhardt, Fux, and Schenker. Contains three large sections, on “problems and assumptions” (which includes fundamentals), species counterpoint, and tonal rhythm. Presented as a scientific theory of music.

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                                                            Issues in Aural Skills

                                                            Friedmann 1990 deals exclusively with the hearing of post-tonal music through the recognition of sets and their features. Karpinski 2000 addresses two areas of perfecting aural skills and musicianship in tonal music: (1) listening, and (2) reading and performance. Karpinski addresses methodologies for each category in varying degrees of complexity (e.g., listening for stylistic traits versus dictation in several parts, or sight-reading piano works versus orchestral scores). Alegant 2008 assesses the use of digital aids to increase students’ hearing of tonal form without a score. He recommends students learn sonata form by filling in “flowcharts” consisting of progressively more information over a given number of weeks.

                                                            • Alegant, Brian. “Listen Up! Thoughts on iPods, Sonata Form, and Analysis without Score.” Journal of Music Theory Pedagogy 22 (2008): 149–176.

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                                                              Detailed and insightful account of the use of student-issued iPods to teach a listening-based approach to form. Explains the pros and cons of the approach. Alegant reports improved comprehension, increased listening skills, and dramatic changes in student listening habits outside of class.

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                                                              • Friedmann, Michael. Ear Training for Twentieth-Century Music. New Haven, CT: Yale University Press, 1990.

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                                                                The major text on post-tonal ear training. Describes strategies for hearing atonal music that emphasize an understanding of set structure.

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                                                                • Karpinski, Gary S. Aural Skills Acquisition: The Development of Listening, Reading and Performing Skills in College-Level Musicians. New York: Oxford University Press, 2000.

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                                                                  A comprehensive exploration of how college-age students develop listening, reading, and performing skills. Draws on research in music perception and cognition, music theory, and pedagogy. Breaks down both simple and complex musical tasks into their component activities in order to understand the requisite mental processes for acquiring these skills.

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                                                                  Journals

                                                                  A majority of scholarly music journals publish articles on all aspects of music theory and analysis that are written both by well-established scholars and newcomers to the field. Many journals are associated with professional organizations or universities; a few are edited, in whole or in part, by graduate students. Journal of Music Theory, Music Analysis, and Music Theory Spectrum are among the oldest and most prestigious in the field and present the majority of work contributed by senior scholars. Gamut, Music Theory Online, and Theory and Practice favor younger scholars and new paradigms. Indiana Theory Review and Intégral are peer-reviewed journals edited by graduate students at Indiana University and the Eastman School of Music, respectively. Dutch Journal of Music Theory is a polyglot journal aimed at international audiences. Although most of these sources appear as print journals, Music Theory Online and Gamut are exclusively online journals; this format can facilitate multimedia approaches.

                                                                  • Dutch Journal of Music Theory (Tijdschrift voor Muziektheorie). 1996–.

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                                                                    Publishes articles in music theory and analysis in Dutch, German, and English. One of the main European journals to address theoretical topics originating in American circles, most recently theories of form by William Caplin and James Hepokoski and Warren Darcy.

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                                                                    • Gamut: The Journal of the Music Theory Society of the Mid-Atlantic. 2008–.

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                                                                      Online journal of the Music Theory Society of the Mid-Atlantic. (The title Gamut was previously used for a now-defunct publication of the Georgia Society of Theorists.) Publishes articles on traditional topics, new paradigms, and practical issues such as the role of diversity in graduate programs of music theory.

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                                                                      • Indiana Theory Review. 1977–.

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                                                                        Founded by graduate students of Indiana University. Originally intended to feature the work of graduate students and recent graduates of Indiana University, it evolved into a general-purpose music theory journal for the field as a whole.

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                                                                        • Intégral: The Journal of Applied Musical Thought. 1987–.

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                                                                          Founded by graduate students of the Eastman School of Music. Emphasizes pluralism in the field of music theory.

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                                                                          • Journal of Music Theory. 1957–.

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                                                                            Oldest American music theory periodical currently being published; edited by Yale University’s music theory faculty. Early issues contain seminal articles on Schenkerian analysis, the history of theory, and set theory. Publishes articles on a wide range of topics in music theory and analysis. For a history of the publication, see David Carson Berry, “Journal of Music Theory under Allen Forte’s Editorship,” Journal of Music Theory 50.1 (2006): 7–23.

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                                                                            • Music Analysis. 1982–.

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                                                                              Journal of the British Society for Music Analysis. Publishes articles on a wide range of topics in music theory and analysis of interest to American scholars.

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                                                                              • Music Theory Online. 1993–.

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                                                                                First online journal of the Society for Music Theory, founded by Lee A. Rothfarb. Publishes broadly both on traditional topics and new areas of scholarship such as disability studies.

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                                                                                • Music Theory Spectrum. 1979–.

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                                                                                  Journal of the Society for Music Theory since its inception in 1977. Publishes on a wide variety of topics in theory.

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                                                                                  • Theory and Practice. 1978–.

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                                                                                    Began as a journal devoted to Schenkerian theory and analysis founded by the music theory faculty of Hunter College, including Hedi Siegel. Began publishing broadly in the late 1980s. Contains many articles first presented at meetings of the Music Theory Society of New York State.

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                                                                                    Specialized Journals

                                                                                    A number of journals focus on specific subfields of music theory and analysis or on specific repertories. Schenkerian theory and analysis is emphasized both in the Journal of Schenkerian Studies and in the six volumes of Music Forum. The history of theory is the focus of Theoria, and Perspectives of New Music emphasizes music of the 20th and 21st centuries. Other specialized journals focus on perception, pedagogy, and mathematics, as noted in their titles.

                                                                                    • Journal of Mathematics and Music. 2007–.

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                                                                                      The youngest specialty journal in music theory. Publishes articles on mathematical approaches, such as transformational studies.

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                                                                                      • Journal of Music Theory Pedagogy. 1987–.

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                                                                                        The main American journal devoted to the pedagogy of music theory, including issues of technological instruction.

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                                                                                        • Journal of Schenkerian Studies. 2005–.

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                                                                                          Journal devoted to recent trends in Schenkerian studies.

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                                                                                          • Music Forum. 1967–1987.

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                                                                                            Editors included William J. Mitchell, Felix Salzer, and Carl Schachter (associate editor). While the stated aim of the journal was to address a broad variety of topics, Schenkerian theory received frequent treatment. Some volumes include translations and reprints of previously unavailable work.

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                                                                                            • Music Perception. 1983–.

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                                                                                              Interdisciplinary journal of research on music perception from the perspectives of music theory, cognition, psychology, and other disciplines.

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                                                                                              • Perspectives of New Music. 1962–.

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                                                                                                The original journal devoted to the contemporary compositional values and practices of New York’s “Uptown” School; founded by the composer-theorists Arthur Berger and Benjamin Boretz. Publishes articles on compositional theories of late 20th- and 21st-century music. Contains early seminal articles on twelve-tone theory and analysis.

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                                                                                                • Theoria: Historical Aspects of Music Theory. 1985–.

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                                                                                                  The main American journal devoted to historical studies in music theory.

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                                                                                                  Schenkerian Theory and Analysis

                                                                                                  The writings of Heinrich Schenker have had a profound effect on American music theory. Schenker’s theories were introduced to America in the 1930s, but the widespread acceptance of his thought was achieved only decades later through the ongoing teachings and writings of Schenker’s students, the émigrés Felix Salzer and Ernst Oster, and of Allen Forte and Carl Schachter, both of whom studied with Salzer. Second- and third-generation Schenkerians, including Matthew Brown, Allen Cadwallader, Poundie Burstein, David Gagné, Frank Samarotto, and William Rothstein, as well as the older generation of Charles Burkhart, Allen Forte, Arthur Komar, John Rothgeb, Salzer, and Schachter, have extended Schenker’s theory into the areas of rhythm, French music, post-tonal theory, and early music. Moreover, all of these theorists have brought significant clarity and rigor to Schenker’s own theoretical concepts and analyses. The acceptance of Schenkerian theory has not been free of skepticism. Dubiel 1990 represents a body of works that question some of the inconsistencies in Schenker’s writing. The inclusion here of the bibliographic-historical guides Ayotte 2004 and Berry 2004 is meant to help the modern researcher begin a journey through the vast Schenkerian literature. For Schenkerian theories of rhythm and meter, see Rhythm, Meter, and Temporality; for Schenker’s Free Composition, see Schenker 1979, under Treatises and Essays; and for extensions of Schenkerian theory, see Extended Tonality.

                                                                                                  • Ayotte, Benjamin. Heinrich Schenker: A Guide to Research. Routledge Music Bibliographies. New York: Routledge, 2004.

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                                                                                                    A compilation of essays, articles, dissertations, theses, and monographs on Schenker’s life and works.

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                                                                                                    • Beach, David, ed. Aspects of Schenkerian Theory. New Haven, CT: Yale University Press, 1983.

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                                                                                                      Collection of ten essays by nine authors on topics of Schenkerian research including pedagogy, performance, themes, motives, and pre-Baroque and post-tonal concerns. Authors include Beach, John Rothgeb, Carl Schachter, Roger Kamien, Charles Burkhart, Saul Novack, Felix Salzer, James Baker, and Ernst Oster. Burkhart’s essay on performance is much cited.

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                                                                                                      • Berry, David Carson. A Topical Guide to Schenkerian Literature: An Annotated Bibliography with Indices. Hillsdale, NY: Pendragon, 2004.

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                                                                                                        Comprehensive guide to Schenkerian research organized by topic.

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                                                                                                        • Brown, Matthew. “The Diatonic and Chromatic in Schenker’s Theory of Harmonic Relations.” Journal of Music Theory 30.1 (1986): 1–33.

                                                                                                          DOI: 10.2307/843407E-mail Citation »

                                                                                                          Shows evidence for Schenker’s understanding of chromatic components (particularly mixture and tonicization) as integral to particularly the deep middleground structure of tonal music. Includes references to Schenker’s Harmony and Free Composition (Schenker 1979, under Treatises and Essays).

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                                                                                                          • Burkhart, Charles. “Schenker’s ‘Motivic Parallelisms.’” Journal of Music Theory 22.2 (1978): 145–175.

                                                                                                            DOI: 10.2307/843395E-mail Citation »

                                                                                                            Explores Schenker’s theory of motivic parallelism (i.e., linear structures repeated on various hierarchical levels). Argues for the analysis of these structures as a means of informing performance decisions. Includes Burkhart’s own examples as well as those of Schenker.

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                                                                                                            • Dubiel, Joseph. “‘When You Are a Beethoven’: Kinds of Rules in Schenker’s Counterpoint.” Journal of Music Theory 34.2 (1990): 291–340.

                                                                                                              DOI: 10.2307/843840E-mail Citation »

                                                                                                              A critical view of Schenker’s philosophical stance in his original works. Questions Schenker’s account of the relationship between counterpoint and composition. Highlights inconsistencies in Schenker’s description of prolongation.

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                                                                                                              • Forte, Allen. “Schenker’s Conception of Musical Structure.” Journal of Music Theory 3.1 (1959): 1–30.

                                                                                                                DOI: 10.2307/842996E-mail Citation »

                                                                                                                One of earliest American articles on Schenkerian theory. Explains prolongational levels through examples by Schenker and others. Argues for the adoption of the Schenkerian approach in standard analysis.

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                                                                                                                • Salzer, Felix. Structural Hearing: Tonal Coherence in Music. New York: Dover, 1962.

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                                                                                                                  The first comprehensive, pedagogically minded presentation of Schenker’s theories. Instrumental in popularizing Schenkerian analysis, particularly in the United States. Presents a systematic approach to understanding tonality.

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                                                                                                                  • Schachter, Carl. Unfoldings: Essays in Schenkerian Theory and Analysis. Edited by Joseph N. Straus. New York: Oxford University Press, 1999.

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                                                                                                                    A collection of eleven of Schachter’s most influential essays spanning over twenty years of Schenkerian scholarship. Topics include meter, modulation, reduction, commentary on Schenker 1979, (cited under Treatises and Essays) and analyses of works by Bach, Mozart, Schubert, and Chopin. Includes a dialogue between Straus and Schachter and a list of Schachter’s publications.

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                                                                                                                    Extended Tonality

                                                                                                                    The music-theoretical community has never been able to draw a precise line between tonal and nontonal events in highly chromatic contexts. The essays below, along with essays from Transformational Theory, represent part of this ongoing debate.

                                                                                                                    Chromaticism

                                                                                                                    In order to explain the presence of certain chromatic elements in tonal harmony including chromatic mediants, mode mixture, and distant key relations, Bribitzer-Stull 2006, Kopp 2002, and Tymoczko 2011 argue for an expanded understanding of the harmonic norms underlying tonal music. In contrast, Harrison 1994 proposes a renewed interest in the 19th-century perspective on chromaticism. See also Rehding 2003, annnotated under Influences on American Theory. Baker 1986 explores chromaticism by tracing Scriabin’s progressive departure from tonality.

                                                                                                                    • Baker, James M. The Music of Alexander Scriabin. New Haven, CT: Yale University Press, 1986.

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                                                                                                                      Describes Scriabin’s compositional transition from tonality to atonality. Employs Schenkerian analysis and set theory to highlight both the tonal and atonal aspects of Scriabin’s works.

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                                                                                                                      • Bribitzer-Stull, Matthew. “The Ab-C-E Complex: The Origin and Function of Chromatic Major Third Collections in Nineteenth-Century Music.” Music Theory Spectrum 28.2 (2006): 167–190.

                                                                                                                        DOI: 10.1525/mts.2006.28.2.167E-mail Citation »

                                                                                                                        Analyzes Ab-C-E as a structural prototype for 19th-century composers. Traces origins of Ab-C-E, takes hierarchic and transformational approaches to Ab-C-E, and describes chromatic third relations as prolongational strategy.

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                                                                                                                        • Harrison, Daniel. Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents. Chicago: University of Chicago Press, 1994.

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                                                                                                                          Examines late 19th- and early-20th-century harmony through the lens of 19th-century theorists including Hauptmann, Helmholtz, Oettingen, and Riemann.

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                                                                                                                          • Kopp, David. Chromatic Transformations in Nineteenth-Century Music. Cambridge, UK: Cambridge University Press, 2002.

                                                                                                                            DOI: 10.1017/CBO9780511481932E-mail Citation »

                                                                                                                            Argues for the acceptance of chromatic mediant motion as an integral part of chromatic tonality rather than as a curiosity. Traces history of chromatic third analysis through Rameau, Marx, Hauptmann, Riemann, Schenker, and Schoenberg, as well as contemporary authors. Includes analysis of Schubert, Beethoven, Chopin, Schumann, Brahms.

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                                                                                                                            • Tymoczko, Dmitri. A Geometry of Music. New York: Oxford University Press, 2011.

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                                                                                                                              Summarizes extensive work on chord relationships mapping harmonic relationships geometrically. Emphasizes the similarities between seemingly divergent genres such as medieval music, common practice tonality, jazz, and post-tonality. Argues for an extended “common-practice period” from the 11th century to the present.

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                                                                                                                              Extensions of Schenkerian Practices

                                                                                                                              The popularity of Schenkerian theory and analysis has generated applications far beyond Schenker’s original intent. Brown 2005 generalizes about rational validity of the Schenkerian approach as a whole, Stein 1983 uses Schenkerian analysis to question traditional harmonic function, and the controversial article Morgan 1976 applies Schenker’s principle of prolongation to dissonant harmonic structures. Finally, Larson 2009 demonstrates the application of Schenkerian analysis to jazz.

                                                                                                                              • Brown, Matthew. Explaining Tonality: Schenkerian Theory and Beyond. Rochester, NY: University of Rochester Press, 2005.

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                                                                                                                                Reviews Schenkerian explanation of tonality, particularly the interaction between melody and harmony. Posits six criteria for evaluating theories of tonality: accuracy, scope, fruitfulness, consistency, simplicity, and coherence.

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                                                                                                                                • Larson, Steve. Analyzing Jazz: A Schenkerian Approach. Harmonologia: Studies in Music Theory. Hillsdale, NY: Pendragon, 2009.

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                                                                                                                                  Presents Schenkerian analyses of selected jazz compositions.

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                                                                                                                                  • Morgan, Robert. “Dissonant Prolongation: Theoretical and Compositional Precedents” Journal of Music Theory 20.1 (1976): 49–91.

                                                                                                                                    DOI: 10.2307/843604E-mail Citation »

                                                                                                                                    Argues for the acceptance of dissonant structures, including the diminished-seventh chord, as prolongational. Highly criticized by Baker 1983, Straus 1987 (see Prolongation in Post-Tonal Music), and others, this article presents an extremely liberal application of Schenkerian prolongation. Analyzes Schubert, Liszt, Wagner, and Scriabin.

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                                                                                                                                    • Stein, Deborah. “The Expansion of the Subdominant in the Late Nineteenth Century.” Journal of Music Theory 27.2 (1983): 153–180.

                                                                                                                                      DOI: 10.2307/843513E-mail Citation »

                                                                                                                                      Employs Schenkerian analysis to highlight the expanded use of subdominant harmony in late-19th-century music. Analyzes lieder of Hugo Wolf to exemplify how the subdominant’s more significant role compels a reassessment of its traditional subservience to the dominant.

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                                                                                                                                      Prolongation in Post-Tonal Music

                                                                                                                                      Although Schenker intended his approach to be confined to tonal music of the common-practice era, some later theorists have attempted to apply his concept of prolongation to extended tonal and atonal music. Baker 1983 uses prolongational analysis as a method for discovering the tonal elements in an otherwise post-tonal piece. Lerdahl 1989 describes a very loose application of prolongation, appropriate for atonal applications. Straus 1987’s conditions of prolongation established general criteria to determine whether or not the concept of prolongation applies to any given passage. Forrest 2010 and Väisälä 2002 employ Straus’s conditions to cite examples of nontriadic prolongation in 20th-century music.

                                                                                                                                      • Baker, James. “Schenkerian Analysis and Post-Tonal Music.” In Aspects of Schenkerian Theory. Edited by David Beach, 153–188. New Haven, CT: Yale University Press, 1983.

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                                                                                                                                        Begins with an evaluative survey of research into post-tonal prolongation to date. Asserts that although many post-tonal prolongational analyses are theoretically flawed, the prolongational approach has potential for describing tonal structure in what Baker calls “borderline” pieces. Demonstrates this position through an analysis of Scriabin’s “Enigme.”

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                                                                                                                                        • Forrest, David. “Prolongation in the Choral Music of Benjamin Britten.” Music Theory Spectrum 32.1 (2010): 1–25.

                                                                                                                                          DOI: 10.1525/mts.2010.32.1.1E-mail Citation »

                                                                                                                                          Uses Straus’s prolongation conditions (see Straus 1987) and theory of pattern completion (see Straus 1982, cited under Set Theory: Voice Leading) to argue for prolongation of symmetrical interval cycles in passages with triadic surfaces. Analyzes early Britten works to reveal interval cycles at various levels of prolongational structure.

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                                                                                                                                          • Lerdahl, Fred. “Atonal Prolongational Structure.” Contemporary Music Review 4.1 (1989): 65–87.

                                                                                                                                            DOI: 10.1080/07494468900640211E-mail Citation »

                                                                                                                                            Lists ten salience conditions that contribute to prolongation, regardless of the tonal context. Lerdahl’s use of the term prolongation is less strict than that of most Schenkerians. Adapts findings from Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, MA: MIT Press, 1983) to analyze three Schoenberg pieces.

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                                                                                                                                            • Straus, Joseph N. “The Problem of Prolongation in Post-Tonal Music.” Journal of Music Theory 31.1 (1987): 1–21.

                                                                                                                                              DOI: 10.2307/843544E-mail Citation »

                                                                                                                                              Lays out four conditions of prolongation that Straus claims are simply not present in most post-tonal music. Describes instead an associative model that is “less ambitious, but theoretically more defensible” than prolongation. Highly cited, this article prompted responses by Larson and Lerdahl, and a reply by Straus.

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                                                                                                                                              • Väisälä, Olli. “Prolongation of Harmonies Related to the Harmonic Series in Early Post-Tonal Music.” Journal of Music Theory 46.1–2 (2002): 207–283.

                                                                                                                                                DOI: 10.1215/00222909-46-1-2-207E-mail Citation »

                                                                                                                                                Reveals how the nontriadic harmonic structure of some early post-tonal music relates to the overtone series and argues that these structures are prolonged in ways similar to tonal, triadic prolongation. Applies the conditions from Straus 1987 to works by Scriabin, Berg, Debussy, and Webern.

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                                                                                                                                                Set Theory

                                                                                                                                                Set theory is one of the fundamental approaches to post-tonal music. With this method, music is conceived of and analyzed in terms of sets (unordered collections of pitch classes) and, more generally, set classes (sets regarded as equivalent, normally under the operations of transposition and inversion). Some of the specific topics engaged by set theory include composers’ use of interval cycles (sets composed by the sequencing of a single interval), the measurement of similarity between set classes, and the study of post-tonal voice leading (the motion between sets and set classes, either in specific compositions or in precompositional activity); this final field of inquiry overlaps significantly with transformational theory. Contour theory employs particular methodologies of set theory to defined registral shapes rather than to sets and set classes. Diatonic set theory applies set-theoretical methodologies to diatonically conceived music and also investigates the properties of diatonic scales, both in the twelve-pitch-class chromatic universe and in chromatic universes of other cardinalities. Set theory shares many properties with twelve-tone theory, the study of ordered sets. In our annotations, we use the terms “set” and “set class” as above, but terminology may vary in some of the sources; Perle 1991, for example, refers to the same structures as “cells” instead. Perle 1991, Forte 1973, and Morris 1987 are classic textbooks on set theory; Joseph Straus’s Introduction to Post-Tonal Theory (Straus 2005, cited under Textbooks) enjoys widespread classroom use today. Block 1990 demonstrates how set theory can be applied to a repertory outside the European post-tonal tradition, and Quinn 2006, a text on chord quality, exemplifies contemporary concerns of set theory. For a historically grounded overview of set theory, see Schuijer 2008, cited under Analytic Methodologies.

                                                                                                                                                • Block, Steven. “Pitch Class Transformation in Free Jazz.” Music Theory Spectrum 12.2 (1990): 181–202.

                                                                                                                                                  DOI: 10.1525/mts.1990.12.2.02a00010E-mail Citation »

                                                                                                                                                  Explains the harmonic language of selected free jazz compositions by employing set theoretical methodologies.

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                                                                                                                                                  • Forte, Allen. The Structure of Atonal Music. New Haven, CT: Yale University Press, 1973.

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                                                                                                                                                    This text is in two parts: the first provides a thorough introduction to pitch-class set theory; the second develops Forte’s theory of K- and Kh-complexes.

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                                                                                                                                                    • Morris, Robert D. Composition with Pitch Classes: A Theory of Compositional Design. New Haven, CT: Yale University Press, 1987.

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                                                                                                                                                      Covers set theory and twelve-tone theory, with an emphasis on composition. Defines a variety of musical spaces (e.g., contour, pitch, or pitch-class space), investigates invariance and combinatoriality within the aggregate under various twelve-tone operations, explores possibilities of composition with arrays, and introduces fundamentals of contour theory.

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                                                                                                                                                      • Perle, George. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern. 6th ed. Berkeley: University of California Press, 1991.

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                                                                                                                                                        Earliest English-language book-length study of atonality, nondodecaphonic serial music, and twelve-tone music. Presents the marking of collections or “cells” as a tool to elucidate selected details rather than overall conceptions of post-tonal works. Considers both ordered and unordered sets in serial composition. Discusses the structural implications of pitch centricities in atonal music and the problem of conceiving harmony in an order-based system such as twelve-tone music.

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                                                                                                                                                        • Quinn, Ian. “General Equal-Tempered Harmony.” Perspectives of New Music 44.2 (2006): 114–159.

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                                                                                                                                                          Also see Perspectives of New Music 45.1 (2007): 4–63. A theory of chord quality for chromatic universes of any cardinality. Chords (set classes) inhabit a quality space, in which qualitative genera are associated with maximally even subgenera and for which different levels of prototypes are defined (via Fourier balances). Investigates intrageneric and intergeneric affinities, and relationships among harmonic chord space, quality space, and Fourier balance space.

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                                                                                                                                                          Interval Cycles

                                                                                                                                                          Several theorists have investigated how composers use sets built of interval cycles, collections of pitch classes created from a sequence of the same interval class (e.g., the augmented triad and the diatonic scale). Lambert 1990 analyzes several compositions by Charles Ives in terms of interval cycles, and Headlam 1996, considering the compositions of Alban Berg, incorporates interval cycles into a broader analytic project. Study of interval cycles can extend to serial music as well, as in Gollin 2007, and to the theory of “twelve-tone tonality” in Perle 1996.

                                                                                                                                                          • Gollin, Edward. “Multi-Aggregate Cycles and Multi-Aggregate Serial Techniques in the Music of Béla Bartók.” Music Theory Spectrum 29.2 (2007): 143–176.

                                                                                                                                                            DOI: 10.1525/mts.2007.29.2.143E-mail Citation »

                                                                                                                                                            Investigates Bartók’s use of compound interval cycles that state the aggregate more than once, particularly cycles in which pitch-class repetitions are distributed as evenly as possible. These maximally distributed cycles permit the greatest variety in pitch-class content while restricting the number of set classes formed by adjacent pitch classes.

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                                                                                                                                                            • Headlam, David. The Music of Alban Berg. New Haven, CT: Yale University Press, 1996.

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                                                                                                                                                              Analyzes Berg’s tonal and post-tonal works, including the twelve-tone music, which Headlam conceives as not entirely row-based. Interval cycles figure prominently in the analyses, as do cycles of durations. Accounts for the importance of symbolism and autobiography in Berg’s music as well as the composer’s dialogue with his tonal heritage.

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                                                                                                                                                              • Lambert, J. Philip. “Interval Cycles as Compositional Resources in the Music of Charles Ives.” Music Theory Spectrum 12.1 (1990): 43–82.

                                                                                                                                                                DOI: 10.1525/mts.1990.12.1.02a00020E-mail Citation »

                                                                                                                                                                Illustrates examples of single-interval and compound cycles that determine pitch content in experimental works by Ives. Provides a method to calculate PCL (pitch-class length, the number of pitch classes that occur before a repetition) in combination cycles. Discusses interval cycles in Ives’s precompositional activity.

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                                                                                                                                                                • Perle, George. Twelve-Tone Tonality. 2d ed. Berkeley: University of California Press, 1996.

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                                                                                                                                                                  Describes ordered sets in which alternating elements derive from inversionally related interval cycles. These cyclic sets address a general problem in twelve-tone music of the relationship between ordered set content and harmony by limiting the variety of verticalities constructed by adjacencies in the set.

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                                                                                                                                                                  Similarity Relations

                                                                                                                                                                  One of set theory’s concerns is the measurable similarity between two different set classes. Allen Forte described a few similarity relations based on interval content or common subsets in The Structure of Atonal Music (Forte 1973, cited under Set Theory). Several other theorists have subsequently constructed additional types of similarity relations; Robert Morris and Eric Isaacson’s relations are representative of this (see Morris 1979–1980 and Isaacson 1990). Quinn 2001 offers new perspectives on how similarity relations should be interpreted.

                                                                                                                                                                  • Isaacson, Eric. “Similarity of Interval-Class Content between Pitch-Class Sets: The IcVSIM Relation.” Journal of Music Theory 34.1 (1990): 1–28.

                                                                                                                                                                    DOI: 10.2307/843860E-mail Citation »

                                                                                                                                                                    Surveys preexisting similarity relations and introduces the IcVSIM (interval-class vector similarity) relation to address some of their shortcomings.

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                                                                                                                                                                    • Morris, Robert D. “A Similarity Index for Pitch-Class Sets.” Perspectives of New Music 18.1–2 (1979–1980): 445–460.

                                                                                                                                                                      DOI: 10.2307/832996E-mail Citation »

                                                                                                                                                                      Defines SIM (similarity index) as a measure of how similar two set classes are to each other; introduces ASIM (absolute similarity) to make more meaningful comparisons among similarity indices of pairs of sets with differing cardinalities.

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                                                                                                                                                                      • Quinn, Ian. “Listening to Similarity Relations.” Perspectives of New Music 39.2 (2001): 108–158.

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                                                                                                                                                                        Argues for an understanding of similarity relations as fuzzy equivalence relations. Questions some common assumptions about similarity relations, including that of intransitivity, and asserts that the information gleaned about the set-class universe from various similarity relations is of more consequence than their functional differences.

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                                                                                                                                                                        Voice Leading

                                                                                                                                                                        The texts below study the linear motion between sets or set classes. Straus 1982 investigates voice leading as an organizing principle in music. Morris 1998 creates a visual representation of voice leading among sets as a compositional space. Straus 2005 explores and visualizes voice-leading connections among set classes. The study of voice leading in post-tonal music is closely connected with the study of prolongation in post-tonal music (see Extensions of Schenkerian Practices), and its methodologies sometimes overlap with those of transformational theory.

                                                                                                                                                                        • Morris, Robert D. “Voice-Leading Spaces.” Music Theory Spectrum 20.2 (1998): 175–208.

                                                                                                                                                                          DOI: 10.1525/mts.1998.20.2.02a00010E-mail Citation »

                                                                                                                                                                          Models all the possible voice leadings between sets and defines a series of restrictions to make studying the voice leadings more viable. Describes two-partition graphs (compositional spaces that display voice leadings between sets) and generates two-partition graphs from voice-leading spaces, which relate set classes instead of sets.

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                                                                                                                                                                          • Straus, Joseph N. “A Principle of Voice Leading in the Music of Stravinsky.” Music Theory Spectrum 4.1 (1982): 106–124.

                                                                                                                                                                            DOI: 10.1525/mts.1982.4.1.02a00070E-mail Citation »

                                                                                                                                                                            Uses the principle of pattern completion to study the background harmonies and the voice leadings among them in the music of Stravinsky. Compares pattern completion to aggregate formation in twelve-tone music and concludes that pattern completion organizes music from all eras of Stravinsky’s compositional career.

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                                                                                                                                                                            • Straus, Joseph N. “Voice Leading in Set-Class Space.” Journal of Music Theory 49.1 (2005): 45–108.

                                                                                                                                                                              DOI: 10.1215/00222909-2007-002E-mail Citation »

                                                                                                                                                                              Creates a parsimonious voice-leading space for set classes, in which each set class is defined by a five-dimensional location vector. Set classes’ proximity to one another in this space indicates their degree of semitonal offset, and chord quality is associated with proximity to maximally even or maximally chromatic set classes.

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                                                                                                                                                                              Contour Theory

                                                                                                                                                                              Friedmann 1985 and Morris 1987 (cited under Set Theory) laid the groundwork for contour theory, the focus of which is the defined melodic or motivically shaped structures independent of set-class identity or exact intervallic content. Further works such as Morris 1993 and Marvin and Laprade 1987 adapt many of the techniques of set theory to explain contour. Morris 1993 considers extensions of contour theory to other musical domains than pitch, and Quinn 1997 demonstrates applications of fuzzy set theory to contour.

                                                                                                                                                                              • Friedmann, Michael L. “A Methodology for the Discussion of Contour: Its Application to Schoenberg’s Music.” Journal of Music Theory 29.2 (1985): 223–248.

                                                                                                                                                                                DOI: 10.2307/843614E-mail Citation »

                                                                                                                                                                                Introduces a vocabulary to discuss musical contour, defines equivalence classes among contours, and considers applications of contour theory to analysis, especially the analysis of polyphonic passages.

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                                                                                                                                                                                • Marvin, Elizabeth West, and Paul A. Laprade. “Relating Musical Contours: Extensions of a Theory for Contour.” Journal of Music Theory 31.2 (1987): 225–267.

                                                                                                                                                                                  DOI: 10.2307/843709E-mail Citation »

                                                                                                                                                                                  Follows the exposition of contour theory in Morris’s textbook (Morris 1987, cited under Set Theory); develops an algorithm to determine csegclasses (classes of csegs, ordered sets of contour pitches in contour space) and defines similarity relations among csegs and csegclasses.

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                                                                                                                                                                                  • Morris, Robert D. “New Directions in the Theory and Analysis of Musical Contour.” Music Theory Spectrum 15.2 (1993): 205–228.

                                                                                                                                                                                    DOI: 10.1525/mts.1993.15.2.02a00040E-mail Citation »

                                                                                                                                                                                    Introduces a contour relation algorithm (CRA), which reduces contours to primes by a process of “pruning.” Defines prime classes based on them. Considers extensions of contour theory to domains other than pitch and time, and to contours with similarities or repetitions. Classifies all the types of contours that may include repetitions, simultaneities, omitted pitches, and omitted timepoints as generalized contour types.

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                                                                                                                                                                                    • Quinn, Ian. “Fuzzy Extensions to the Theory of Contour.” Music Theory Spectrum 19.2 (1997): 232–263.

                                                                                                                                                                                      DOI: 10.1525/mts.1997.19.2.02a00050E-mail Citation »

                                                                                                                                                                                      Applies fuzzy set theory to the study of musical contour to determine whether potential contours should be added to a given family of similar contours; demonstrates analytic applications with Reich’s The Desert Music.

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                                                                                                                                                                                      Diatonic Sets and Scales

                                                                                                                                                                                      Essential aims of diatonic set theory include the application of set-theoretical methodologies to diatonic music or to music in a tonal language, as well as the study of diatonic scales, either in a twelve-note chromatic universe or in chromatic universes of different cardinalities. The former focus is exemplified most clearly in Clough 1979. Browne 1981 introduces some of the concerns of the latter principle, and Clough and Douthett 1991 provides a mathematically grounded investigation. Van den Toorn 1983 offers some analytic applications of diatonic set theory through the investigation of the octatonic scale.

                                                                                                                                                                                      • Browne, Richmond. “Tonal Implications of the Diatonic Set.” Theory Only 5.6–7 (1981): 3–21.

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                                                                                                                                                                                        Explores some basic properties of the diatonic set of tonal music, particularly those that arise from the unique multiplicity property that it exhibits: that each interval class in its interval-class vector occurs a different number of times.

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                                                                                                                                                                                        • Clough, John. “Aspects of Diatonic Sets.” Journal of Music Theory 23.1 (1979): 45–61.

                                                                                                                                                                                          DOI: 10.2307/843693E-mail Citation »

                                                                                                                                                                                          Develops basic methodologies from atonal set theory to operate in seven-note diatonic collections, and presents analyses that apply diatonic set theory to the music of Beethoven and Mozart.

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                                                                                                                                                                                          • Clough, John, and Jack Douthett. “Maximally Even Sets.” Journal of Music Theory 35.1–2 (1991): 93–173.

                                                                                                                                                                                            DOI: 10.2307/843811E-mail Citation »

                                                                                                                                                                                            Defines, presents properties of, and classifies maximally even sets. Defines diatonic sets (both in the twelve-pitch-class chromatic universe and in other chromatic universes) as a subset of the set of maximally even sets. Discusses generation and complementation of maximally even sets, interval cycles, and second-order maximally even sets.

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                                                                                                                                                                                            • Van den Toorn, Pieter. The Music of Igor Stravinsky. New Haven, CT: Yale University Press, 1983.

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                                                                                                                                                                                              Classic text on the analysis of Igor Stravinsky’s music using octatonic scales, with emphasis given to The Rite of Spring.

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                                                                                                                                                                                              Twelve-Tone Theory

                                                                                                                                                                                              Twelve-tone theory investigates music constructed from ordered sets consisting of all twelve pitch classes in the chromatic universe; for the earliest texts in twelve-tone composition, see Schoenberg 1984, cited under Treatises and Essays. Twelve-tone theory, though dealing with ordered collections, shares many techniques with set theory; for the most basic overviews of the subfield, see the textbooks Perle 1991, Morris 1987, and Straus 2005 (cited under Set Theory and Pedagogy). Twelve-tone theory in the 1960s investigated combinatoriality and invariance in array structures, as in Babbitt 1960, Babbitt 1961, and Martino 1961. Babbitt 1960, “Twelve Tone Invariants,” proposed a theory of combinatoriality developed to its greatest extent by Morris and Starr 1977. Twelve-tone theory as an aid to composition figures prominently in several sources, including Morris and Starr 1974 on the all-interval series and Mead 1994 on the application of Babbitt’s twelve-tone theories to his own music. Peles 1983–1984 and Alegant 2001 demonstrate analysis based on twelve-tone theory. Dubiel 1990 represents a listener-oriented approach to twelve-tone music. Beyond invariance and combinatoriality, concerns of twelve-tone theory include the verticalization of row adjacencies and time-point studies. For the former, see, in addition to Alegant 2001, Perle 1991 (cited under Set Theory); for the latter, see Babbitt 1962 (cited under Twentieth-Century Music). As with set theory, different authors’ terminology varies; rows may also be referred to as “sets” or “series.”

                                                                                                                                                                                              • Alegant, Brian. “Cross-Partitions as Harmony and Voice Leading in Twelve-Tone Music.” Music Theory Spectrum 23.1 (2001): 1–40.

                                                                                                                                                                                                DOI: 10.1525/mts.2001.23.1.1E-mail Citation »

                                                                                                                                                                                                A study of harmony and voice leading in twelve-tone music. Partitions rows into two-dimensional grids, which can be subject to permutations, and which can be read horizontally or vertically to derive tetrachords and trichords. Analyzes music of Webern, Schoenberg, and Dallapiccola using cross partitions.

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                                                                                                                                                                                                • Babbitt, Milton. “Twelve-Tone Invariants as Compositional Determinants.” Musical Quarterly 46.2 (1960): 246–259.

                                                                                                                                                                                                  DOI: 10.1093/mq/XLVI.2.246E-mail Citation »

                                                                                                                                                                                                  Defines twelve-tone operations as order permutations. Briefly introduces the group structure of the twelve transpositions of a set and the twelve-tone operations inversion, retrograde, and retrograde inversion (as well as identity). Presents an overview of pitch, interval, and order relationships that may be held invariant under transposition and inversion.

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                                                                                                                                                                                                  • Babbitt, Milton. “Set Structure as a Compositional Determinant.” Journal of Music Theory 5.1 (1961): 72–94.

                                                                                                                                                                                                    DOI: 10.2307/842871E-mail Citation »

                                                                                                                                                                                                    Shows how invariants arise in specific sets by virtue of their construction. Presents the conditions under which I, R, RI, and prime hexachordal combinatoriality arise, and considers how some combinatorialities imply others. Defines all-combinatorial hexachords; provides examples of hexachordal combinatoriality and secondary sets in Schoenberg.

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                                                                                                                                                                                                    • Dubiel, Joseph. “Three Essays on Milton Babbitt.” Perspectives of New Music 28.2 (1990): 216–261.

                                                                                                                                                                                                      DOI: 10.2307/833020E-mail Citation »

                                                                                                                                                                                                      Discusses Babbitt’s appropriation of the twelve-tone system as well as nuances of his precompositional planning. The third essay takes a listener-oriented approach to understanding Babbitt’s music. Published over three separate issues. Continued in 29.1 (1991): 90–122; 30.1 (1992): 82–131.

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                                                                                                                                                                                                      • Martino, Donald. “The Source Set and its Aggregate Formations.” Journal of Music Theory 5.2 (1961): 224–273.

                                                                                                                                                                                                        DOI: 10.2307/843226E-mail Citation »

                                                                                                                                                                                                        Summarizes all conceivable ways to present equally partitioned aggregates composed of Babbitt’s source sets; also comments on asymmetrical partitioning. Discusses vertical relations within a variety of arrays.

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                                                                                                                                                                                                        • Mead, Andrew W. An Introduction to the Music of Milton Babbitt. Princeton, NJ: Princeton University Press, 1994.

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                                                                                                                                                                                                          The classic study of the application of Milton Babbitt’s theories to his own twelve-tone music.

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                                                                                                                                                                                                          • Morris, Robert D., and Daniel Starr. “The Structure of All-Interval Series.” Journal of Music Theory 18.2 (1974): 364–389.

                                                                                                                                                                                                            DOI: 10.2307/843642E-mail Citation »

                                                                                                                                                                                                            Describes the properties of All-Interval Series, rows in which every possible interval is represented once. Partitions the set of all All-Interval Series into constellations of sets, each of which is represented by a single source series. Introduces ways to generate All-Interval Series and investigates combinatorial properties.

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                                                                                                                                                                                                            • Morris, Robert D., and Daniel Starr. “A General Theory of Combinatoriality and the Aggregate.” Perspectives of New Music 16.1 (1977): 3–35.

                                                                                                                                                                                                              DOI: 10.2307/832847E-mail Citation »

                                                                                                                                                                                                              Part two of article published in Perspectives of New Music 16.2 (1978): 50–84. The most complete study of combinatoriality to date. Summarizes earlier study of combinatoriality and presents techniques for generating combinatorialities with both even and uneven partitions of sets; advocates combination matrices as a tool for studying, visualizing, and generating combinatorialities. Considers compositional implications of combinatorialities.

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                                                                                                                                                                                                              • Peles, Stephen. “Interpretations of Sets in Multiple Dimensions: Notes on the Second Movement of Arnold Schoenberg’s String Quartet #3.” Perspectives of New Music 22.1–2 (1983/84): 303–352.

                                                                                                                                                                                                                DOI: 10.2307/832952E-mail Citation »

                                                                                                                                                                                                                An analysis that regards the set not as just an ordered collection of pitch classes but as a “super motive” that governs compositional choices. Demonstrates how analysis based on dimensions other than pitch, such as register, instrumentation, and rhythm, reveals relationships among set statements that are not given in the row structure itself.

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                                                                                                                                                                                                                Transformational Theory

                                                                                                                                                                                                                Transformational theory in principle has focused on the operations by which two or more musical structures relate. Much of recent transformational theory, conceived by David Lewin and extended by Richard Cohn, Julian Hook, Brian Hyer, and others, represents a renewed interest in operations suggested by the theories of Hugo Riemann. Below is a brief sampling of their work. Lewin 1982–1983 sets the stage for modern transformational theory, and Lewin 2007 provides theoretical templates by which transformations and networks can be described. Cohn 1996 demonstrates the facility with which previously problematic 19th-century harmonic progressions can be described using transformational labels. Hyer 1995 and Cohn 1997 apply specific transformations to triadic music and make use of a modern adaptation of Riemann’s 19th-century Tonnetz. Hook 2007 discusses transformations of nontriadic sets. A special issue of Journal of Music Theory (Satyendra 1998) explores a range of Neo-Riemannian issues including cognition, seventh-chord transformation, and application to a variety of musical styles, and a special issue of Music Theory Spectrum (Harrison 2002) is dedicated specifically to Klumpenhouwer networks. For a general overview of transformational theory, see Cohn 1998, cited under Analytic Methodologies.

                                                                                                                                                                                                                • Cohn, Richard. “Maximally Smooth Cycles.” Music Analysis 15.1 (1996): 9–40.

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                                                                                                                                                                                                                  Identifies the twenty-four consonant triads as uniquely capable of cyclic motion involving single half-step displacement. Shows how recognition of this property reveals harmonic logic in passages of 19th-century music that resist traditional tonal analysis. Describes the emergent relationships in terms of Lewin’s Generalized Interval Systems. Often cited in neo-Riemannian literature.

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                                                                                                                                                                                                                  • Cohn, Richard. “Neo-Riemannian Operations, Parsimonious Trichords and Their Tonnetz Representations.” Journal of Music Theory 41.1 (1997): 1–66.

                                                                                                                                                                                                                    DOI: 10.2307/843761E-mail Citation »

                                                                                                                                                                                                                    Focuses on parallel (P), leading-tone (L), and relative (R) transformations and their various combinations; explores the logic of the transformations by mapping certain 19th-century harmonic progressions on a geometric representation of triad parsimony, an adaptation of Hyer’s Tonnetz (see Hyer 1995).

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                                                                                                                                                                                                                    • Harrison, Daniel, ed. Music Theory Spectrum 24.2 (2002).

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                                                                                                                                                                                                                      Devoted to the topic of Klumpenhouwer networks (K-nets). Philip Lambert examines the analytic uses of isographic networks; David Lewin analyzes Schoenberg and Webern to expose the relationships between K-nets and Perle-Lansky cycles; Philip Stoecker extends K-net theory by describing axial isography; David Headlam places recent research on K-nets in the context of George Perle’s work. Includes a comprehensive bibliography.

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                                                                                                                                                                                                                      • Hook, Julian. “Cross-Type Transformations and the Path Consistency Condition.” Music Theory Spectrum 29.1 (2007): 1–40.

                                                                                                                                                                                                                        DOI: 10.1525/mts.2007.29.1.1E-mail Citation »

                                                                                                                                                                                                                        Extends Lewin 2007 by proposing a model for transformations that map different types of elements such as triads and seventh chords; argues for a relaxation of Lewin’s path consistency condition. Prompted a response: Dmitri Tymoczko, “Lewin, Intervals, and Transformations: A Comment on Hook,” Music Theory Spectrum 30.1 (2008): 164–168.

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                                                                                                                                                                                                                        • Hyer, Brian. “Reimag(in)ing Riemann.” Journal of Music Theory 39.1 (1995): 101–138.

                                                                                                                                                                                                                          DOI: 10.2307/843900E-mail Citation »

                                                                                                                                                                                                                          Casts Riemann’s dominant (D), parallel (P), relative (R), and Leittonwechsel (L) transformations against an equal-tempered version of the Tonnetz, a chart of triad relationships popular in the 19th century. Thus provides a geometric model for discussing triad relations without reference to a tonal center or traditional tonic/subdominant/dominant progression. Builds from Hyer’s 1989 dissertation.

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                                                                                                                                                                                                                          • Lewin, David. “Transformational Techniques in Atonal and Other Music Theories.” Perspectives of New Music 21.1–2 (1982–1983): 312–371.

                                                                                                                                                                                                                            DOI: 10.2307/832879E-mail Citation »

                                                                                                                                                                                                                            Lays the groundwork for a rebirth of Riemannian transformational theory by describing relationships between musical structures in terms of transformations and networks of transformations; applies these transformations to pieces by Webern and Schoenberg.

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                                                                                                                                                                                                                            • Lewin, David. Generalized Musical Intervals and Transformations. New York: Oxford University Press, 2007.

                                                                                                                                                                                                                              DOI: 10.1093/acprof:oso/9780195317138.001.0001E-mail Citation »

                                                                                                                                                                                                                              Originally published 1987. Formalizes transformational and network study in music to the extent that the book serves as a reference for all relevant research. Presents mathematical and geometric templates for describing relationships between pitches, pitch classes, intervals, and rhythms; defines set theory in terms of a generalized interval system subject to transformations.

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                                                                                                                                                                                                                              • Satyendra, Ramon, ed. Special Issue: Neo-Riemannian Theory. Journal of Music Theory 42.2 (1998).

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                                                                                                                                                                                                                                This unique topical issue includes twelve articles from neo-Riemannian theorists. Richard Cohn gives an introduction and history; Adrian Childs discusses a transformational model for seventh chords; Carol Krumhansl considers perceptual issues; Edward Gollin explores three-dimensional Tonnetze; David Lewin offers analyses of Bach; Clifton Callender analyzes Scriabin. Includes a comprehensive bibliography.

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                                                                                                                                                                                                                                Rhythm, Meter, and Temporality

                                                                                                                                                                                                                                Precise definitions of rhythm and meter are elusive; indeed, the sources cited here may regard the two phenomena as oppositional, interdependent, or fundamentally the same. Nevertheless, in many sources, meter refers to the partitioning of musical time and the inference of periodic accents in music, whereas rhythm refers to patterns arising from duration, tonal motion, and phrasing, as well as a variety of different accents. Studies of temporality may overlap with studies of rhythm and meter but also consider the experience of musical time. In addition to the general theories of rhythm, meter, and temporality cited here, several of the texts in Schenkerian Theories function as overviews. Although most studies on rhythm and meter consider the tonal repertory, several theorists have made studies of rhythm and meter in 20th-century music by focusing on specific pieces or composers; such analyses adopt a wide range of methodologies. Theories of rhythm and meter operate within a broad range of assumptions but share some fundamental concerns. First is the relationship between meter and rhythm: although many theories, such as Cooper and Meyer 1960, regard meter as something distinct from rhythm, as a regular pattern of accents separate from but able to influence the structure of rhythmic events, others view the relationship differently; Hasty 1997, for example, regards meter as a fundamentally rhythmic phenomenon. Another concern is the extent to which meter and rhythm are interpreted in time or retrospectively. Most sources probably favor the latter orientation; again, Hasty 1997 is an exception. Still another concern is the different qualities of accent that arise in music’s temporal unfolding: in addition to Cooper and Meyer 1960 and Hasty 1997, Lester 1986 discusses accent in detail. A fourth popular topic, especially in the Schenkerian theories, concerns the existence of meter at higher levels of structure (hypermeter). In addition, several theorists have pursued questions of rhythmic and metric dissonance arising from the interactions of different rhythmic layers, or strata; Krebs 1999 and Cohn 2001 exemplify this interest, as does Maury Yeston, whose short volume (Yeston 1976) appears under Schenkerian Theories. Kramer 1988 investigates broad philosophical questions of the experience of musical time, and Agawu 2006 considers the rhythmic organization of a non-Western repertory. See also Justin London’s Hearing in Time for a perspective on musical time influenced by cognitive studies (London 2004, cited under Cognition).

                                                                                                                                                                                                                                • Agawu, V. Kofi. “Structural Analysis or Cultural Analysis? Competing Perspectives on the ‘Standard Pattern’ of West African Rhythm.” Journal of the American Musicological Society 59.1 (2006): 1–46.

                                                                                                                                                                                                                                  DOI: 10.1525/jams.2006.59.1.1E-mail Citation »

                                                                                                                                                                                                                                  Discusses and evaluates various perspectives on the “standard pattern,” a timeline in West African music. Topics include additive rhythm, rotations of the standard pattern, isomorphisms between pitch and rhythmic structures, relationships to dance, and generative approaches. Maintains the need for both structural and cultural perspectives in analyzing African rhythm.

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                                                                                                                                                                                                                                  • Cohn, Richard. “Complex Hemiolas, Ski-Hill Graphs, and Metric Spaces.” Music Analysis 20.3 (2001): 295–326.

                                                                                                                                                                                                                                    DOI: 10.1111/1468-2249.00141E-mail Citation »

                                                                                                                                                                                                                                    Describes situations of hemiola in which 2:3 rhythmic relationships exist at more than one hierarchical level of rhythm. Visualizes the multiplicity of two- and three-part divisions of time spans with “ski-hill graphs,” in which each path on the graph defines a metric state. How those metric states are disposed within a composition can be conceptualized as a metric space.

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                                                                                                                                                                                                                                    • Cooper, Grosvenor W., and Leonard B. Meyer. The Rhythmic Structure of Music. Chicago: University of Chicago Press, 1960.

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                                                                                                                                                                                                                                      Analyzes rhythms as series of metrical feet derived from prosody; these feet occur on lower and higher architectonic levels. Regards rhythm as distinct from meter, and interprets rhythm in relation to notions of mobility and tension, and to form.

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                                                                                                                                                                                                                                      • Hasty, Christopher. Meter as Rhythm. New York: Oxford University Press, 1997.

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                                                                                                                                                                                                                                        Presents a theory of musical meter involving projection, in which perceived durations imply that they will be reproduced, and in which beginnings of durations imply continuations. In this theory, meter exists in a process of becoming, and as a creative force it is regarded as fundamentally rhythmic.

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                                                                                                                                                                                                                                        • Kramer, Jonathan D. The Time of Music: New Meanings, New Temporalities, New Listening Strategies. New York: Macmillan, 1988.

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                                                                                                                                                                                                                                          Comprehensive source on experiences of musical time. Defines five different musical temporalities: goal-directed linear time, nondirected linear time, moment time, multiply-directed time, and vertical time. Considers the effects of technology on musical time.

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                                                                                                                                                                                                                                          • Krebs, Harald. Fantasy Pieces: Metrical Dissonance in the Music of Robert Schumann. New York: Oxford University Press, 1999.

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                                                                                                                                                                                                                                            Describes states of metrical consonance and dissonance in the music of Schumann. The latter exists in two varieties, grouping dissonance and displacement dissonance, and may be articulated directly or indirectly. Regards the interaction of dissonant strata as constituting meter.

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                                                                                                                                                                                                                                            • Lester, Joel. The Rhythms of Tonal Music. Carbondale: Southern Illinois University Press, 1986.

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                                                                                                                                                                                                                                              Theory of rhythm and meter in 18th- and 19th-century music. Discusses how meter is cued musically with accents; considers hypermeter and relationships of rhythm and meter to form.

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                                                                                                                                                                                                                                              Schenkerian Theories

                                                                                                                                                                                                                                              Schenker wrote a chapter on rhythm and meter in Free Composition (Schenker 1979, cited under Treatises and Essays), but his work has sometimes been criticized for undervaluing these important dimensions. His writings, as well as such criticism, inspired Carl Schachter’s three essays on rhythm (see Schacter 1999). The pitch-to-rhythm methodology in Yeston 1976 is based on Schenker’s concept of structural levels, and Rothstein 1989, on phrase rhythm, also adopts a Schenkerian perspective. Komar 1971 builds on Schenker’s theory of pitch relations to construct a theory of meter. Principal concerns in these texts include interactions between tonal structures and temporal structures, the hierarchical organization of rhythmic and metric units, and techniques of phrase expansion or contraction. McClelland 2006 offers several rhythmic and metric analyses from a Schenkerian perspective, and Westergaard 1975, cited under Textbooks, offers pedagogical applications of a Schenkerian approach to rhythm.

                                                                                                                                                                                                                                              • Komar, Arthur J. Theory of Suspensions: A Study of Metrical and Pitch Relations in Tonal Music. Princeton, NJ: Princeton University Press, 1971.

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                                                                                                                                                                                                                                                Derived largely from Komar’s doctoral dissertation. Includes a theory of meter as a necessary prerequisite to discussion of suspensions. Builds on Schenkerian theories of pitch relations.

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                                                                                                                                                                                                                                                • McClelland, Ryan. “Extended Upbeats in the Classical Minuet: Interactions with Hypermeter and Phrase Structure.” Music Theory Spectrum 28.1 (2006): 23–56.

                                                                                                                                                                                                                                                  DOI: 10.1525/mts.2006.28.1.23E-mail Citation »

                                                                                                                                                                                                                                                  Analytic article that considers the effects of extended upbeat gestures on hypermetric structure in minuet movements by Haydn, Mozart, and Brahms.

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                                                                                                                                                                                                                                                  • Rothstein, William. Phrase Rhythm in Tonal Music. New York: Schirmer, 1989.

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                                                                                                                                                                                                                                                    Defines phrase rhythm as the interaction of phrase structure with meter and hypermeter. Discusses techniques of phrase overlap and expansion, the manipulation of hypermeter and general relationships between phrase rhythm and form. Offers analytic chapters on Chopin, Haydn, Mendelssohn, and Wagner.

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                                                                                                                                                                                                                                                    • Schachter, Carl. “Rhythm and Linear Analysis.” In Unfoldings: Essays in Schenkerian Theory and Analysis. Edited by Joseph N. Straus, 17–188. New York: Oxford University Press, 1999.

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                                                                                                                                                                                                                                                      Series of three articles. Introduces Schenker’s theories of rhythm and meter, presents the technique of durational reduction as an analytic tool, and considers qualities of accent, hypermeter, and rhythmic dissonance.

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                                                                                                                                                                                                                                                      • Yeston, Maury. The Stratification of Musical Rhythm. New Haven, CT: Yale University Press, 1976.

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                                                                                                                                                                                                                                                        Employs pitch-to-rhythm and rhythm-to-pitch methodologies to analyze rhythmic subpatterns as strata. These strata can exist in relationships of consonance or dissonance; meter results from the interaction of two consonant strata. Describes abstract inclusion relationships of rhythmic patterns, influenced by Allen Forte’s set-complex theory.

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                                                                                                                                                                                                                                                        Twentieth-Century Music

                                                                                                                                                                                                                                                        Nearly all studies of rhythm and meter in tonal music recognize the importance of harmony in the interpretation of rhythmic and metric events. Music that does not rely on tonal conventions challenges theorists to conceive of new ways to explain temporalities. Babbitt 1962 considers how timepoints can be analogous to pitch classes in twelve-tone music, and their implications in electronic music. Hasty 1984 investigates the in-time formation of phrases in post-tonal music. John Roeder analyzes rhythm in terms of strata in Schoenberg’s music and adopts an approach based on set theory to analyze Reich’s music (see Roeder 2003 and Roeder 1994). Hook 1998 characterizes the rhythms that occur in Messaien’s Turangalîla Symphony using an algebraic approach. See Hasty 1997 and Kramer 1988, cited under Rhythm, Meter, and Temporality, for additional investigations of post-tonal rhythm and meter.

                                                                                                                                                                                                                                                        • Babbitt, Milton. “Twelve-Tone Rhythmic Structure and the Electronic Medium.” Perspectives of New Music 1.1 (1962): 49–79.

                                                                                                                                                                                                                                                          DOI: 10.2307/832179E-mail Citation »

                                                                                                                                                                                                                                                          First considers how invariants under basic twelve-tone operations have rhythmic implications. Continues to develop serial techniques for timepoints, interpreted analogously to pitch classes (with some exceptions). Argues that the precision of electronic media is required to realize fully the possibilities of twelve-tone rhythmic structures.

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                                                                                                                                                                                                                                                          • Hasty, Christopher. “Phrase Formation in Post-Tonal Music.” Journal of Music Theory 28.2 (1984): 167–190.

                                                                                                                                                                                                                                                            DOI: 10.2307/843531E-mail Citation »

                                                                                                                                                                                                                                                            An investigation into how listeners group musical events into phrases in post-tonal music. Suggests an in-time process that draws on the psychological work of William James, in which phrase constituents are perceived as simultaneously present. Demonstrates how these constituents cohere as phrases, and how phrase closure is articulated. Includes analyses of Stravinsky and Webern.

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                                                                                                                                                                                                                                                            • Hook, Julian. “Rhythm in the Music of Messiaen: An Algebraic Study and an Application to the Turangalîla Symphony.” Music Theory Spectrum 20.1 (1998): 97–120.

                                                                                                                                                                                                                                                              DOI: 10.1525/mts.1998.20.1.02a00040E-mail Citation »

                                                                                                                                                                                                                                                              Develops a system to describe and classify durational patterns in Messiaen’s Turangalîla Symphony. Represents these patterns algebraically, describes several operations that can be performed on them, and shows ways that they can be generated from smaller “seeds.” Discusses interactions of pitch and rhythm.

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                                                                                                                                                                                                                                                              • Roeder, John. “Interacting Pulse Streams in Schoenberg’s Atonal Polyphony.” Music Theory Spectrum 16.2 (1994): 231–249.

                                                                                                                                                                                                                                                                DOI: 10.1525/mts.1994.16.2.02a00050E-mail Citation »

                                                                                                                                                                                                                                                                Separates the irregular rhythmic surfaces of Schoenberg’s music into layers of pulse streams of regular accents; the interactions of pulse streams are shown to influence form.

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                                                                                                                                                                                                                                                                • Roeder, John. “Beat-Class Modulation in Steve Reich’s Music.” Music Theory Spectrum 25.2 (2003): 275–304.

                                                                                                                                                                                                                                                                  DOI: 10.1525/mts.2003.25.2.275E-mail Citation »

                                                                                                                                                                                                                                                                  An analysis of Reich’s post-phase music that interprets rhythmic patterns using techniques of set theory (identifying beat-class sets, rather than pitch-class sets, based on Cohn 1992, cited under Post-Tonal Music). Recognizes the interdependence of pitch and meter in this music. Based on several defined categories of accent, understands beat-class sets as analogous to pitch structures, with modes and tonics.

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                                                                                                                                                                                                                                                                  Form

                                                                                                                                                                                                                                                                  European 19th-century theorists established the Formenlehre tradition, i.e., the school-forms descriptions of sonata, rondo, variation, and so on. By the early 20th century, theorists such as Heinrich Schenker questioned the value of mechanistically labeling functional parts, key areas, and the themes associated with them. However, recent research dealing with common-practice sonata form has attempted to wed the notion of functioning parts with Schenkerian practice. Other literature specifically concerned with extended tonal music has used either neo-Riemannian theory or the idea of a “double-tonic complex” to elucidate form. By contrast, there are virtually no general theories of form in post-tonal music. Research largely consists of the analysis of a broad spectrum of works exhibiting different types of formal processes: open form, moment form, chance form, minimalist palindromes, or twelve-tone form generated by time-point structures.

                                                                                                                                                                                                                                                                  Tonal Music

                                                                                                                                                                                                                                                                  Schoenberg 1967 introduces crucial notions in his study of tonal form (e.g., sentence form, motivic reduction, liquidation, and tonal problem), which have influenced generations of later theorists, including Schoenberg’s student Erwin Ratz and the Canadian theorist William Caplin. (For further discussion of sentence form, motivic reduction, liquidation, and tonal problem in Schoenberg’s theories, see Carpenter and Neff 1995, cited under Influences on American Theory.) Caplin 1998 and Hepokoski and Darcy 2006 propose theories of sonata form for common-practice music. On the one hand, Caplin 1998 asserts that several grouping structures or formal functions (e.g., the sentence and the period) can most successfully describe the inner and outer workings of a sonata. On the other, Hepokoski and Darcy 2006 understands the sonata as a rotational form, consistently reworking aspects of works’ opening themes. Forms other than sonata have received little treatment in the scholarly literature. Donald Tovey’s classic, stylistically based work about the forms of tonal music (e.g., sonata, variation, and rondo) and Robert Nelson’s book on variation remain significant reference works (Tovey 1956 and Nelson 1948). Renwick 1995, which applies Schenkerian analysis to Baroque contrapuntal pieces, is unique in topic. Robert Bailey’s theory of the double-tonic complexes focuses on the works of Wagner and the highly chromatic Austro-German literature of the early 20th century (Bailey 1985).

                                                                                                                                                                                                                                                                  • Bailey, Robert. Prelude and Transfiguration from Tristan and Isolde. Norton Critical Scores. New York: Norton, 1985.

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                                                                                                                                                                                                                                                                    Defines a theory of form determined by double-tonic complex, e.g., the pairing of A minor and C major as a background for Wagner’s Tristan and Isolde. Allows such multiple meanings on simultaneous levels of a work. Theory allows compositions to end on a composite, dissonant sonority.

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                                                                                                                                                                                                                                                                    • Caplin, William E. Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven. New York: Oxford University Press, 1998.

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                                                                                                                                                                                                                                                                      Extension and Schenkerian-influenced reinterpretation of the Formenlehre theories of Schoenberg’s student Erwin Ratz. Investigates the use of Ratz’s formal functions (e.g., the sentence and the period) and their variants in hundreds of instrumental works by Haydn, Mozart, and Beethoven. Offers an extended glossary of terms associated with the method.

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                                                                                                                                                                                                                                                                      • Hepokoski, James, and Warren Darcy. The Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata. Oxford: Oxford University Press, 2006.

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                                                                                                                                                                                                                                                                        Claims that sonata form is not so much ternary, binary, or symmetrical but cyclic and rotational instead. Defines rotation in several varieties: double, tri- or quadrirotational resulting in five sonata types; views the basic theme as the “Essential Sonata Trajectory,” an ordered succession influencing large-scale structures. Analyzes numerous compositions of the Classical era.

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                                                                                                                                                                                                                                                                        • Nelson, Robert. The Technique of Variation: A Study of the Instrumental Variation from Antonio de Cabezón to Max Reger. Berkeley: University of California Press, 1948.

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                                                                                                                                                                                                                                                                          A historical chronology of works in and techniques of the theme and variation. Commentary is less a general theory than the analysis of particular works; shows influence of notion of “developing variation” of Nelson’s teacher and colleague Arnold Schoenberg.

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                                                                                                                                                                                                                                                                          • Renwick, William. Analyzing Fugue: A Schenkerian Approach. Stuyvesant, NY: Pendragon, 1995.

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                                                                                                                                                                                                                                                                            The major work considering the role of Schenkerian theory in the analysis of contrapuntal works.

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                                                                                                                                                                                                                                                                            • Schoenberg, Arnold. Fundamentals of Musical Composition. Edited by Gerald Strang and Leonard Stein. London: Faber and Faber, 1967.

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                                                                                                                                                                                                                                                                              A text on tonal form containing the first published discussions of sentence form, motivic reduction, liquidation, and tonal problem; these concepts are fundamental to the work of Schoenberg’s Viennese student Erwin Ratz, whose work strongly influenced the theories of Canadian theorist William Caplin.

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                                                                                                                                                                                                                                                                              • Tovey, Donald. The Forms of Music. New York: Meridian, 1956.

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                                                                                                                                                                                                                                                                                A stylistic approach to the study of form that is piece-specific. Considers sonata, variation, rondo, and other school forms.

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                                                                                                                                                                                                                                                                                Post-Tonal Music

                                                                                                                                                                                                                                                                                Tenney 1971 is one of the few sources attempting to characterize 20th-century form as a whole. Tenney proposes that all form consists of three levels (elements, the Klang, and the sequence) treated either isomorphically, metamorphically, or heteromorphically. By contrast, Kramer 1978 sees Stockhausen’s technique of “moment form” as a common practice in a variety of 20th-century music. Mead 1985 and Babbitt 1962 (cited under Twentieth-Century Music) describe large-scale form in twelve-tone music. DeLio 1980–1981 considers the formal elements of Cage’s “chance” piece Variations II, differentiating between those elements that remain fixed in Cage’s conceptual framework and those that are continually altered by “chance” procedures. Cohn 1992 discusses the formal implications of phasing and beat patterning in Reich’s minimalist works. Welsh 1994 discusses Earle Brown’s notion of “Open Form.” Hirata 1996 investigates the temporal/spatial designs of Feldman impacting his sense of form. For the relationship of form and transformational theory, see Cohn 1996 and Cohn 1997 (both cited under Transformational Theory).

                                                                                                                                                                                                                                                                                • Cohn, Richard. “Transpositional Combination of Beat-Class Sets in Steve Reich’s Phase-Shifting Music.” Perspectives of New Music 30.2 (1992): 146–177.

                                                                                                                                                                                                                                                                                  DOI: 10.2307/3090631E-mail Citation »

                                                                                                                                                                                                                                                                                  A discussion of what Reich means by form and process. Discusses deep scale structures, attack-point patterning, and beat patterning in Phase Patterns and Violin Phase.

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                                                                                                                                                                                                                                                                                  • DeLio, Thomas. “John Cage’s Variations II: The Morphology of a Global Structure.” Perspectives of New Music 19.1–2 (1980–1981): 351–371.

                                                                                                                                                                                                                                                                                    DOI: 10.2307/832599E-mail Citation »

                                                                                                                                                                                                                                                                                    Discusses the dimensions of form in chance with a case study of Variations II by Cage. Concludes that there are certain dimensions that remain the same no matter how the processes of the chance piece are realized.

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                                                                                                                                                                                                                                                                                    • Hirata, Catherine Costello. “The Sounds of the Sounds Themselves: Analyzing the Early Music of Morton Feldman.” Perspectives of New Music 34.1 (1996): 6–27.

                                                                                                                                                                                                                                                                                      DOI: 10.2307/833482E-mail Citation »

                                                                                                                                                                                                                                                                                      Engages what memory and continuity mean in Morton Feldman’s work when the composer offers the advice to “listen to the sounds themselves.” Analyzes Feldman’s “Last Pieces” in this regard, and discusses the meaning of its temporal and registral space.

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                                                                                                                                                                                                                                                                                      • Kramer, Jonathan. “Moment Form in Twentieth Century Music.” Musical Quarterly 64.2 (1978): 177–194.

                                                                                                                                                                                                                                                                                        DOI: 10.1093/mq/LXIV.2.177E-mail Citation »

                                                                                                                                                                                                                                                                                        Extends composer Karlheinz Stockhausen’s compositional approach in which the logical continuity of a work’s structure is deliberately avoided. Sees “moment form” as a major formal principle in 20th-century music.

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                                                                                                                                                                                                                                                                                        • Mead, Andrew. “Large-Scale Strategy in Arnold Schoenberg’s Twelve-Tone Music.” Perspectives of New Music 24.1 (1985): 120–157.

                                                                                                                                                                                                                                                                                          DOI: 10.2307/832765E-mail Citation »

                                                                                                                                                                                                                                                                                          Discusses how details of a twelve-tone composition assimilate into its large-scale structure. Proposes that short prominent passages before the final cadence act as a nexus for recalling all the significant materials, thus rounding out the form.

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                                                                                                                                                                                                                                                                                          • Tenney, James. “Form.” In Dictionary of Contemporary Music. Edited by John Vinton, 242–247. New York: E. F. Dutton, 1971.

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                                                                                                                                                                                                                                                                                            Names three levels of form: the element (i.e., basic configurations of pitches and rhythms), the Klang (i.e., the overall sound of the elements and their implications for or against tonality), and the sequence (i.e., the functions of units [Gestalten] within a form). Interactions of these levels describe the three generic processes at work in large-scale forms: isomorphic (i.e., repetitive), metamorphic (i.e., developmental), and heteromorphic (i.e., using juxtapositions).

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                                                                                                                                                                                                                                                                                            • Welsh, John P. “Open Form and Earle Brown’s Modules I and II (1967).” Perspectives of New Music 32.1 (1994): 254–290.

                                                                                                                                                                                                                                                                                              DOI: 10.2307/833173E-mail Citation »

                                                                                                                                                                                                                                                                                              A discussion of Earle Brown’s concept of “Open Form,” i.e., a set of fixed modules the order of which is chosen during performance by the conductor. Relates the history and characteristics of form to mobiles in visual art. Presents an analysis of Brown’s Modules I and II, showing the strong coherence of materials in the work—whatever their order.

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                                                                                                                                                                                                                                                                                              Performance

                                                                                                                                                                                                                                                                                              Theorists are often performers as well; indeed, the pianist Heinrich Schenker’s writings on theory and analysis were conceived in light of his performances. Schenker maintained that only a performer’s deep knowledge of a work’s structural features could shape successful performances. Many of the sources cited here consider how performance can be guided by and can reveal structures uncovered through analysis. Burkhart 1983 presents examples of the relationship of Schenkerian analysis to performance, and Schmalfeldt 1985 considers both the role of analysis in performance and how analysis can address the questions of performers. For Edward T. Cone performance consists of articulated structures chosen from many such options in any given work (see Cone 1968). Alexandra Pierce adopts a pedagogical stance toward performance and analysis in her book on embodied interpretation (Pierce 2007). A few scholars have explored other interfaces of performance and analysis. Dodson 2008, for example, takes particular recorded performances as objects of analysis. Another possibility is the analysis of the act of performance, embracing the threefold study of movement, performance psychology, and communication. Rink 1995 contains examples of all three of these possibilities. Finally, Cook 1999 locates the act of analysis itself in the realm of performance and discusses its performative aspects.

                                                                                                                                                                                                                                                                                              • Burkhart, Charles. “Schenker’s Theory of Levels and Musical Performance.” In Aspects of Schenkerian Theory. Edited by David Beach, 95–112. New Haven, CT: Yale University Press, 1983.

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                                                                                                                                                                                                                                                                                                Considers how performance influenced by Schenkerian analysis can be guided by background structures and motivic parallelisms; in the case of piano music, the choice of fingering may be helpful in articulating structure.

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                                                                                                                                                                                                                                                                                                • Cone, Edward T. Musical Form and Musical Performance. New York: Norton, 1968.

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                                                                                                                                                                                                                                                                                                  Trilogy of essays on the relationships between performance and form. Form is largely conceived rhythmically, and rhythmic principles are demonstrated to shape entire compositions. Rhythmic characteristics of various styles are described. An epilogue discusses some of the philosophical bases of this volume.

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                                                                                                                                                                                                                                                                                                  • Cook, Nicholas. “Analysing Performance and Performing Analysis.” In Rethinking Music. Edited by Nicholas Cook and Mark Everist, 239–261. Oxford: Oxford University Press, 1999.

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                                                                                                                                                                                                                                                                                                    Criticizes the structuralist orientation of prescriptive performance studies, in which performances can only express a priori musical structures. Instead raises the possibility that structures are constituted through performance; applies this distinction to the act of analysis itself, and shows how analysis has performative aspects favoring pluralism.

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                                                                                                                                                                                                                                                                                                    • Dodson, Alan. “Performance, Grouping, and Schenkerian Alternative Readings in Some Passages from Beethoven’s ‘Lebewohl’ Sonata.” Music Analysis 27.1 (2008): 107–134.

                                                                                                                                                                                                                                                                                                      DOI: 10.1111/j.1468-2249.2008.00269.xE-mail Citation »

                                                                                                                                                                                                                                                                                                      Develops a methodology to study recorded performances by comparing them with Schenkerian analyses. Focuses on rhythmic grouping of passages in which more than one Schenkerian reading may be possible and discusses how multiple groupings can be projected in performance.

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                                                                                                                                                                                                                                                                                                      • Pierce, Alexandra. Deepening Musical Performance through Movement: The Theory and Practice of Embodied Interpretation. Bloomington: Indiana University Press, 2007.

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                                                                                                                                                                                                                                                                                                        Pedagogically oriented study showing the ways an embodied understanding of music can guide performance and interpretation. Adopts a Schenkerian approach to musical structure, and maps different structural features of music to different aspects of movement.

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                                                                                                                                                                                                                                                                                                        • Rink, John, ed. The Practice of Performance: Studies in Musical Interpretation. Cambridge, UK: Cambridge University Press, 1995.

                                                                                                                                                                                                                                                                                                          DOI: 10.1017/CBO9780511552366E-mail Citation »

                                                                                                                                                                                                                                                                                                          Diverse collection of essays by Edward T. Cone, Joel Lester, William Rothstein, and others on musical performance and analysis. Includes writing on the analysis of performance, both of specific performances and of the act of performing, as well as on projecting analytic decisions through performance.

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                                                                                                                                                                                                                                                                                                          • Schenker, Heinrich. The Art of Performance. Edited by Heribert Esser. Translated by Irene Schreier Scott. New York: Oxford University Press, 2000.

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                                                                                                                                                                                                                                                                                                            Originally published as Der Kunst des Vortrags. Schenker’s thoughts on performance, especially of piano music. Assembled from unfinished writings.

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                                                                                                                                                                                                                                                                                                            • Schmalfeldt, Janet. “On the Relation of Analysis to Performance: Beethoven’s Bagatelles Op. 126, Nos. 2 and 5.” Journal of Music Theory 29.1 (1985): 1–31.

                                                                                                                                                                                                                                                                                                              DOI: 10.2307/843369E-mail Citation »

                                                                                                                                                                                                                                                                                                              Explores relationships between analysis and performance by alternately assuming the point of view of a theorist and a pianist. Specifically discusses two Beethoven bagatelles and considers both how the theorist’s work can affect a performer’s interpretation and, conversely, how a theorist can respond to questions raised by performance.

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                                                                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                                                                              The citations below describe the nature of Western music theory and composition from ancient Greece to the 20th century. Mathiesen 1999 explores the ancient Greeks’ interpretation of music’s mathematical constructions as well as their role in society. Essays in Judd 1998 engage tonal aspects of Medieval and Renaissance composition. Lester 1992 describes issues in contrapuntal theory and pedagogy from the late Renaissance to the middle of the 18th century. Bent 1996 considers issues of chromatic tonality and Romantic aesthetics in the 19th century. Wason 1985 elucidates the influence of the 19th-century Viennese theorist Simon Sechter on Schenker and Schoenberg. The dictionary entry Powers, et al. 2010 on the meaning of mode from ancient Greece to the 20th century is a classic article. Lindley 1982 offers exhaustive older bibliography for each historical era and recommends course plans for graduate seminars in the subject. See also Christensen 2002, cited under General Overviews.)

                                                                                                                                                                                                                                                                                                              • Bent, Ian. Music Theory in the Age of Romanticism. Cambridge, UK: Cambridge University Press, 1996.

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                                                                                                                                                                                                                                                                                                                Theoretical concepts in the era termed “Romantic.” Topics include piano pedagogy and touch, Schelling and hermeneutics, the nature of Fétis’s concept of tonality, reception of the “Eroica,” Vogler’s and Weber’s work as a precursor of pitch-class invariance, and others; attention also given to the theories of Reicha and Marx.

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                                                                                                                                                                                                                                                                                                                • Damschroder, David, and David Russell Williams. Music Theory from Zarlino to Schenker: A Bibliography and Guide. Stuyvesant, NY: Pendragon, 1990.

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                                                                                                                                                                                                                                                                                                                  A basic introduction to the theorists and treatises of the 16th to early 20th centuries; written for the nonspecialist in history of theory.

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                                                                                                                                                                                                                                                                                                                  • Judd, Cristle Collins. Tonal Structures in Early Music. New York: Garland, 1998.

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                                                                                                                                                                                                                                                                                                                    Collection of essays using historical models to trace tonal ideas to earlier centuries. Includes analyses of Josquin, Machaut, and others. Argues that 17th-century key signatures are related to Renaissance practice.

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                                                                                                                                                                                                                                                                                                                    • Lester, Joel. Compositional Theory in the 18th Century. Cambridge, MA: Harvard University Press, 1992.

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                                                                                                                                                                                                                                                                                                                      Classic study of theory in the 18th century. Shows how theory in this era develops from Zarlino and Rameau; comments on a wide range of theorists (e.g. Matheson, Marpurg, and Riepel); includes Mozart’s commentary on his students’ species counterpoint.

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                                                                                                                                                                                                                                                                                                                      • Lindley, Mark. “Preface to a Graduate Course in the History of Music Theory.” College Music Symposium 22.2 (1982): 83–102.

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                                                                                                                                                                                                                                                                                                                        Contains exhaustive bibliography of general history of theory and suggestions for constructing graduate seminars in the history of theory.

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                                                                                                                                                                                                                                                                                                                        • Mathiesen, Thomas. Apollo’s Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages. Lincoln: University of Nebraska Press, 1999.

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                                                                                                                                                                                                                                                                                                                          Classic text discussing Western music theory in the ancient and medieval eras.

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                                                                                                                                                                                                                                                                                                                          • Powers, Harold, et al. “Mode.” In Grove Music Online. 2010.

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                                                                                                                                                                                                                                                                                                                            Classic discussion of the meaning of mode in all historical eras and in non-Western repertories. Available online by subscription.

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                                                                                                                                                                                                                                                                                                                            • Wason, Robert. Viennese Harmonic Theory from Albrechtsberger to Schenker and Schoenberg. Ann Arbor: UMI Research Press, 1985.

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                                                                                                                                                                                                                                                                                                                              Traces the Viennese tradition of theory. Shows Sechter’s harmonic work as leading to the later harmonic treatise of Schoenberg. Reveals Sechter’s contrapuntal theory as strongly influencing Schenker.

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                                                                                                                                                                                                                                                                                                                              • Williams, David Russell, and C. Matthew Balensuela. Music Theory from Boethius to Zarlino: A Bibliography and Guide. Hillsdale, NY: Pendragon, 2007.

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                                                                                                                                                                                                                                                                                                                                The companion volume to Damschroder and Williams 1990.

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                                                                                                                                                                                                                                                                                                                                Treatises and Essays

                                                                                                                                                                                                                                                                                                                                The following treatises have strongly influenced the content of a tripartite course of study required by American theory programs. The species counterpoint of Fux 1971 (highly influenced by Zarlino 1976) is a mainstay of Schenkerian analysis. Schoenberg’s compositional thought (Schoenberg 1984 to the need for set theory and Babbitt’s theories of twelve-tone music. Rameau 1971 is a major source for Schoenberg’s ideas about harmony.

                                                                                                                                                                                                                                                                                                                                • Fux, Johannes Joseph. The Study of Counterpoint : From Johann Joseph Fux’s Gradus ad Parnassum. Translated and edited by Alfred Mann. New York: Norton, 1971.

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                                                                                                                                                                                                                                                                                                                                  Originally published 1725. A practical description of the art of counterpoint based largely on the music of Palestrina, broken down into pedagogical steps, or species. This text was used by many composers including Haydn, Mozart, and Beethoven.

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                                                                                                                                                                                                                                                                                                                                  • Rameau, Jean-Philippe. Treatise on Harmony. Translated by Philip Gossett. New York: Dover, 1971.

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                                                                                                                                                                                                                                                                                                                                    Originally published 1722. Establishes the basis for Western harmonic theory; novel to contemporary theory by distinguishing between harmony and counterpoint. Book 1 describes Rameau’s mathematical basis; Book 2, historically the most influential, describes the nature of chords and inversions. Books 3 and 4 are practical, dealing with composition and accompaniments, respectively.

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                                                                                                                                                                                                                                                                                                                                    • Schenker, Heinrich. Free Composition (Der freie Satz). Translated by Ernst Oster. New York: Longman, 1979.

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                                                                                                                                                                                                                                                                                                                                      The culmination of Schenker’s theories on tonal structure.

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                                                                                                                                                                                                                                                                                                                                      • Schoenberg, Arnold. Style and Idea. Edited by Leonard Stein. Translated by Leo Black. Berkeley: University of California Press, 1984.

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                                                                                                                                                                                                                                                                                                                                        Collection of essays of Schoenberg’s thoughts on extended tonality, counterpoint, the nature of twelve-tone tonality, twelve-tone music, and tonal form.

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                                                                                                                                                                                                                                                                                                                                        • Zarlino, Gioseffo. The Art of Counterpoint. Translated by Guy A. Marco and Claude Palisca. New York: Norton, 1976.

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                                                                                                                                                                                                                                                                                                                                          Originally published 1558. One of main treatises on Renaissance counterpoint; discusses tuning, mode, consonance-dissonance, invertible counterpoint; strong influence on the work of Fux.

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                                                                                                                                                                                                                                                                                                                                          Influences on American Theory

                                                                                                                                                                                                                                                                                                                                          The following texts address the work of late-19th- and early-20th-century theorists whose concepts had a major impact on American theory. Berry 2005 discusses the role of Schenker’s thought in American theoretical circles. Carpenter and Neff’s introduction to The Musical Idea (Carpenter and Neff 1995) discusses Schoenberg’s philosophical-musical values and notions of theory and analysis. Rehding 2003 is an intellectual history of Riemann that elucidates his influential theories of function. Rothfarb 1988 emphasizes Kurth’s notions of energetics—concepts that have arisen in many recent articles about the apperception of form.

                                                                                                                                                                                                                                                                                                                                          • Berry, David Carson. “Schenkerian Theory in the United States: A Review of Its Establishment and a Survey of Current Research Topics.” Zeitschrift der Gesellschaft für Musiktheorie 2.2–3 (2005): 101–137.

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                                                                                                                                                                                                                                                                                                                                            Traces the history of how and why Schenkerian theory found an audience in the United States.

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                                                                                                                                                                                                                                                                                                                                            • Carpenter, Patricia, and Severine Neff. “Commentary.” In The Musical Idea and the Logic, Technique and Art of its Presentation by Arnold Schoenberg. By Arnold Schoenberg, 1–86. New York: Columbia University Press, 1995.

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                                                                                                                                                                                                                                                                                                                                              Abridged edition, Bloomington: Indiana University Press, 2006. Edition and translation of Schoenberg’s 1934–1936 treatise on the “musical idea and its presentation.” Discusses Schoenberg’s notion of idea, its sources in German Idealism, and its impact on his compositional and analytic notions including “developing variation,” “Grundgestalt,” “contrapuntal combination,” and “unity of the musical space.” Includes Schoenberg’s analytic notes on Bach, Beethoven, Brahms, and Mozart.

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                                                                                                                                                                                                                                                                                                                                              • Rehding, Alexander. Hugo Riemann and the Birth of Modern Musical Thought. Cambridge, UK: Cambridge University Press, 2003.

                                                                                                                                                                                                                                                                                                                                                DOI: 10.1017/CBO9780511481369E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                Intellectual biography of theorist Hugo Riemann. Discusses aesthetics, dualism, and other theories; compares Riemann’s theories to those of Hermann von Helmholtz; points out his self-serving attitude to music-theoretical history (e.g., the dubious statement that Zarlino, too, was a harmonic dualist).

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                                                                                                                                                                                                                                                                                                                                                • Rothfarb, Lee. Ernst Kurth as Theorist and Analyst. Philadelphia: University of Pennsylvania Press, 1988.

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                                                                                                                                                                                                                                                                                                                                                  Considers Kurth’s theories of “energetics” focusing on “developmental motive” (i.e., one gradually changes or grows, becoming a structural carrier of development) and dynamic form.

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                                                                                                                                                                                                                                                                                                                                                  New Paradigms and Approaches

                                                                                                                                                                                                                                                                                                                                                  The following subject categories discuss paradigms and approaches that do not contribute strongly to the traditional tripartite study of Schenkerian studies, set theory, history of theory, and its extensions but offer new areas of theoretical inquiry instead.

                                                                                                                                                                                                                                                                                                                                                  Challenges from the New Musicology and Music Criticism

                                                                                                                                                                                                                                                                                                                                                  In the 1980s, the musicologists Kerman, Subotnik, Tomlinson, and Treitler questioned the value of formalist music theories such as Babbitt’s and Forte’s and argued instead for a culturally based music criticism aware of social, political, and interdisciplinary issues. Their critiques at the expense of the field of positivist music theory and analysis motivated the investigation of new paradigms for music scholarship. Their stance was labeled the New Musicology. Kerman 1980 recommends the expansion of analytic study beyond the methodologies finding types of organic unity in masterpieces of the Austro-German canon. Kerman 1985 and Treitler 1989 credit positivistic and formalist approaches with limiting the power of musical research. Tomlinson 1984 supports anthropologist Clifford Geertz’s research methodologies of “thick” description for music criticism. Subotnik 1983 advocates the values of Continental philosophy for determining a new form of criticism for musicology. One of the emphases of McClary 1991 is the relationship of gender to music analysis. The work of these musicologists has encouraged many responses from theorists.

                                                                                                                                                                                                                                                                                                                                                  • Kerman, Joseph. “How We Got into Analysis and How We Can Get Out.” Critical Inquiry 7.2 (1980): 311–332.

                                                                                                                                                                                                                                                                                                                                                    DOI: 10.1086/448101E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                    Describes analysis as a type of musical criticism empirically defining the functional coherence or “organic unity” of musical masterpieces; the practice of analysis propounds the ideology of the German canon and Hanslick’s formalist view of musical study. Traces the historical path of analytic activity from Forkel to the works of Schenker and Babbitt; recommends the need for alternatives to formalist analysis.

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                                                                                                                                                                                                                                                                                                                                                    • Kerman, Joseph. Contemplating Music: Challenges to Musicology. Cambridge, MA: Harvard University Press, 1985.

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                                                                                                                                                                                                                                                                                                                                                      A classic text changing the direction of a discipline. Claims that the agendas, priorities, and methodologies of musicology are dominated by the ideology of positivism, and advocates music criticism that encourages study beyond the compiling of empirical data, such as matters of affect, expression, and meaning in cultural contexts. Values the study of the musical and the extramusical.

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                                                                                                                                                                                                                                                                                                                                                      • McClary, Susan. Feminine Endings: Music, Gender, and Sexuality. Minneapolis: University of Minnesota Press, 1991.

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                                                                                                                                                                                                                                                                                                                                                        Collection of essays on gender and sexuality and musical signification. Investigates not only how gender is constructed in music and how metaphors of sexuality underlie musical narratives, but also how discourse about music and music theory is cast in gendered terms. Analyzes music from diverse repertories, including common-practice tonal music, Monteverdi, and popular music.

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                                                                                                                                                                                                                                                                                                                                                        • Subotnik, Rose Rosengard. “The Role of Ideology in the Study of Western Music.” Journal of Musicology 2.1 (1983): 1–12.

                                                                                                                                                                                                                                                                                                                                                          DOI: 10.1525/jm.1983.2.1.03a00010E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                          Discussion of the role of ideology in musical discourse. Explains that the point of departure for inquiry in Continental philosophy is an ideology, not an artifact; by contrast, Anglo-American philosophy begins and ends with empirical assertions about an object. Recommends the Continental view to lead toward a new criticism for musicology.

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                                                                                                                                                                                                                                                                                                                                                          • Tomlinson, Gary. “The Web of Culture: A Context for Musicology.” 19th-Century Music 7.3 (1984): 350–362.

                                                                                                                                                                                                                                                                                                                                                            DOI: 10.1525/ncm.1984.7.3.02a00140E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                            Values the nontheoretical, antipositivist criteria of “thick” description as conceived by cultural anthropologist Clifford Geertz. Believes, like Treitler, that musicology should aim for contextual historiography aimed at producing cultural meaning, not the logical proofs of positivist theory.

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                                                                                                                                                                                                                                                                                                                                                            • Treitler, Leo. Music and the Historical Imagination. Cambridge, MA: Harvard University Press, 1989.

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                                                                                                                                                                                                                                                                                                                                                              Collection of his essays addressing the topic of “historical understanding,” encompassing, among other issues, extensive critiques of formalist approaches without regard to social concerns (compare Tomlinson 1984). Advocates hermeneutic analyses.

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                                                                                                                                                                                                                                                                                                                                                              Responses by Theorists

                                                                                                                                                                                                                                                                                                                                                              Subotnik 1991 offers Adorno-laden, post-positivistic consideration of musical structures and finds new critical vantage points within them; nine essays in Dell’Antonio 2004 offer various responses to Subotnik’s concept of “structural listening.” The Plenary Session of the 1995 Annual Meeting of the Society for Music Theory featured the topic “Contemporary Music Theory and the New Musicology,” and its contents appeared in published form in a 1997 volume of the Journal of Musicology. Among these, Agawu 1997 questions the scholarly identity of New Musicology and asks why new musicologists have not acknowledged work in theory that is not formalist; Brown 1997 lambasts New Musicology for rejecting empirical study as well as not conceiving of an alternative set of guidelines for analytic discourse; and Burnham 1997 supports studying the autonomous musical work because music is indeed a language independent of other forms of expression. McCreless 1997 advocates a serious consideration of the disciplinary spaces that separate cultural studies and formalist theory with an eye toward closing the gaps; Korsyn 2003 takes up issues in McCreless 1997 and suggests a paradigm of reflexive musical scholarship between theory and history. The collection Rethinking Music (Cook and Everist 1999) takes stock of New Musicology in the mid-1990s and the nature of its criticism. Guck 2006 supports cultural values in activities involving music analysis and interprets the nature of analysis as fundamentally listener-oriented.

                                                                                                                                                                                                                                                                                                                                                              • Agawu, Kofi. 1997. “Analyzing Music under the New Musicological Regime.” Journal of Musicology 15.3 (1997): 297–307.

                                                                                                                                                                                                                                                                                                                                                                DOI: 10.1525/jm.1997.15.3.03a00030E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                Summarizes the debate between theory and New Musicology about analysis and its value. Defines New Musicology as a pluralistic field with no essential, foundational, or totalizing discourse. Notes that new musicologists, when analyzing a piece through “social discourse,” do not offer reasons why their commentary cannot take advantage of the detail of traditional analysis. Questions why New Musicology has not acknowledged extensive work in theory that is not formalist.

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                                                                                                                                                                                                                                                                                                                                                                • Brown, Matthew. “‘Adrift on Neurath’s Boat’: The Case for a Naturalized Music Theory.” Journal of Musicology 15.3 (1997): 330–342.

                                                                                                                                                                                                                                                                                                                                                                  DOI: 10.1525/jm.1997.15.3.03a00060E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                  Believes in a theory based on foundations of empirical knowledge. Uses philosopher Otto Neurath’s metaphor of a boat as a representation of knowledge: if sailors on an open sea must reconstruct a ship, any part can be replaced only if there is enough floor on which to stand. Damns New Musicology for rejecting empiricism and not offering a coherent set of guidelines for valuable analytic discourse.

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                                                                                                                                                                                                                                                                                                                                                                  • Burnham, Scott. “Theorists and ‘The Music Itself.’” Journal of Musicology 15.3 (1997): 316–329.

                                                                                                                                                                                                                                                                                                                                                                    DOI: 10.1525/jm.1997.15.3.03a00050E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                    Asserts the validity of studying the autonomous musical work because music is a language that speaks in its own voice without reference to other forms of expression, and at times without external association; yet theorists should make more effort to relate this language to general human values also crucial to musicology. Also suggests that the mind-body problem is most successfully addressed in the field of music.

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                                                                                                                                                                                                                                                                                                                                                                    • Cook, Nicholas, and Mark Everist. Rethinking Music. New York: Oxford University Press, 1999.

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                                                                                                                                                                                                                                                                                                                                                                      Reevaluation of thinking about music in the light of the expansion of the musicological agenda to include a broad range of sociological and ideological issues. Essays address two topics: possible approaches to musical texts and the nature of the discipline of musicology and its future. Examines other issues of reception, canon, gender, and historiography in the New Musicology.

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                                                                                                                                                                                                                                                                                                                                                                      • Dell’Antonio, Andrew ed. Beyond Structural Listening? Postmodern Modes of Hearing. Berkeley: University of California Press, 2004.

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                                                                                                                                                                                                                                                                                                                                                                        Nine essays concerning topics emanating from Rose Subotnik’s discussions of “structural listening.” Articles address several topics: the notion of mastery in structural listening (e.g., analysis and the sexual rhetoric of dominance and control); listening and pain, pleasure, and the sublime (e.g., a reinterpretation of McClary’s association of Beethoven’s Ninth Symphony and rape); and the variety of ways to negotiate the political/social contexts of analytic power (e.g., collective listening on MTV).

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                                                                                                                                                                                                                                                                                                                                                                        • Guck, Marion. “Analysis as Interpretation: Interaction, Intentionality, Invention.” Music Theory Spectrum 28.2 (2006): 191–209.

                                                                                                                                                                                                                                                                                                                                                                          DOI: 10.1525/mts.2006.28.2.191E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                          Advocates a cultural approach to analysis by emphasizing the relationship between music and an active listener. Contends that analysis is not directed at works of music but hearings of music; thus, music is something that exists between sounds and listeners. Presents several examples of such relations.

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                                                                                                                                                                                                                                                                                                                                                                          • Korsyn, Kevin. Decentering Music: A Critique of Contemporary Musical Research. New York: Oxford University Press, 2003.

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                                                                                                                                                                                                                                                                                                                                                                            Diagnoses a crisis of discourse in music scholarship provoking tensions among subdisciplines of theory and history. Embraces pluralist, reflexive musical scholarship and advocates changes in scholarly writing, peer review, and the tenure process.

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                                                                                                                                                                                                                                                                                                                                                                            • McCreless, Patrick. “Rethinking Contemporary Music Theory.” In Keeping Score: Music, Disciplinarity, Culture. Edited by David Schwarz, Anahid Kassabian, and Lawrence Siegel, 13–53. Charlottesville: University of Virginia Press, 1997.

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                                                                                                                                                                                                                                                                                                                                                                              Asserts that the questions and methodologies of “new musicology” as well as the cultural values it embraces are useful and relevant to music theory. Suggests ways to bridge the gap between the subdisciplines of theory and musicology.

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                                                                                                                                                                                                                                                                                                                                                                              • Subotnik, Rose Rosengard. Developing Variations: Style and Ideology in Western Music. Minneapolis: University of Minnesota Press, 1991.

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                                                                                                                                                                                                                                                                                                                                                                                Collection of Subotnik’s essays offering, in the Adorno tradition, a post-positivistic discussion of musical structures embodying ideology (i.e., “the conceptual context that allows the definition of musical utterances”). Following Adorno, interprets late Beethoven as an amalgam of musical materials, techniques, and technology constituting an analogue for “the essential tendencies of a given historical moment.” Also discusses semiotics and post-Kantian aesthetics in relation to Romanticism in music.

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                                                                                                                                                                                                                                                                                                                                                                                Musical Meaning

                                                                                                                                                                                                                                                                                                                                                                                Interpretive texts on the meaning of music engage its power to express emotion, represent the extramusical (e.g., characters, locations, events, and so on), and simulate language. In general, methodologies in this area are aligned either with nonanalytic philosophy, semiotics, or cognition (compare Huron 2006, cited under Cognition).

                                                                                                                                                                                                                                                                                                                                                                                Approaches from Nonanalytic Philosophy

                                                                                                                                                                                                                                                                                                                                                                                Texts beginning in the early 1960s have taken approaches to music’s meaning based on issues in nonanalytic philosophy. Meyer 1961 on emotion and Cone 1974 on voice have remained influential to the present day; Maus 1988, which applies inferences of agency to the study of musical meaning, is a frequently cited work as well.

                                                                                                                                                                                                                                                                                                                                                                                • Cone, Edward T. The Composer’s Voice. Berkeley: University of California Press, 1974.

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                                                                                                                                                                                                                                                                                                                                                                                  Considers music as a type of utterance, and interprets musical meaning in both texted and instrumental compositions according to the various personae or agencies that they may enact.

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                                                                                                                                                                                                                                                                                                                                                                                  • Maus, Fred Everett. “Music as Drama.” Music Theory Spectrum 10 (1988): 56–73.

                                                                                                                                                                                                                                                                                                                                                                                    DOI: 10.1525/mts.1988.10.1.02a00050E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                    Exemplifies description of music’s dramatic structure as a series of actions by indeterminate agents, which can be explained through the inference of psychological states. Responds to the exigency for music criticism described in Kerman 1985 (see Challenges from the New Musicology and Music Criticism), and also challenges scholarship that regards structure and affect as two separate domains.

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                                                                                                                                                                                                                                                                                                                                                                                    • Meyer, Leonard B. Emotion and Meaning in Music. Chicago: University of Chicago Press, 1961.

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                                                                                                                                                                                                                                                                                                                                                                                      Presents a theory of emotion in music, in which affect arises when expectations are inhibited. Noteworthy for its inclusion of examples of non-Western as well as of Western music.

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                                                                                                                                                                                                                                                                                                                                                                                      Semiotic Approaches

                                                                                                                                                                                                                                                                                                                                                                                      Many authors have applied semiotics to musical meaning. In this connection, Hatten 1994 qualifies not only as a semiotic approach but also as a broad theory of music’s meaning, the analytic utility of which has been well established. Several theorists have studied music’s potential for signification, drawing in particular from the semiotic theories of Peirce and Saussure. Agawu 1991, Allenbrook 1992, Hatten 1994, and Hatten 2004 analyze classical music in terms of topics (culturally shared stylistic markers that convey intra- or extramusical associations), an approach previously suggested in Ratner 1980. Cumming 2000 explores how music can signify subjectivity. McCreless 1991 analyzes chromaticism through analogies with syntagmatic and paradigmatic relations in language.

                                                                                                                                                                                                                                                                                                                                                                                      • Agawu, V. Kofi. Playing with Signs: A Semiotic Interpretation of Classic Music. Princeton, NJ: Princeton University Press, 1991.

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                                                                                                                                                                                                                                                                                                                                                                                        Develops a semiotic approach to music of the classical era influenced by Saussure, in which musical topics are regarded as extroversive signs, and voice-leading and formal structures (approached through Schenkerian analysis and beginning-middle-end paradigms) are regarded as introversive; explores the relationships between the two categories of signs in compositions.

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                                                                                                                                                                                                                                                                                                                                                                                        • Allenbrook, Wye J. “Two Threads through the Labyrinth: Topic and Process in the First Movements of K. 332 and K. 333.” In Convention in Eighteenth- and Nineteenth-Century Music: Essays in Honor of Leonard G. Ratner. Edited by Wye J. Allanbrook, Janet M. Levy, and William P. Mahrt, 125–172. Stuyvesant, NY: Pendragon, 1992.

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                                                                                                                                                                                                                                                                                                                                                                                          Analyses of two Mozart sonata movements, demonstrating different ways that topics can be disposed musically, how opposing topics can interact and be integrated, and how continuity can be maintained across diverse topics.

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                                                                                                                                                                                                                                                                                                                                                                                          • Cumming, Naomi. The Sonic Self: Musical Subjectivity and Signification. Bloomington: Indiana University Press, 2000.

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                                                                                                                                                                                                                                                                                                                                                                                            Applies the semiotics of Peirce to the study of musical subjectivity, of the “sonic self” signified through music. Addressed to both performance and listening, with examples drawn from the violin repertory.

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                                                                                                                                                                                                                                                                                                                                                                                            • Hatten, Robert. Musical Meaning in Beethoven: Markedness, Correlation, and Interpretation. Bloomington: Indiana University Press, 1994.

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                                                                                                                                                                                                                                                                                                                                                                                              Develops a theory of musical meaning grounded in Peirce’s semiotics. Applies theories of markedness and correlations to the interpretation of topics; discusses the role of musical topics in shaping expressive genres, and how the troping of topics invokes concepts of metaphor and irony.

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                                                                                                                                                                                                                                                                                                                                                                                              • Hatten, Robert. Interpreting Musical Gestures, Topics, and Tropes: Mozart, Beethoven, Schubert. Bloomington: Indiana University Press, 2004.

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                                                                                                                                                                                                                                                                                                                                                                                                Develops the semiotic theories from Hatten 1994 further, with analyses of Mozart, Beethoven, and Schubert. Introduces a theory of musical gestures, energetic shapings of sound, that encompasses issues of embodiment and agency. Applies a gestural understanding to the marked opposition between continuity and discontinuity in classical music.

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                                                                                                                                                                                                                                                                                                                                                                                                • McCreless, Patrick. “Syntagmatics and Paradigmatics: Some Implications for the Analysis of Chromaticism in Tonal Music.” Music Theory Spectrum 13.2 (1991): 147–178.

                                                                                                                                                                                                                                                                                                                                                                                                  DOI: 10.1525/mts.1991.13.2.02a00020E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                  Applies Saussure’s notion of syntagmatic and paradigmatic relations to musical analysis through analogies to event space and tonal space, respectively. A further analogy is drawn between paradigmatic relations and associative relationships of motives in compositions; these analogies are shown to be useful in the study of chromaticism.

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                                                                                                                                                                                                                                                                                                                                                                                                  • Ratner, Leonard G. Classic Music: Expression, Form, and Style. New York: Schirmer, 1980.

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                                                                                                                                                                                                                                                                                                                                                                                                    Textbook on 18th-century music grounded in historical treatises. Includes sections on rhetoric and form, but also introduces the identification and classification of topics and styles to the analysis of this music.

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                                                                                                                                                                                                                                                                                                                                                                                                    Phenomenological Approaches

                                                                                                                                                                                                                                                                                                                                                                                                    Phenomenological approaches to music theory concentrate on experiential, subjective aspects of music and may avoid conventional approaches to analysis entirely. Clifton 1983 serves as an introduction to issues of phenomenology in music theory and develops methodologies for phenomenological investigation. Lochhead 1995 considers pedagogical uses for phenomenology. Lewin 1986 develops an analytic model of musical perceptions based on the so-called West Coast School of phenomenology.

                                                                                                                                                                                                                                                                                                                                                                                                    • Clifton, Thomas. Music as Heard: A Study in Applied Phenomenology. New Haven, CT: Yale University Press, 1983.

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                                                                                                                                                                                                                                                                                                                                                                                                      An introduction to phenomenological musical analysis, which is based on the phenomenological writings of Heidegger, Husserl, and Merleau-Ponty. Locates musical meaning in listeners’ experiences and identifies four essences of musical experience: time, space, play, and feeling.

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                                                                                                                                                                                                                                                                                                                                                                                                      • Lewin, David. “Music Theory, Phenomenology, and Modes of Perception.” Music Perception 3.4 (1986): 327–392.

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                                                                                                                                                                                                                                                                                                                                                                                                        Develops a model of listeners’ perceptions of music that comprises musical events, contexts, their relations to other perceptions, and generalized statements that can be made about perceptions. Demonstrates the model with a passage by Schubert. Uses Bloom’s literary theories to bridge analytically oriented perceptions and those arising from composition or performance.

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                                                                                                                                                                                                                                                                                                                                                                                                        • Lochhead, Judy. “Hearing New Music: Pedagogy from a Phenomenological Perspective.” Philosophy of Music Education Review 3.1 (1995): 34–42.

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                                                                                                                                                                                                                                                                                                                                                                                                          Approaches problems in the pedagogy of 20th-century music through the phenomenological theories of Merleau-Ponty, in which perception is an activity mediated through the body, which in turn engages the senses holistically. Recommends pedagogical activities that involve videos of performances and rehearsals, as well as those that invite students to represent the music they hear pictorially.

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                                                                                                                                                                                                                                                                                                                                                                                                          Approaches from Literary Theories

                                                                                                                                                                                                                                                                                                                                                                                                          Since the 1980s, many diverse approaches to music theory and analysis have stemmed from literary theories. Interpreting music as narrative has proven to be fruitful in many studies. The volume of Indiana Theory Review (Littlefield 1991) listed here surveys a wide variety of narrative approaches, and Almén 2008 develops a full-fledged narrative theory. Harold Bloom’s theories of influence and misreadings have influenced Straus 1990 on musical Modernism and Klein 2005 on intertextuality. Guck 1981 and Guck 1994 explore the value of metaphorical language in musical analysis, and Spitzer 2003 describes a historically grounded theory of musical metaphor. Subotnik 1996 applies theories of deconstruction to music.

                                                                                                                                                                                                                                                                                                                                                                                                          • Almén, Byron. A Theory of Musical Narrative. Bloomington: Indiana University Press, 2008.

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                                                                                                                                                                                                                                                                                                                                                                                                            Defines narrative in terms of transvaluation; surveys earlier work on musical narrative, and presents a theory of musical narrative based on four archetypes (derived from the work of Frye and Liszka): romance, tragedy, irony, and comedy. Offers several analytic demonstrations of this theory.

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                                                                                                                                                                                                                                                                                                                                                                                                            • Guck, Marion. “Musical Images as Musical Thoughts: The Contribution of Metaphor to Analysis.” In Theory Only 5.5 (1981): 29–42.

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                                                                                                                                                                                                                                                                                                                                                                                                              Describes a pedagogical activity in which a group of students interprets a piece of music aurally by using an intersubjective, organizing metaphor; concludes that interpretations based on image and metaphor correlate with musical structures and can lead to compelling analyses.

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                                                                                                                                                                                                                                                                                                                                                                                                              • Guck, Marion. “Analytical Fictions.” Music Theory Spectrum 16.2 (1994): 217–230.

                                                                                                                                                                                                                                                                                                                                                                                                                DOI: 10.1525/mts.1994.16.2.02a00040E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                Draws analogy between a reader of fiction and the music analyst. Describes selected analytic texts as “fictions” that demonstrate how the authors engage with the analyzed works.

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                                                                                                                                                                                                                                                                                                                                                                                                                • Klein, Michael L. Intertextuality in Western Art Music. Bloomington: Indiana University Press, 2005.

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                                                                                                                                                                                                                                                                                                                                                                                                                  A transhistorical study of intertextuality drawing from Bloom’s literary theories. Includes discussions of semiotics, narrativity, and the uncanny in music (after Freud).

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                                                                                                                                                                                                                                                                                                                                                                                                                  • Littlefield, Richard, ed. Indiana Theory Review 12 (1991).

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                                                                                                                                                                                                                                                                                                                                                                                                                    Special issue on music and narrative theory. Contains articles by Claus Clüver, Robert Hatten, Lawrence Kramer, Fred Everett Maus, Patrick McCreless, and Eero Tarasti.

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                                                                                                                                                                                                                                                                                                                                                                                                                    • Spitzer, Michael. Metaphor in Musical Thought. Chicago: University of Chicago Press, 2003.

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                                                                                                                                                                                                                                                                                                                                                                                                                      Argues that both discourse about music and music itself are inherently metaphorical. Surveys separately contemporary discourse and music from the Baroque, Classical, and Romantic eras to document metaphorical thought and reveal the activities of the metaphor.

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                                                                                                                                                                                                                                                                                                                                                                                                                      • Straus, Joseph N. Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition. Cambridge, MA: Harvard University Press, 1990.

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                                                                                                                                                                                                                                                                                                                                                                                                                        Applies Harold Bloom’s anxiety of influence to the analysis of Stravinsky, Schoenberg, Bartók, Webern, and Berg, in order to interpret the presence and reinterpretation of past musical traditions in their works.

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                                                                                                                                                                                                                                                                                                                                                                                                                        • Subotnik, Rose Rosengard. Deconstructive Variations: Music and Reason in Western Society. Minneapolis: University of Minnesota Press, 1996.

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                                                                                                                                                                                                                                                                                                                                                                                                                          Collection of Subotnik’s essays asserting that critical subjectivity must be related to arguments about reason. Considers types of musical reason by correlating Derrida’s deconstruction to music criticism; offers deconstructive analyses of Mozart’s The Magic Flute and Chopin’s “A-major Prelude” using the principle of contradictory dialectics.

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                                                                                                                                                                                                                                                                                                                                                                                                                          Popular Music

                                                                                                                                                                                                                                                                                                                                                                                                                          The study of popular repertories has grown since the 1990s, when theorists began increasingly to expand their purview beyond the European canon. The theory and analysis of popular music and studies of rock music in particular have demonstrated that the structures of popular music provide considerable challenges for theory and that individual compositions can inspire compelling analyses. The methodological approaches to the popular music vary greatly, from the formalist to the cultural. The articles Everett 2004, Ricci 2000, and Biamonte 2010 offer perspectives on the tonal language of rock; the collection of essays in Covach and Boone 1997 consider tonality alongside other structural dimensions. The collections of articles in Everett 2000 and Moore 2003 attend to social meanings and contexts of rock music. Krims 2000 and Butler 2006 step outside the rock repertory with book-length studies of rap and electronic dance music, respectively.

                                                                                                                                                                                                                                                                                                                                                                                                                          • Biamonte, Nicole. “Triadic Modal and Pentatonic Patterns in Rock Music.” Music Theory Spectrum 32.2 (2010): 95–110.

                                                                                                                                                                                                                                                                                                                                                                                                                            DOI: 10.1525/mts.2010.32.2.95E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                            Investigates content and function of harmonic structures unique to rock music that cannot be interpreted in conventional tonal terms: double-plagal and Aeolian progressions, and triad-doubled scale systems.

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                                                                                                                                                                                                                                                                                                                                                                                                                            • Butler, Mark J. Unlocking the Groove: Rhythm, Meter, and Musical Design in Electronic Dance Music. Bloomington: Indiana University Press, 2006.

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                                                                                                                                                                                                                                                                                                                                                                                                                              Theorizes rhythmic and formal structures in electronic dance music, a repertory typically characterized by repetition. Noteworthy for combining detailed analytic work with ethnographic research.

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                                                                                                                                                                                                                                                                                                                                                                                                                              • Covach, John, and Graeme M. Boone, eds. Understanding Rock: Essays in Musical Analysis. New York: Oxford University Press, 1997.

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                                                                                                                                                                                                                                                                                                                                                                                                                                Collection of essays on the analysis of various rock repertories. Focuses largely on harmonic language, chromaticism, melody and motive, and rhythm; includes contributions by Graeme Boone, Matthew Brown, Lori Burns, John Covach, Walter Everett, Daniel Harrison, and Dave Headlam.

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                                                                                                                                                                                                                                                                                                                                                                                                                                • Everett, Walter. “Making Sense of Rock’s Tonal Systems.” Music Theory Online 10.4 (2004).

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                                                                                                                                                                                                                                                                                                                                                                                                                                  Classifies six tonal systems of rock music. Compares the interactions of harmony and voice leading in rock music of 1957–1958 to that of 1999–2000, and analyzes Beck’s “Lonesome Tears.”

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                                                                                                                                                                                                                                                                                                                                                                                                                                  • Everett, Walter, ed. Expression in Pop-Rock Music: A Collection of Critical and Analytical Essays. New York: Garland, 2000.

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                                                                                                                                                                                                                                                                                                                                                                                                                                    Collection of essays on the analysis of popular and especially rock repertories with contributions by Nadine Hubbs, Susan Fast, Ellie Hisama, Mark Spicer, John Covach, James Borders, Jonathan Bernard, Lori Burns, Timothy Koozin, and Walter Everett; focuses include politics, progressive rock and jazz-rock fusion, and Frank Zappa.

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                                                                                                                                                                                                                                                                                                                                                                                                                                    • Krims, Adam. Rap Music and the Poetics of Identity. New Perspectives in Music History and Criticism. Cambridge, UK: Cambridge University Press, 2000.

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                                                                                                                                                                                                                                                                                                                                                                                                                                      A study of rap music, its meanings, and its reception. Identifies several musical and textual characteristics significant to the analysis of rap music and describes their role in various subgenres of rap; explores how listeners negotiate and construe meaning in rap music, and how its reception is related to community identities.

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                                                                                                                                                                                                                                                                                                                                                                                                                                      • Moore, Allan F., ed. Analyzing Popular Music. Cambridge, UK: Cambridge University Press, 2003.

                                                                                                                                                                                                                                                                                                                                                                                                                                        DOI: 10.1017/CBO9780511482014E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                        Collection of essays on the analysis of popular music with emphasis on situating it within cultural contexts. Includes contributions by Allan Moore, Robert Walser, Dai Griffiths, Robynn Stilwell, Stan Hawkins, Rob Bowman, Adam Krims, John Covach, Chris Kennett, and Martin Stokes.

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                                                                                                                                                                                                                                                                                                                                                                                                                                        • Ricci, Adam. “A ‘Hard Habit to Break’: The Integration of Harmonic Cycles and Voice-Leading Structure in Two Songs by Chicago.” Indiana Theory Review 21 (2000): 129–146.

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                                                                                                                                                                                                                                                                                                                                                                                                                                          Analyzes modulations upward by half or whole step at the end of two songs by Chicago, with reference to Harald Krebs’s work on dual-key pieces (“Alternatives to Monotonality in Early Nineteenth-Century Music,” Journal of Music Theory 25.1 [1981]: 1–16). Discusses how these modulations relate to the songs’ harmonic cycles.

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                                                                                                                                                                                                                                                                                                                                                                                                                                          Non-Western Approaches

                                                                                                                                                                                                                                                                                                                                                                                                                                          One way in which music theory has grown since the mid-20th century is by investigating non-Western music. The ethnomusicologist Marc Perlman considers possible bridges between Western and non-Western theory (see Perlman 2004), and Scherzinger 2001 considers formalist theories and their value to ethnomusicologists. Morris and Ravikiran 2006 analyzes Indian fusion music. See also Tenzer 2006 (cited under Analytic Methodologies) for the analysis of non-Western music.

                                                                                                                                                                                                                                                                                                                                                                                                                                          • Morris, Robert, and Chitravina N. Ravikiran. “Ravikiran’s Concept of Melharmony: An Inquiry into Harmony in South Indian Ragas.” Music Theory Spectrum 28.2 (2006): 255–276.

                                                                                                                                                                                                                                                                                                                                                                                                                                            DOI: 10.1525/mts.2006.28.2.255E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                            Discusses Indian fusion and its relation to Ravikiran’s concept of melharmony, that is, the means of deriving voice-leading structures from the combinational and melodic structure of a raga. Scrutinizes a raga’s scales, networks of pitch classes, hierarchy of tones, and inherent harmonies.

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                                                                                                                                                                                                                                                                                                                                                                                                                                            • Perlman, Marc. Unplayed Melodies: Javanese Gamelan and the Genesis of Music Theory. Berkeley: University of California Press, 2004.

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                                                                                                                                                                                                                                                                                                                                                                                                                                              Provides introductory material about Javanese gamelan traditions. Interprets and compares the work of three Javanese theorists of karawitan by situating it in its cultural context and evaluating its cognitive foundations. Compares conclusions drawn from the study of Javanese music theory with aspects of Western music theory.

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                                                                                                                                                                                                                                                                                                                                                                                                                                              • Scherzinger, Martin. “Negotiating the Music-Theory/African-Music Nexus: A Political Critique of Ethnomusicological Anti-Formalism and a Strategic Analysis of the Harmonic Patterning of the Shona Mbira Song Nyamaropa.” Perspectives of New Music 39.1 (2001): 5–117.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                Discusses theoretical concepts explicating Mbira song in relation to the purely cultural values of the field of ethnomusicology.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                Multimedia Studies

                                                                                                                                                                                                                                                                                                                                                                                                                                                Multimedia studies (involving music in film or theater or in cultural milieus influenced by media) aim at unveiling meanings of music beyond those given by scores alone. Cook 1998 is an overview of the field of multimedia analysis. Lewin 2006 considers the relationship between analysis and drama in an article about an operatic ensemble, and Leydon 2001 applies observations of contemporary film conventions to the analysis of Debussy’s music.

                                                                                                                                                                                                                                                                                                                                                                                                                                                • Cook, Nicholas. Analysing Musical Multimedia. New York: Oxford University Press, 2000.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                  Discusses analysis of music combined with visual media such as films and music videos. Offers three models of multimedia relationships: conformance, contest, and complementation. Concludes with three case studies of music combined with visual art.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                  • Lewin, David. “Musical Analysis as Stage Direction.” In Studies in Music with Text. Oxford Studies in Music Theory. By David Lewin, 19–30. New York: Oxford University Press, 2006.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                    A short “analysis-cum-direction,” based on the premise that analysis and drama are inseparable in Classical musical theater, of the trio “Cosa sento!” from Mozart’s The Marriage of Figaro. Interprets aspects of the dramatic situation in Mozart’s response to his libretto, and translates musical observations into stage directions.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                    • Leydon, Rebecca. “Debussy’s Late Style and the Devices of the Early Silent Cinema.” Music Theory Spectrum 23.2 (2001): 217–241.

                                                                                                                                                                                                                                                                                                                                                                                                                                                      DOI: 10.1525/mts.2001.23.2.217E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                                      Analyzes Debussy’s late works by comparing their fragmentary character to the effects of editing techniques in contemporary French silent film.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                      Timbre

                                                                                                                                                                                                                                                                                                                                                                                                                                                      The study of timbre has received little emphasis in American theoretical circles over the past few decades. The composer-theorist Robert Cogan has proposed a method of analyzing timbre though the use of spectral photographs (see Cogan 1984), composer-theorist Fred Lerdahl a method of understanding the hierarchical implications of timbre through his generative theory (see Lerdahl 1987), Wayne Slawson a theory of timbre based on vowel sounds (see Slawson 1985), Alfred Cramer a theory of Schoenberg’s Klangfarbenmelodie (see Cramer 2002), and Danuta Mirka an analysis of timbre in Penderecki’s music (see Mirka 2001). By contrast, for decades composer-theorists based at Stanford and Columbia Universities and the Institut de Recherche et Coordination Acoustique/Musique in Paris have devised theories of so-called spectral music—any music that brings timbre to the fore as an important element of structure or musical language. A special issue of Contemporary Music Review (Fineberg 2000), Rose 1996, and the collection Reigle and Whitehead 1998 highlight this viewpoint. Stanford University currently offers a doctoral degree in music theory aimed at composer-theorists who work with such novel aspects of timbre in their compositions.

                                                                                                                                                                                                                                                                                                                                                                                                                                                      • Cogan, Robert. New Images of Musical Sound. Cambridge, MA: Harvard University Press, 1984.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                        Applies sound spectrum analysis to musical recordings to reveal information not available from score analysis; provides photographs of the analyses. Uses phonology-based theories to interpret contrasts or oppositions found in these analyses. Includes non-Western repertories in its investigations.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                        • Fineberg, Joshua, ed. Special Issue: Spectral Music: History and Techniques. Contemporary Music Review 19.2 (2000).

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                                                                                                                                                                                                                                                                                                                                                                                                                                                          Special issue devoted to the history, composition, and analysis of spectral music; articles deal with various topics including acoustics, technology, and the development of the genre.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                          • Cramer, Alfred. “Schoenberg’s Klangfarbenmelodie: A Principle of Early Atonal Harmony.” Music Theory Spectrum 24.1 (2002): 1–34.

                                                                                                                                                                                                                                                                                                                                                                                                                                                            DOI: 10.1525/mts.2002.24.1.1E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                                            A dual interpretation of Schoenberg’s Klangfarbenmelodie: both as a sensation encompassing pitch, making the music resemble phonetic sounds, and as the emergent timbre of chords.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                            • Lerdahl, Fred. “Timbral Hierarchies.” Contemporary Music Review 2.1(1987): 135–160.

                                                                                                                                                                                                                                                                                                                                                                                                                                                              DOI: 10.1080/07494468708567056E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                                              Proposes that timbre can be organized hierarchically. Comments on hierarchical order of timbral dimensions of consonance and dissonance in the construction of multidimensional timbral arrays. Examples employing IRCAM’s CHANT sound-synthesis program are discussed.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                              • Mirka, Danuta. “To Cut the Gordian Knot: The Timbre System of Krzysztof Penderecki.” Journal of Music Theory 45.2 (2001): 435–456.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                DOI: 10.2307/3653444E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                                                Reconstructs Penderecki’s timbre system, which was based on the materials of sound generation: metal, wood, leather, felt, hair. Describes the syntactical properties of this system as it was disposed across pieces of music.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                • Reigle, Robert, and Paul Whitehead, eds. Spectral World Musics: Proceedings of the Istanbul Spectral Music Conference. Istanbul: Pan Yayýncýlýk, 1998.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                  A collection of essays by composer-theorists, ethnomusicologists, musicologists, and performers on the history and practice of timbre and spectral thinking.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                  • Rose, François. “Introduction to the Pitch Organization of French Spectral Music.” Perspectives of New Music 34.2 (1996): 6–39.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                    DOI: 10.2307/833469E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Describes and provides examples of harmonicity and inharmonicity, microphony and macrophony, subharmonicity, filtering techniques, combination tones, frequency modulations, and interpolation in the spectral music of Gerard Grisey and Tristan Murail. Concludes that this music requires new listening strategies and attitudes toward musical time.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                    • Slawson, Wayne. Sound Color. Berkeley: University of California Press, 1985.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Develops a theory of sound color, an aspect of musical timbre, in steady-state electronic sounds; this theory, based on vowel sounds, encompasses four dimensions of sound color: openness, acuteness, laxness, and smallness. Discusses relationships of sound color to other parameters of sound, and describes operations on sound-color space based on set-theoretical applications on pitch space. Presents compositional applications of sound-color theory.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Cognition

                                                                                                                                                                                                                                                                                                                                                                                                                                                                      The prolific work Krumhansl 1990 established the perceptual foundations for research in music cognition, a hybrid discipline combining music theory with cognitive psychology. Hallam, et al. 2009 presents this dichotomy by featuring contributions by researchers from both parent disciplines. Lerdahl 2001 represents a fresh approach to music theory from a cognitive/perceptual, rather than from a purely structural, point of view. Gjerdingen 1988 examines the expressive potential involved with the phenomenon of established cognitive schemata. Temperley 2001 explores the use of computer models for testing theories of perception. Zbikowski 2002 examines how the development of certain cognitive skills affects our comprehension of music. London 2004 takes a cognitive approach to understanding musical meter. Huron 2006 traces music’s emotional content to the mental processes involved in expectation.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                      • Gjerdingen, Robert. A Classic Turn of Phrase: Music and the Psychology of Convention. Philadelphia: University of Pennsylvania Press, 1988.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Examines how the conventions of 18th-century musical phrases established cognitive schemata that allow the listener to respond to subtle changes in established melodic, harmonic, rhythmic, and formal patterns.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                        • Hallam, Susan, Ian Cross, and Michael Thaut, eds. The Oxford Handbook of Music Psychology. New York: Oxford University Press, 2009.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Comprehensive reference text. Sixty-six contributors, about half from music and half from psychology, writing fifty-two chapters on both experimental and theoretical research; broad topics include music and the brain, performance, human development, learning musical skills, and music therapy.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                          • Huron, David. Sweet Anticipation: Music and the Psychology of Expectation. Cambridge, MA: MIT Press, 2006.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Describes five psychological response systems that govern how the brain processes expectation and emotion; applies these systems to musical events and demonstrates how emotion is evoked through certain musical devices. Takes into account physical and cultural concerns.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                            • Krumhansl, Carol. Cognitive Foundations of Musical Pitch. New York: Oxford University Press, 1990.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Tests listeners’ responses to explain tonal relations; analyzes how listeners retain, organize, and interpret pitch-based musical stimuli. Uses the cognitive analysis to describe certain elements of musical structure.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                              • Lerdahl, Fred. Tonal Pitch Space. New York: Oxford University Press, 2001.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Develops a model for listeners’ intuitions about relative perceptual distances in music. Builds critically on Lerdahl and Ray Jackendoff’s earlier theories including A Generative Theory of Tonal Music (Cambridge, MA: MIT Press, 1983), as well as on Krumhansl 1990. Applies the cognitive model to music-theoretical constructs such as prolongation, tension, and attraction. Includes applications to chromatic and atonal music.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                • London, Justin. Hearing in Time: Psychological Aspects of Musical Meter. New York: Oxford University Press, 2004.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Explores how the brain processes musical meter. Discusses the limitations of perceiving meter based on psychological data, and discusses psychological grouping structures to compare various rhythmic and metrical traditions. Analyzes music-theoretical terminology through the lens of cognitive science.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  • Temperley, David. The Cognition of Basic Musical Structures. Cambridge, MA: MIT Press, 2001.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Investigates comprehension of musical elements including meter, phrase structure, contrapuntal structure, harmony, and key through the use of computer models. These models are based on preference rules, analysis of which reveals clues to the cognitive process and provides for new modes of musical analysis.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    • Zbikowski, Lawrence. Conceptualizing Music: Cognitive Structure, Theory, and Analysis. New York: Oxford University Press, 2002.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Theoretical rather than experimental; Zbikowski argues that our understanding of music results from the training of basic cognitive skills, which, in turn, inform music theory. Aims to understand how humans structure musical experiences in their minds regardless of musical genre.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Social Issues

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Music theory and analysis has largely remained a conservative field of study. Nevertheless, some scholarship since the 1990s has focused on groups underrepresented either in histories of music or in musical academia. Many authors have addressed music theory and analysis, as well as musical disciplinary structures, from a feminist perspective. Other issues of recent concern include ethnic diversity, disability, and sexual orientation.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Feminism

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      The work of Susan McClary, which combines musical analysis with cultural critique, is largely responsible for bringing feminist approaches to the attention of music scholars (see McClary 1991, cited under Challenges from the New Musicology and Music Criticism). She and three other scholars, Suzanne Cusick, Marion Guck, and Marianne Kielian-Gilbert, contributed articles to “Toward a Feminist Music Theory,” a colloquy on feminist music theory in Perspectives of New Music that provides a general overview of the topic. The analyses in Hisama 2001 combine formalist techniques with interpretations guided by feminist theory, and Lewin 1992 examines examples of gendered discourse about musical register and offers pedagogical recommendations as a response. Maus 1993 is a unique article that criticizes the “masculine discourse” pervading music theory.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      • Cusick, Suzanne, Marion Guck, Marianne Kielian-Gilbert, and Susan McClary. “Toward a Feminist Music Theory.” Perspectives of New Music 32.1 (1994): 8–91.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Originated as a special session at the Society for Music Theory’s 1992 meeting. Contains essays by four scholars traditionally associated with feminism and music scholarship, as well as a response by Eric Gans.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        • Hisama, Ellie. Gendering Musical Modernism: The Music of Ruth Crawford, Marion Bauer, and Miriam Gideon. Cambridge, UK: Cambridge University Press, 2001.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Six analyses of music by three 20th-century composers; employs formalist analytic techniques yet produces hermeneutic readings of pieces embracing issues of gender, subjectivity, and biography.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          • Lewin, David. “Women’s Voices and the Fundamental Bass.” Journal of Musicology 10.4 (1992): 464–482.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            DOI: 10.1525/jm.1992.10.4.03a00020E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Discusses gendered assumptions about musical register, with reference to the work of Lawrence Kramer (Music as Cultural Practice 1800–1900 [Berkeley: University of California Press, 1990]) and Susan McClary (McClary 1991, cited under Challenges from the New Musicology and Music Criticism. Implicates Rameau’s depiction of the fundamental bass as a male voice that engenders female voices, and recommends students of harmony and composition attain fluency on keyboard instruments and instruments outside of their speaking register.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            • Maus, Fred Everett. “Masculine Discourse in Music Theory.” Perspectives of New Music 31.2 (1993): 264–293.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              DOI: 10.2307/833390E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Suggests that certain styles of writing prevalent in music theory reflect their authors’ desire not to appear feminine, and that recognizing and challenging this trend may benefit the field. Refers to the pairs of opposites in Rahn 1979 (cited under General Overviews:Traditional Texts), and demonstrates how they map onto masculine and feminine modes of discourse.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Other Issues

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              The forum “Ethnic Diversity in Music Theory: Voices from the Field” in Gamut gives expression to the growing concerns for ethnic diversity that have influenced some of the texts cited throughout this bibliography; the field of music theory still has much to learn from these perspectives. Joseph Straus’s efforts have been instrumental in introducing disability studies to music theory; Straus 2006, the collection of essays Lerner and Straus 2006, and a double issue of Music Theory Online (Shaftel 2009) consider the manifold ways the discipline of music theory can be influenced and enriched through such studies. The collection of essays in Brett, et al. 1994 provides an overview on the role of queer studies in musical scholarship. Some of the texts cited under Feminism also treat issues of diversity.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              • Brett, Philip, Elizabeth Wood, and Gary C. Thomas, eds. Queering the Pitch: The New Gay and Lesbian Musicology. New York: Routledge, 1994.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                The initial major collection advocating the importance of gay voices within music scholarship, including theory.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                • Lerner, Neil, and Joseph Straus, eds. Sounding Off: Theorizing Disability in Music. New York: Routledge, 2006.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Collection of essays on cultural disability studies and music theory and analysis. Focuses include narratives of disability, performance, and composition. Essays encompass classical and popular repertories as well as film music.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  • Shaftel, Matthew, ed. Music Theory Online 15.3–4 (2009).

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Double issue on disability studies organized from papers presented at the 2008 joint meeting of the Society for Music Theory and the American Musicological Society, with an introduction by Joseph Straus. Focuses include disability in academic communities and pedagogy.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    • Straus, Joseph N. “Normalizing the Abnormal: Disability in Music and Music Theory.” Journal of the American Musicological Society 59.1 (2006): 113–184.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      DOI: 10.1525/jams.2006.59.1.113E-mail Citation »

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Argues for the relevance of disability studies to the analysis of music. Demonstrates how disability can be interpreted in the embodiment metaphors of the German Formenlehre tradition and in the theoretical work of Schenker and Schoenberg, and presents analyses of Beethoven and Schubert to illustrate musical approaches to a master narrative of overcoming disability.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      • Various authors. “Ethnic Diversity in Music Theory: Voices from the Field.” Gamut 2.1 (2009): 45–196.

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Originated as a special session at the Society for Music Theory’s 1992 meeting. Contains essays discussing the importance of ethnic and racial diversity among the authors of theoretical texts; speculates on how a minority presence might alter the scholarly literature in music theory.

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