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David Lewin (July 2, 1933–May 5, 2003) was an American music theorist, music critic and composer. Called "the most original and far-ranging theorist of his generation" (Cohn 2001), he did his most influential theoretical work on the development of transformational theory, which involves the application of mathematical group theory to music.



Lewin was born in New York City and studied piano from a young age. He graduated from Harvard in 1954 with a degree in mathematics. Lewin then studied theory and composition with Roger Sessions, Milton Babbitt, Edward Cone, and Earl Kim at Princeton University, earning an M.F.A. in 1958. He returned to Harvard as a Junior Fellow in the Harvard Society of Fellows from 1958–61. Following teaching positions at the University of California, Berkeley (1961–1967), the State University of New York at Stony Brook (1967–1979), and Yale University (1979–1985), he returned to Harvard as the Walter W. Naumberg Professor of Music in 1985. Lewin was a Guggenheim Foundation Fellow in 1983–1984, served as the president of the Society for Music Theory from 1985–1988 and was a member of the American Academy of Arts and Sciences. He received honorary doctoral degrees from the University of Chicago in 1995, from the New England Conservatory of Music in 2000, and posthumously from Université Marc Bloch de Strasbourg, France, in 2006.


While Lewin is primarily known as a theorist, he was also an active composer who wrote works for a wide range of forces, from solo voice to full orchestra. In 1961, he became the first professional musician to a compose computer-generated piece at Bell Laboratories (Cohen 2001).


Lewin's theoretical work may best be understood against his background in 1950/60s avant-garde compositional circles on the North American East Coast. Most of these composers were also music critics. Benjamin Boretz, Edward T. Cone, and Milton Babbitt wrote music criticism. Starting during the late 1960s (with articles on Schoenberg, crystallized in his debate with Cone), Lewin began work with text/music relations. During the late 1970s, Lewin's work in this area became more explicitly concerned with issues in literary theory, publishing articles in 19th-Century Music. "Studies in Music with Text," published posthumously, demonstrates Lewin's concerns in this area, while also demonstrating a synthesis of critical/theoretical insights/methods/etc. His most far-reaching essay in this area is "Music Theory, Phenomenology, Modes of Perception."


David Lewin's work in music theory was both influential and eclectic. Broadly, his writings can be divided into three overlapping groups: formal or mathematically-based theory, more interpretive writing on the interaction of music and text, and metatheoretical discussions on the methodology and purpose of contemporary music theory.

The first group includes his innovations in transformational theory, as expressed in numerous articles and in his treatise Generalized Musical Intervals and Transformations. In this work, Lewin applied group theory to music, investigating the basic concepts, interval and transposition, and extending them beyond their traditional application to pitch. Based on a powerful metaphor of musical space, this theory can be applied to pitch, rhythm and metre, or even timbre. Moreover, it can be applied to both tonal and atonal repertories.

Lewin's writing on the relationship between text and music in song and opera involves composers from Mozart to Wagner to Schoenberg. In one interesting example, "Music Analysis as Stage Direction," he discusses how structural aspects of the music can suggest dramatic interpretations.

Important writings for the discipline of music theory include "Behind the Beyond" (1968–9), a response to Edward Cone, and "Music Theory, Phenomenology, and Modes of Perception" (1986).

While Lewin's rigorous formal theory may seem forbidding, his writing is marked by a sense of poetry and a critical awareness of disciplinary issues and cultural biases. He often makes clear which dense sections can be skipped by readers unfamiliar with mathematics, and connects his abstract theory to practical musical considerations, such as performance and music perception. For example, in Musical Form and Transformation: Four Analytic Essays, Lewin provides ear-training exercises to develop an ability to hear more difficult musical relationships. His work has influenced later theorists, such as Richard Cohn, Robert Morris, Henry Klumpenhouwer, John Clough, Brian Hyer, and Norman Carey and David Clampitt. Posthumously, in 2003, a symposium on David Lewin's theories was conducted at the Mannes Institute for Advanced Studies in Music Theory.

Publication list

  • "Re Intervallic Relations Between Two Collections of Notes." Journal of Music Theory 3/2 (1959): 298–301
  • "The Intervallic Content of a Collection of Notes, Intervallic Relations between a Collection of Notes and its Complement: an Application to Schoenberg’s Hexachordal Pieces." Journal of Music Theory 4/1 (1960): 98–101
  • "A Metrical Problem in Webern's Op. 27." Journal of Music Theory 6/1 (1962): 125-132
  • "A Theory of Segmental Association in 12 tone music." Perspectives of New Music 1/1 (1962): 89-116
  • "Berkeley. Arnold Elston Quartet. Seymour Shifrin Quartet No. 2." Review in Perspectives of New Music 2/2 (1964): 169-175
  • "Communication on the Invertibility of the Hexachord." Perspectives of New Music 4/1 (1965): 182-186
  • "Is it Music?" Proceedings, First Annual Conference of the American Society of University Composers (1966): 50-53, on computer music.
  • "Congruence-Invarian Measures in Uniform Spaces." Transactions of the American Mathematical Society 124/3 (1966): 50-53
  • "On Certain Techniques of Re-Ordering in Serial Music." Journal of Music Theory 10/2 (1966): 276-287
  • "A Study of Hexachord Levels in Schoenberg's Violin Fantasy." Perspectives of New Music 6/1 (1967-8): 18-32
  • "Moses und Aron: Some General Remarks, and Analytic Notes for Act I, Scene I." Perspectives of New Music 6/1 (1967–8): 18–32; repr. in The Garland Library of the History of Western Music, ed. E. Rosand, xii (New York, 1965): 327–43
  • "Inversional Balance as an Organizing Force in Schoenberg’s Music and Thought." Perspectives of New Music: 6/2 (1967–8): 1–21
  • "Some Applications of Communication Theory to the Study of Twelve-Tone Music." Journal of Music Theory, 12 (1968): 50–84
  • "Some musical jokes in Mozart's Le Nozze di Figaro." In Studies in Music History : Essays for Oliver Strunk, edited by Harold Powerspp. 443–47; reprinted in "Figaro’s Mistakes", Current Musicology, no.57 (1995): 45–60; reprinted in Studies in Music with Text, Oxford University Press, 2006.
  • "Behind the Beyond … a Response to Edward T. Cone", Perspectives of New Music, vii (1968–9), 59–69
  • "Toward the Analysis of a Schoenberg Song - Op.15 no.1", Perspectives of New Music, xii/1-2 (1973-74), 43–86
  • "On Partial Ordering", Perspectives of New Music, xiv/2 (1976), 252-257
  • "On the Interval Content of Invertible Hexachords", Journal of Music Theory, xx/2 (1976), 185-188
  • "A Label-Free Development for 12-PC Systems", Journal of Music Theory, xxi/1 (1977), 29-48
  • "Some Notes on Schoenberg's Op. 11", In Theory Only, iii/1 (1977), 3-7
  • "Forte’s Interval Vector, my Interval Function, and Regener’s Common-Note Function", Journal of Music Theory, xxi (1977), 194–237
  • "A Communication on Some Combinational Problems", Perspectives of New Music, xvi/2 (1978), 251-254
  • "Two Interesting Passages in Rameau's Traité de l'harmonie", In Theory Only, iv/3 (1978), 3-11
  • "A Response to a Response On PCSet Relatedness", Perspectives of New Music, xviii/1-2 (1979-80), 498-502
  • "On Generalized Intervals and Transformations", Journal of Music Theory, xxiv/2 (1980), 243-251
  • "Some New Constructs Involving Abstract PCSets, and Probabilistic Applications", Perspectives of New Music, xviii/1-2 (1979-80), 433-444
  • "Some Investigations into Foreground Rhythmic and Metric Patterning", Music Theory: Special Topics, ed. R. Browne (New York, 1981), 101–37
  • "On Harmony and Meter in Brahms's Op.76 No.8", 19-Century Music, iv/3 (1981), 261-265
  • "A way into Schoenberg's opus 15, number 7", In Theory Only, vi/1 (1981) 3-24
  • "Comment: "On Joel Lester, 'Simultaneity structures and harmonic functions in tonal music', In theory only 5/5: 3-28, and Marion Guck, 'Musical images as musical thoughts: the contribution of metaphor to analysis', In theory only 5/5: 29-42", In Theory Only v/8 (1981) 12-14
  • "Vocal Meter in Schoenberg’s Atonal Music, with a Note on a Serial Hauptstimme", In Theory Only, vi/4 (1982), 12–36
  • "A Formal Theory of Generalized Tonal Functions", Journal of Music Theory, xxvi (1982), 23–60
  • "An example of serial technique in early Webern", Theory and Practice, vii/1 (1982) 40-43
  • "On extended Z-triples", Theory and Practice, vii/1 (1982) 38-39
  • "Auf dem Flusse: Image and Background in a Schubert Song", 19th-Century Music, vi (1982–3), 47–59; rev. as Auf dem Flusse … Schubert: Critical and Analytical Studies, ed. W. Frisch (Lincoln, NE, 1986), 126–52
  • "Transformational Techniques in Atonal and Other Music Theories", Perspectives of New Music, xxi (1982–3), 312–71
  • "Brahms, his Past, and Modes of Music Theory", Brahms Studies: Washington DC 1983, 13–27
  • "An Interesting Global Rule for Species Counterpoint", In Theory Only, vi/8 (1983), 19–44
  • "Amfortas’s Prayer to Titurel and the role of D in Parsifal: the Tonal Spaces of the Drama and the Enharmonic C/B", 19th-Century Music, vii (1983–4), 336–49
  • "Studying with Roger", Perspectives of New Music, xxiii/2 (1982–3), 152-154
  • "On Formal Intervals Between Time-Spans", Music Perception: An interdisciplinary journal, i/4 (1984) 414-23
  • "On Ellwood Derr's 'Deeper Examination of Mozart's 1-2-4-3 Theme.'" In Theory Only viii/6 (1985) 3
  • "Music Theory, Phenomenology, and Modes of Perception", Music Perception, iii (1986), 327–92
  • Generalized Musical Intervals and Transformations (Yale University Press: New Haven, CT, 1987; reprint Oxford University Press, 2007)
  • "On the 'ninth-chord in fourth inversion' from Verklärte Nacht", Journal of the Arnold Schoenberg Institute, X/1 (1987) 45-64
  • "Concerning the inspired revelation of F. J. Fétis", Theoria, ii (1987) 1-12
  • "Some Instances of Parallel Voice-Leading in Debussy", 19th-Century Music, xi (1987–8), 59–72
  • "Klumpenhouwer Networks and Some Isographies that Involve Them", Music Theory Spectrum, xii (1990), 83–120
  • "Some Problems and Resources of Music Theory" Journal of Music Theory Pedagogy, v/2, (1991) 111-132
  • "Musical Analysis as Stage Direction", Music and Text: Critical Inquiries, ed. S.P. Scher (Cambridge, 1992), 163–76
  • "Women’s Voices and the Fundamental Bass", Journal of Musicology, x (1992), 464–82
  • "Some Notes on Analyzing Wagner: The Ring and Parsifal", 19th-Century Music, xvi (1992–3), 49–58
  • "A Metrical Problem in Webern’s Op.27", Music Analysis, xii (1993), 343–54
  • Musical Form and Transformation: Four Analytic Essays (Yale University Press: New Haven, CT, 1993; reprint Oxford University Press, 2007)
  • "A Tutorial on Klumpenhouwer Networks, using the Chorale in Schoenberg’s Opus 11 No.2", Journal of Music Theory, xxxviii (1994), 79–101
  • "Comment on John Roeder's article", Music Theory Online, 0/6(1994)
  • "Generalized Interval Systems for Babbitt’s Lists, and for Schoenberg’s String Trio", Music Theory Spectrum, xvii (1995), 81–118
  • "Cohn Functions", Journal of Music Theory, xl (1996), 181–216
  • "Some Notes on Pierrot Lunaire", Music Theory in Concept and Practice, ed. J.M. Baker, D.W. Beach and J.W. Bernard (Rochester, NY, 1997), 433–57
  • "Conditions Under Which, in a Commutative GIS, Two 3-Element Sets Can Span the Same Assortment of GIS-Intervals; Notes on the Non-Commutative GIS in This Connection", Integral 11 (1997) 37-66
  • "The D major Fugue Subject from WTCII: Spatial Saturation?", Music Theory Online, iv/4 (1998)
  • "Some Notes on the Opening of the F Fugue from WTCI", Journal of Music Theory, 42/2 (1998), 235-239
  • "Some Ideas about Voice-Leading Between PCSETS", Journal of Music Theory, 42/1 (1998), 15-72
  • "All Possible GZ-Related 4-Element Paris of Sets, in All Possible Commutative Groups, Found and Categorized", Integral 14-15 (2000-2001) 77-120
  • "Special Cases of the Interval Function Between Pitch-Class Sets X and Y", Journal of Music Theory, 42/2 (2001), 1-29
  • "Thoughts on Klumpenhouwer Networks and Perle-Lansky Cycles", Music Theory Spectrum, 45/1 (2002), 196-230
  • "Some Compositional Uses of Projected Geometry", Perspectives of New Music, 42/2 (2004), 12-65
  • "Studies in Music and Text" (New York: Oxford University Press, 2006)

See also

External links


  • Cohn, Richard. 2001. "Lewin, David". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
  • Cohn, Richard. "David Lewin", Grove Music Online, ed. L. Macy (Accessed March 6, 2006)
  • Gewertz, Ken. 2003. "Composer, Music Theorist, David Lewin Dies at 69". Harvard University Gazette (May 15).
  • Klumpenhouwer, Henry. 2006. "In Order to Stay Asleep as Observers: The Nature and Origins of Anti-Cartesianism in Lewin's Generalized Musical Intervals and Transformations". Music Theory Spectrum 28, no. 2:
  • Nolan, Catherine. 2002. "Music Theory and Mathematics". In The Cambridge History of Western Music Theory, ed. Thomas Christensen,. Cambridge: Cambridge University Press.
  • Quinn, Ian. 2004. "A Unified Theory of Chord Qualities in Equal Temperament." Ph. D. diss, Eastman School of Music, U. of Rochester
  • Rothstein, Edward. 2003. "A Seeker of Music's Poetry in the Mathematical Realm," New York Times (June 28).
  • Satyendra, Ramon. 2004. "An Informal Introduction to Some Formal Concepts from Lewin's Transformational Theory." Journal of Music Theory 48, no. 1:.


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