David Benjamin 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.
5 Publication list
6 See also
8 Further reading
9 External links
Lewin was born in New York City and studied piano from a young age and
was for a time a pupil of Eduard Steuermann. 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
to 1961. After holding teaching positions at the University of
California, Berkeley (1961–67), the State University of New York at
Stony Brook (1967–79), and
Yale University (1979–85), he returned
to Harvard as the Walter W. Naumburg Professor of Music in 1985. Lewin
was a Guggenheim Foundation Fellow in 1983–84, served as the
president of the
Society for Music Theory from 1985 to 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 compose a computer-generated piece at
Bell Laboratories (Cohn
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 those composers, such as Benjamin Boretz, Edward
T. Cone, and Milton Babbitt, were also music critics and
theorists/analysts. During the late 1970s, Lewin's work in this area
became more explicitly concerned with issues in literary theory; he
published articles in 19th-Century Music. Studies in Music with Text,
published posthumously, demonstrates Lewin's concerns in this area
while also synthesizing his critical/theoretical methods.
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 (e.g. Lewin
1986 and Lewin 1991).
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 (Rings 2011,
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
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). Lewin also undertakes
considerable methodological and disciplinary reflection in writings
that are chiefly oriented around other claims. This aspect of Lewin's
intellectual style is evident as early as "A Theory of Segmental
Association in Twelve-Tone Music" (1962).
Lewin 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. Posthumously, in
2003, a symposium on David Lewin's theories was conducted at the
Mannes Institute for Advanced Studies in Music Theory. Lewin's papers
are now at the Library of Congress.
"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): 125–32.
"A Theory of Segmental Association in Twelve-Tone Music." Perspectives
of New Music 1/1 (Fall 1962): 89–116.
"Berkeley. Arnold Elston Quartet. Seymour Shifrin Quartet No. 2."
Review in Perspectives of New Music 2/2 (Fall–Winter 1964):
"Communication on the Invertibility of the Hexachord." Perspectives of
New Music 4/1 (Fall–Winter 1965): 182–86.
"Is it Music?" Proceedings, First Annual Conference of the American
Society of University Composers (1966): 50-53, on computer music.
"Congruence-Invariant 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): 276–87.
"A Study of Hexachord Levels in Schoenberg's Violin Fantasy."
Perspectives of New Music 6/1 (Fall–Winter 1967): 18-32.
"Moses und Aron: Some General Remarks, and Analytic Notes for Act I,
Scene I." Perspectives of New Music 6/1 (Fall–Winter1967): 18–32;
reprinted in The Garland Library of the History of Western Music, ed.
E. Rosand, 12 (New York, 1965): 327–43.
"Inversional Balance as an Organizing Force in Schoenberg’s Music
and Thought." Perspectives of New Music: 6/2 (Spring–Summer 1968):
"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 Powers,
443–47; reprinted in "Figaro’s Mistakes". Current Musicology,
no. 57 (1995), 45–60; reprinted in Studies in Music with
Text,[full citation needed]. Oxford and New York: Oxford University
"Behind the Beyond: A Response to Edward T. Cone". Perspectives of New
Music 7/2 (Spring–Summer 1969), 59–69.
"Toward the Analysis of a Schoenberg Song—Op. 15 No. 1",
Perspectives of New Music 12/1-2 (Fall–Winter 1973/Spring–Summer
"On Partial Ordering", Perspectives of New Music 14/2–15/1
(Spring–Summer/Fall–Winter 1976), 252–57.
"On the Interval Content of Invertible Hexachords", Journal of Music
Theory 20/2 (1976), 185–88.
"A Label-Free Development for 12-PC Systems", Journal of Music Theory
21/1 (1977), 29–48.
"Some Notes on Schoenberg's Op. 11", In Theory Only 3/1 (1977), 3–7.
"Forte’s Interval Vector, My Interval Function, and Regener’s
Common-Note Function", Journal of Music Theory, 21 (1977), 194–237.
"A Communication on Some Combinational Problems". Perspectives of New
Music 16/2 (Spring–Summer 1978), 251–54.
"Two Interesting Passages in Rameau's Traité de l'harmonie". In
Theory Only 4/3 (1978), 3-11.
"A Response to a Response On PCSet Relatedness". Perspectives of New
Music 18/1-2 (Fall–Winter 1979/Spring–Summer 1980), 498-502.
"On Generalized Intervals and Transformations". Journal of Music
Theory 24/2 (1980), 243–51.
"Some New Constructs Involving Abstract PCSets, and Probabilistic
Applications". Perspectives of New Music 18/1-2 (Fall–Winter
1979/Spring–Summer 1980), 433–44.
"Some Investigations into Foreground Rhythmic and Metric Patterning".
In Music Theory:
Special Topics, edited by Richmond Browne, 101–37.
New York:[full citation needed], 1981.
"On Harmony and Meter in Brahms's Op. 76 No. 8".
19th-Century Music 4/3 (1981), 261–65.
"A Way into Schoenberg's Opus 15, Number 7". In Theory Only 6/1 (1981)
"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 5/8 (1981)
"Vocal Meter in Schoenberg’s Atonal Music, with a Note on a Serial
Hauptstimme". In Theory Only, 6/4 (1982), 12–36.
"A Formal Theory of Generalized Tonal Functions". Journal of Music
Theory 26 (1982), 23–60.
"An Example of Serial Technique in Early Webern". Theory and Practice
7/1 (1982) 40-43.
"On Extended Z-triples", Theory and Practice. 7/1 (1982) 38-39.
"Auf dem Flusse: Image and Background in a Schubert Song",
19th-Century Music 6 (1982–3), 47–59; revised as Auf dem Flusse
… Schubert: Critical and Analytical Studies, edited by W. Frisch,
126–52. Lincoln: University of Nebraska Press, 1986.
"Transformational Techniques in Atonal and Other Music Theories",
Perspectives of New Music 21 (Fall–Winter 1982/Spring–Summer
"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
6/8 (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
7 (1983–84), 336–49.
"Studying with Roger", Perspectives of New Music 23/2 (1982–83),
"On Formal Intervals between Time-Spans". Music Perception: An
Interdisciplinary Journal 1/4 (1984), 414–23
"On Ellwood Derr's 'Deeper Examination of Mozart's 1-2-4-3 Theme.'" In
Theory Only 8/6 (1985), 3.
"Music Theory, Phenomenology, and Modes of Perception". Music
Perception 3 (1986), 327–92.
Generalized Musical Intervals and Transformations. New Haven, CT, and
Yale University Press, 1987. Reprinted, Oxford and New York:
Oxford University Press, 2007.
"On the 'ninth-chord in fourth inversion' from Verklärte Nacht",
Journal of the Arnold Schoenberg Institute, 10/1 (1987) 45–64.
"Concerning the inspired revelation of F. J. Fétis", Theoria 2 (1987)
"Some Instances of Parallel Voice-Leading in Debussy", 19th-Century
Music 11 (1987–88), 59–72.
"Klumpenhouwer Networks and Some Isographies That Involve Them", Music
Theory Spectrum 12 (1990), 83–120.
"Some Problems and Resources of Music Theory" Journal of Music Theory
Pedagogy 5/2 (1991) 111–32.
"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 10
"Some Notes on Analyzing Wagner: The Ring and Parsifal", 19th-Century
Music 16 (1992–93), 49–58.
"A Metrical Problem in Webern’s Op.27", Music Analysis 12 (1993),
Musical Form and Transformation: Four Analytic Essays New Haven, CT,
Yale University Press, 1993; reprinted, Oxford and New
York: Oxford University Press, 2007.
"A Tutorial on Klumpenhouwer Networks, Using the Chorale in
Schoenberg’s Opus 11 No.2",
Journal of Music Theory 38 (1994),
"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 17 (1995),
Journal of Music Theory 40 (1996), 181–216.
"Some Notes on Pierrot Lunaire". In Music Theory in Concept and
Practice, ed. J. M. Baker, David W. Beach, and Jonathan W. Bernard.
Rochester, NY,[full citation needed] 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 4/4 (1998).
"Some Notes on the Opening of the F♯ Fugue from WTCI", Journal of
Music Theory, 42/2 (1998), 235–39.
"Some Ideas about Voice-Leading Between PCSETS", Journal of Music
Theory, 42/1 (1998), 15-72.
"All Possible GZ-Related 4-Element Pairs of Sets, in All Possible
Commutative Groups, Found and Categorized", Integral 14-15
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.
"The Form of Rhythm, the Rhythm of Form." In The Philosophical Horizon
of Composition in the Twentieth Century, ed. Gianmario Borio. Venice:
Fondazione Ugo e Olga Levi, 2003.
"Some Compositional Uses of Projected Geometry", Perspectives of New
Music, 42/2 (Summer 2004), 12–65.
"Some Theoretical Thoughts about Aspects of Harmony in Mahler's
Symphonies." In Music and the Aesthetics of Modernity: Essays, ed.
Karol Berger, and Anthony Newcomb. Cambridge: Harvard University
"Studies in Music and Text". New York: Oxford University Press, 2006.
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, edited by Laura Macy
(Accessed March 6, 2006).
Gewertz, Ken. 2003. "Composer, Music Theorist,
David Lewin Dies at
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.
Nolan, Catherine. 2002. "Music Theory and Mathematics". In The
Cambridge History of Western Music Theory, edited by Thomas
Christensen, 272–304. Cambridge: Cambridge University Press.
Quinn, Ian. 2004. "A Unified Theory of Chord Qualities in Equal
Temperament." Ph. D. diss. Rochester: Eastman School of Music,
University of Rochester.
Rings, Steven. 2011. Tonality and Transformation. New York: Oxford
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. 1:99–141
Bard-Schwartz, David, and Richard Cohn (eds.). 2015. David Lewin's
"Morgengruß": Text, Context, Commentary. Oxford and New York: Oxford
University Press. ISBN 978-0-19-984478-4.
Harvard Gazette: Obituary and Faculty Memorial[permanent dead link].
ISNI: 0000 0001 1476 4042
BNF: cb14767138t (data)