I'm a music theorist and Associate Professor of Music Theory at the Boston University School of Music. My research applies mathematics to topics in music theory, music analysis, and music cognition, and I'm interested in how theorists, composers, and listeners conceptualize tonal and rhythmic spaces and structures.

What I'm working on right now

• Computational analysis of tonal harmony using windowing and DFT on pitch-class vectors
• Relating the Fourier spectra and phase spaces to voice-leading spaces through a factorizing method
• David Lewin's interval function as a tool for analyzing non-bijective voice leading
• Pitch-class vectors as a representation of jazz harmony
• Irregular rhythmic patterns in Ligeti's late music and recent jazz and periodicity based descriptions of them (using rhythmic qualities)
• Linear dependencies between Fourier coefficients that result from filtering functions
• Flexible definitions of tuning systems using Fourier transforms

Publications

Books

• Organized Time: Rhythm, Tonality, and Form: Oxford University Press, 2018

Winner of the Society for Music Theory’s 2019 Wallace Berry Award:

. . . a book that is astonishing in both its ambition and its achievement. It offers a theory of tonal music that treats harmony, rhythm, and form as separate dimensions that might either reinforce or contradict each other, providing an appealing notation system that permits direct comparison of these dimensions. It profoundly rethinks aspects of tonal theory that we had thought pretty well settled. The theoretical framework is powerful and the analyses—of both familiar and unfamiliar tonal works—are deeply revealing. (Society for Music Theory Publication Awards Committee, 2019)

Journal Articles

2021

• Periodicity-Based Descriptions of Rhythms and Steve Reich’s Rhythmic Style (preprint), Journal of Music Theory 65/1
• Steve Reich’s Signature Rhythm, and an Introduction to Rhythmic Qualities (preprint), Music Theory Spectrum 43/1
• With Alexandre Popoff: Meter Networks: A Categorical Framework for Metrical Analysis (preprint), Journal of Mathematics and Music

2019–20

• Dimensions of Atonality: A Response and Extension of von Hippel and Huron (2020), Empirical Musicology Review (website)
• Generalized Tonnetze and Zeitnetze and the Topology of Music Concepts (preprint), Journal of Mathematics and Music 14/2, Special Issue on Topology and Geometry
• Ganymed's Heavenly Descent (preprint), Music Analysis 39/1
• Wreaths for Rahn, and Valuable Exchanges (preprint), Perspectives of New Music 57/1–2
• Stylistic Information in Pitch-Class Distributions (preprint), Journal of New Music Research 48/3

2016–2017

• Harmonic Qualities in Debussy's "Les sons et les parfums tournent en l'air du soir," (preprint) Journal of Mathematics and Music 11/2–3, Special Issue on Perfect Balance and the DFT (2017)
• Special Collections: Renewing Set Theory (preprint), Journal of Music Theory 60/2 (2016)
• Analysis of Analysis: Using Machine Learning to Evaluate the Importance of Music Parameters for Schenkerian Analysis (with Phillip B. Kirlin) (preprint), Journal of Mathematics and Music 10/2, Special Issue on Machine Learning and Music Generation (2016)

2015

• Voice-Leading Transformations and Generative Theories of Tonal Structure, Music Theory Online 21/4
• Schubert's Harmonic Language and Fourier Phase Space (preprint), Journal of Music Theory 59/1
• Distorted Continuity: Chromatic Harmony, Uniform Sequences, and Quantized Voice Leadings (preprint), Music Theory Spectrum 37/1

2013

• A Space for Inflections: Following up on JMM's Special Issue (preprint), Journal of Mathematics and Music 7/3
• Tonal Prisms: Iterated Quantization in Chromatic Tonality and Ravel's "Ondine" (preprint), Journal Of Mathematics and Music 7/2

Book Chapters

• Geometrical Generalizations of the Tonnetz and their Relation to Fourier Phase Spaces (preprint), Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological, and Applied Approaches, edited by M. Monteil, R.W. Peck (World Scientific, 2019)
• Restoring the Structural Status of Keys through DFT Phase Space (preprint), The Musical-Mathematical Mind: Patterns and Transformations, edited by G. Payeron, S. Pina-Romero, O.A. Agustín-Aquino, E. Lluis-Puebla (Springer, 2017)
• Methods of Large-Scale Rhythmic and Tonal Organization as Stylistic Features of Haydn's Keyboard Sonatas, Haydn and his Contemporaries, edited by S. Murray (Steglein, 2011)

Conference Proceedings Articles

•  (with Phillip B. Kirlin) The Multileveled Rhythmic Structure of Ragtime (preprint), Human-Computer Interaction 2021, Springer. 
•  (with Mark Gotham)  Serial Analysis: A Digital Library of Rows in the Repertoire and their Properties, with Applications for Teaching and Research. Digital Libraries for Musicology 2021.
• Fourier Methods for Computational Analysis of Enharmonicism and Other Harmonic Properties, Journées d'Informatique Musicale 2020 (Proceedings)
• Fourier Phase and Pitch-Class Sum (with Dmitri Tymockzo) (preprint), Mathematics and Computation in Music, Seventh International Conference, edited by O. Agustín-Aquino, F. Gomez-Martin, M. Monteil (Springer, 2019)
• Decontextualizing Contextual Inversion (preprint), Mathematics and Computation in Music, Seventh International Conference, edited by O. Agustín-Aquino, F. Gomez-Martin, M. Monteil (Springer, 2019)
• Probing Questions about Keys: Tonal Distributions through the DFT (preprint), Mathematics and Computation in Music, Sixth International Conference, edited by O. Agustín-Aquino, E. Lluis-Puebla, M. Monteil (Springer, 2017)
• Applications of the DFT to the Theory of Twentieth-Century Harmony (preprint), Mathematics and Computation in Music, Fifth International Conference, edited by T. Collins, D. Meredith, A. Volk (Springer, 2015)
• Testing Schenkerian Theory: An Experiment in the Percpetion of Key Distances (preprint), Proceedings of the 2012 International Conference for Music Perception and Cognition
• Diatonic Categorization in the Perception of Melodies (preprint), Proceedings of the 2010 International Conference for Music Perception and Cognition
• The Geometry of Melodic, Harmonic, and Metrical Hierarchy (preprint), Mathematics and Computation in Music: Second International Conference (Springer, 2009)
• The Step-Class Automorphism Group in Tonal Analysis (preprint). Mathematics and Computation in Music: First International Conference, edited by T. Klouche and T. Noll (Springer, 2007)

Other Writings

• Cyclic Rhythms and Rhythmic Qualities: Introduction to the DFT and an Application to Steve Reich's Phase Music (unpb. lecture notes, 2018)
• Review of Music through Fourier Space: Discrete Fourier Transform in Music Theory (Springer, 2016) by Emmanuel Amiot, Music Theory Online 23/3 (2017)
• Report: Sixth New Beethoven Research Conference, Nov. 3–4, 2017, Vancouver, BC, Eighteenth-Century Music 14/2 (2017)
• Report: From Where do These Chords Come?: Theoretical Traditions in the Enlightenment, Boston University, 23 Oct. 2015, Eighteenth-Century Music 13/2 (2016)
• Editorial: Introduction to the Special Issue on Pedagogies of Mathematical Musical Theory (with Thomas M. Fiore), Journal of Mathematics and Music 8/2
• Review of Richard Cohn, Audacious Euphony: Chromaticism and the Triad's Second Nature (Oxford University Press, 2012), Music Theory Online 18/3 (2012)
• Storm and Stress, Form and Process: C.P.E. Bach, Josef Haydn, and the Symphony in the Early 1770s (unpub. MS)
• Formal Models of Prolongation (pdf), PhD Diss., University of Washington, Seattle (2006)

Presentations

2021

• Harmonic Qualities as Key to Scriabin's Late Harmonic Practice (with Thomas Noll), Euromac 202 , Moscow (September 2021)
pdf slides
•  (with Phillip B. Kirlin) The Multileveled Rhythmic Structure of Ragtime, Human-Computer Interaction International Conference (July 2021)
•  (with Mark Gotham)  Serial Analysis: A Digital Library of Rows in the Repertoire and their Properties, with Applications for Teaching and Research. Digital Libraries for Musicology 2021.   
• Flexibly Defined Tuning Systems Using Continuous Fourier Transforms. (pdf slides) (Mathematical and Computational Models in Music Workshop), University of Pavia, June 2021
• Response to John Gingerich’s “Beethoven’s Op. 95, Ignaz Schuppanzigh, and the Path to the Late Style” Boston University Center for Beethoven Research, Symposium on Op.95, April 2021(powerpoint slides)(text)

2020

• Materials of Tonality: Harmonic Spectra and Phase Spaces for Classical Music, Blues, and Jazz. Northwestern University Music Theory and Cognition Colloquium, Nov. 17, 2020 (powerpoint)
• Dimensions of Atonality (powerpoint), presentation to Ohio State University Music Cognition Seminar, Nov. 16, 2020
• Fourier Methods for Computational Analysis of Enharmonicism and Other Harmonic Properties, Journées d'Informatique Musicale 2020, Strasbourg, France. 26 Oct, 2020 (website) (powerpoint)
• Sailing Off the Edge of Tonality: Debussy and Scriabin's Harmonic Adventurism Explained with Harmonic Spectra and Tonal Spaces, Lousiana State University Music Forum (powerpoint)
• Tonality, Fuzzy Voice Leading, and all that Jazz (powerpoint), Eastman Music Theory Colloquium

2019

• Rhythmic Qualities, Meter, and Reich's Cyclic Canons (powerpoint), Society for Music Theory, Columbus, Ohio
• Hypermeter and Form as Temporal Structure, and Beethoven’s Formal Innovations (powerpoint), McGill Doctoral Research Colloquium.
• Fourier Phase and Pitch-Class Sum (with Dmitri Tymoczko) (powerpoint), International Conference on Mathematics and Computation in Music, Madrid
• Decontextualizing Contextual Inversion (powerpoint), International Conference on Mathematics and Computation in Music, Madrid — this presentation also included a recording and animated analysis of my composition “Not Marble”
• Rhythmic Qualities, Meter, and Reich's Cyclic Canons (powerpoint), New England Conference of Music Theorists, Montreal
• Getting Stylistic Information from Pitch-Class Distributions Using the DFT (powerpoint), Northeast Music Cognition Group, Cambridge, Mass.

2017

• Generalized Trichordal and Tetrachordal Tonnetze: Geometry and Analytical Applications, Society for Music Theory (powerpoint), Arlington, VA
• Probing Questions about Keys: Pitch-Class Distributions through the DFT (powerpoint), International Conference for Mathematics and Computation in Music, Mexico City
• Generalized Trichordal and Tetrachordal Tonnetze: Geometry and Analytical Applications, New England Conference of Music Theorists, Amherst, Mass.
• Michael Haydn, Mozart, and the Invention of the Sonata-Rondo (pdf), Music Theory Society of New York State, Geneva, NY
• Harmony from Tonal to Atonal through Fourier Phase Space, University of Massachusetts, Amherst Research in Music Lecture Series
• Geometrical Realizations of Two- and Three-Dimensional Generalized Tonnetze (pdf), American Mathematical Society Special Session on Mathematical Music Theory, Joint Mathematics Meetings, Atlanta

2016

• Hypermeter, Form, and Closure in Haydn's and Beethoven's Codas (pdf), Sixth International New Beethoven Research Conference
• A Three-Dimensional Model of Tonality (pdf), American Mathematical Society Special Session on Mathematical Music Theory, Athens, GA

2015

• The Fourier Transform and a Theory of Harmony for the Twentieth Century (pdf), Society of Music Theory, St. Louis, MO
• Mathematical Approaches to Scale Degrees and Harmonic Functions in Analytical Dialogue (with Thomas Noll and Karst de Jong) (pdf), Society for Music Theory, St. Louis, MO
• Analysis of Analysis: Importance of Different Musical Parameters for Schenkerian Analysis (with Phillip B. Kirlin), 8th International Workshop for Music and Machine Learning, Vancouver, BC
• Applications of DFT to the Theory of Twentieth-Century Harmony, International Conference for Mathematics and Computation in Music, London
• Analysis of Twentieth-Century Music Using the Fourier Transform, Music Theory Society of New York State, Binghamton, NY
• A Spatial Perspective on Long-Range Voice Leading and Beethoven's Heiliger Dankgesang (pdf), University of Connecticut Music Theory / Music History Colloquium

2014

• Restoring the Structural Status of Keys through DFT Phase Space (powerpoint), International Congress on Music and Mathematics, Puerta Vallarta, Mexico

2013

• Chromaticism in Schubert and a New Derivation of the Tonnetz (pdf), Society for Music Theory, Charlotte, NC
• Schubert's Harmonic Language and the Tonnetz as a Continuous Geometry, Music Theory Society of the Mid-Atlantic, Philadelphia

2012

• Expressive Text Setting in Partch's Early Vocal Music, and the Harmonic and Voice-Leading Resources of Extended Just Intonation (powerpoint), The Harry Partch Legacy Symposium, Boston, Mass.
• Testing Schenkerian Theory: An Experiment on the Perception of Key Distances, International Conference for Music Perception and Cognition, Thessaloniki, Greece
• Voice-Leading Geometry, Maximal Evenness, and Acoustic-Scale Harmony in Ravel's Ondine, John Clough Memorial Conference, New Haven, Conn.
• C.P.E. Bach's Symphonies and the Composer-Specific Study of Form (powerpoint), Music Theory Society of New York State, New York

2011

• Storm and Stress, Form and Process: Compositional Strategies in Haydn's and C.P.E. Bach's Symphonies of the Early 1770s, Music Theory Society of the Mid-Atlantic, Washington, D.C.
• Storm and Stress, Form and Process: Compositional Strategies in Haydn's and C.P.E. Bach's Symphonies of the Early 1770s, Music Theory Southeast and the South Central Society for Music Theory, Tallahasee, FL
• Mathematics of Contrapuntal Hierarchy in Music, American Mathematical Society Special Session on Mathematical Techniques in Music Analysis, Joint Mathematics Meetings, New Orleans

2010

• Upright Petrouchka, Proper Scales, and Sideways Neapolitans (with Rachel Hall and Dmitri Tymoczko) (powerpoint), Society for Music Theory and the American Musicology Society Joint Conference, Indianapolis
• Diatonic Categorization in the Perception of Melodies, International Conference for Music Perception and Cognition, Seattle
• Scalar Transposition, Fractional Pitch-Classes, and Harmonic Sequences, New England Conference of Music Theorists, Storrs, Conn.
• Problems of Contrapuntal Representation in Schenkerian Theory, Music Theory Society of New York State, New York
• Scalar Transposition, Fractional Pitch-Classes, and Harmonic Sequences, Music Theory Society of the Mid-Atlantic, College Park, PA

2009

• The Geometry of Melodic, Harmonic, and Metrical Hierarchy, International Conference for Mathematics and Computation in Music and John Clough Memorial Conference, New Haven, CT
• Counterpoint and Sequence in Schenkerian Theory, Canadian University Music Society Annual Meeting, Ottawa

2008

• Methods of Large-Scale Rhythmic and Tonal Organization as Stylistic Features of Haydn's Keyboard Sonatas, Joint Conference for the Society for Eighteenth-Century Music and the Haydn Society of North America, Claremont, Calif.
• Large-Scale Rhythmic Organization in the Music of Haydn, Seventeenth Annual Meeting of the West-Coast Conference of Music Theory and Analysis, Seattle

2007

• The Step-Class Automorphism Group in Tonal Analysis, International Conference for the Society for MAthematics and Computation in Music, Berlin