Post-Tonal Theory


Music and Mathematics

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Aceff-Sánchez, Flor, et al. 2014. An Introduction to Group Theory: Applications to Mathematical Music Theory. {Bookboon}

Agmon, Eyton 2013. The Languages of Western Tonality. New York: Springer. {GB}

Amiot, Emmanuel. 2016. Music Through Fourier Space: Discrete Fourier Transform in Music Theory. New York: Springer. {GB}

Ashton, Anthony. 2003. Harmonograph: A Visual Guide to the Mathematics of Music. New York: Bloomsbury. {GB}

Arom. Simha. 2004. African Polyphony and Polyrhythm. Cambridge: Cambridge University Press. {GB}

Babbitt, Milton. 2003. The Collected Essays of Milton Babbitt, edited by Stephen Peles, Stephen Dembski, Andrew Mead, and Joseph N. Straus. Princeton: NJ: Princeton University Press. {GB}

Bamberger, Jeanne. 2000. Developing Musical Intuitions: A Project-based Introduction to Making and Understanding Music. New York: Oxford University Press. {GBd}

Benson, David. 2007. Music: A Mathematical Offering. Cambridge: Cambridge University Press. {GB | Website}

Brindle, Reginald Smith. 1987. The New Music: The Avant-Garde Since 1945, 2nd ed. New York: Oxford University Press. {GBd}

Calter, Paul A. 2008. Squaring the Circle: Geometry in Art and Architecture. New York: John Wiley & Sons Inc. {GBd | Website}

Chew, Elaine. 2013. Mathematical and Computational Modeling of Tonality: Theory and Applications. New York: Springer. {GB}

Christensen, Thomas. 2002. The Cambridge History of Western Music Theory. Cambridge: Cambridge University Press. {GB}

Cohn, Richard. 2012. Audacious Euphony. New York: Oxford. {GB}

Cowell, Henry. 1996/1996. New Musical Resources. Cambridge, MA: Harvard University Press. {GB}

Devlin, Keith. 1994. Mathematics: The Science of Patterns: The Search for Order in Life, Mind, and in the Universe. New York: Scientific American Library. {GB;}

Douthett, Jack M. Martha M. Hyde, Charles J. Smith, and John Clough, 2008. Music Theory and Mathematics: Chords, Collections, and Transformations. Rochester, NY: University of Rochester Press. {GB}

Dummit, David S. and Richard M. Foote. 2003. Abstract Algebra, 3rd ed. New York: John Wiley & Sons. {GB}

Fauvel, John, Raymond Flood, and Robin J. Wilson, eds. 2006. Music and Mathematics: From Pythagoras to Fractals. New York: Oxford University Press. {GB}

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

Gann, Kyle. 2019. The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician. Champaign, IL: University of Illinois Press. {GBd; Companion Website}

_________. 2006/1995. The Music of Conlon Nancarrow. Cambridge: Cambridge University Press. {GB}

Gollin, Michael and Alexander Rehding, eds. 2011. The Oxford Handbook of Neo-Riemannian Music Theories. New York: Cambridge University Press. {GB}

Hardy, G.H. and E.M. Wright. 2008/1938. An Introduction to the Theory of Numbers, 6th ed. New York: Oxford University Press. {GB}

Headlam, David. 1996. The Music of Alban Berg. New Haven: Yale University Press. {GB}

Hofstadter, Douglas. 1979. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books. {GBd; WP}

Hook, Julian. 2022. Exploring Musical Spaces: A Synthesis of Mathematical Approaches. New York: Oxford. {GB}

Howat, Roy. 1983. Debussy in Proportion. Cambridge: Cambridge University Press. {GB}

Jedrejewski, Frank. 2006. Mathematical Theory of Music. Paris: Ircam-Centre Pompidou. {Delatour}

Johnson, Tim. 2008. Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Lanham, MD: Scarecrow Press. {GB}

Johnson, Tom. 2014. Other Harmony. Paris: Editions 75. {GB; E75}

___________. 1996. Self-Similar Melodies. Paris: Editions 75. {GB; E75}

Johnson, Tom and Franck Jedrzejewski. 2013. Looking at Numbers. New York: Springer. {GB}

Keith, Michael. 1991. From Polychords to Polya: Adventures in Musical Combinatorics. Princeton: Vinculum Press. {GB}

Kung, David. 2013. How Music and Mathematics Relate. DVD. Chantilly, VA: The Great Courses. {Website}

Lerdahl, Fred. 2001. Tonal Pitch Space. New York: Oxford University Press. {GB}

Lerdahl, Fred and Ray Jackendoff. 1983. A Generative Theory of Tonal Music. Cambridge: MIT Press. {GB}

Lewin, David. 1987/2007. Generalized Musical Intervals and Transformations. New York: Oxford University Press. {GB}

Lipschutz, Seymour. 1998. Schaum's Outline of Set Theory and Related Topics, 2nd ed. New York: McGraw Hill.

Lipschutz, Seymour and Marc Lipson. 2009. Schaum's Outline of Discrete Mathematics, 3rd ed. New York: McGraw Hill.

Loy, D. G. 2006. Musimathics: The Mathematical Foundations of Music, Vol. 1-2. Cambridge, Mass: MIT Press. {GB1; GB2; Website}

Madden, Charles B. 1999. Fractals in Music: Introductory Mathematics for Musical Analysis. Salt Lake City: High Art Press. {GB}

Maor, Eli. 2020. Music by the Numbers: From Pythagoras to Schoenberg. Princeton, NJ: Princeton University Press.

Mazzola, Guerino. 2018. The Topos of Music. Vol. I: Theory; Vol. II: Performance; Vol. III: Gestures; Vol. IV: New York: Springer. {GB1; GB2; GB3; GB4}

Mazzola, Guerino, Maria Mannone, and Yan Pang. 2016. Cool Math for Hot Music: A First Introduction to Mathematics for Music Theorists. New York: Springer. {GB}

Messiaen, Olivier. 1956/1944. The Technique of My Musical Language, translated by John Satterfield. Paris: A. Leduc. {GBd}

Montiel, Mariana and Francisco Gómez. 2018. Theoretical and Practical Pedagogy of Mathematical Music Theory: Music for Mathematics and Mathematics for Musicians, from School to Postgraduate Levels. Singapore: World Scientific. {GB; Full-text: UofSC OPAC}

Montiel, Mariana and Robert William Peck. 2018. Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological and Applied Approaches to Understanding Musical Phenomena. Singapore: World Scientific. {GB; Full-text: UofSC OPAC}

Morris, Robert. 1987. Composition with Pitch Classes. New Haven: Yale University Press. {GBd}

___________. 2001a. Class Notes for Atonal Theory. Lebanon, NH: Frog Peak. {GBd}

___________. 2001b. Class Notes for Advanced Atonal Theory. Lebanon, NH: Frog Peak. {GBd}

Papadopoulos, Athanase. 2015. "Mathematics and Group Theory in Music." Handbook of Group Actions, 2/32:  525-572. {HAL}

Pareyon, et al., ed. The Musical-Mathematical Mind : Patterns and Transformations. New York: Springer. {Full text: Ebook Central}

The Musical-Mathematical Mind : Patterns and Transformations, edited by Gabriel Pareyon, et al., Springer International Publishing AG, 2017. ProQuest Ebook Central,

Pierce, John. 1992. The Science of Musical Sound. W H Freeman. {GBd}

Pinter, Charles. 1990. A Book of Abstract Algebra, 2nd ed. Mineola, NY: Dover {GB}

Rahn, John. 1980. Basic Atonal Theory. New York: Longman. {GBd}

Rings, Steven. 2011. Tonality and Transformation. New York: Oxford University Press. {GBd}

Roberts, Gareth E. 2016. From Music to Mathematics: Exploring the Connections. Baltimore, MD: John Hopkins University Press. {GB}

Roederer, Juan. 2008. The Physics and Psychophysics of Music: An Introduction, 4th ed. New York: Springer. {GB}

Rothstein, Edward. 2006/1995. Emblems of Mind: The Inner Life of Music and Mathematics. Chicago: University of Chicago Press. {GBd}

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

Schillinger, Joseph. 1943. The Mathematical Basis of the Arts. New York: Philosophical Library. {GBd;}

_______________. 1946. The Schillinger System of Musical Composition. New York: Carl Fischer. {GBd1; GBd2;}

Straus, Joseph N. 2016. Introduction to Post-Tonal Theory, 4th ed. New York: Norton. {GBd}

Tatlow, Ruth. 2015. Bach's Numbers: Compositional Proportion and Significance. Cambridge: Cambridge University Press. {GB}

Temperley, David. 2010. Music and Probability. Cambridge: MIT Press. {GBd}

Toussaint, Godfried T. 2019/2013. The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good?, 2nd ed. Boca Raton, FL: CRC Press. {GB}

Tymoczko, Dmitri. 2011. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. New York: Oxford University Press. {Full text: Ebook Central; GB | OUP | Companion Website | Author's Website}

Walker, James S. and Gary Don. 2013. Mathematics and Music. Boca Raton, FL: CRC Press. {GB}

Wolfram, Stephen. 2002. A New Kind of Science. Champaign, IL: Wolfram Media. {Full-text:}

Xenakis, Iannis. 1992. Formalized Music: Thought and Mathematics in Composition. Pendragon Revised Edition. Hillsdale, NY. {GB}


Bridges: Mathematics, Art, Music, Architecture, Culture {The Bridges Organization}

Journal of Music and Mathematics {Taylor & Francis}

Leonardo {MIT Press} & Leonardo Music Journal {MIT Press}

Proceedings of the Mathematics and Computation in Music (MCM) Conference: 2007 | 2009 | 2011 | 2013 | 2015 | 2017 | 2019 | 2022

Theory Journals: Music Theory Online {MTO}; Music Theory Spectrum {Oxford Academic}; Perspectives of New Music {PNM}

Learning Abstract Algebra

Socratica, Abstract Algebra

Related Bibliographies

Bain, MUSC 525 Post-Tonal Theory: Bibliography & Articles

Bain, MUSC 726T Tuning Theory Bibliography & Articles

Computer Music Journal, Computer Music {MIT Press}

Huygens-Fokker Foundation, Tuning and Temperament {HFF}

IRCAM, Pitch Class-Set Theory, Diatonic Theory and Neo-Riemannian Theory {IRCAM}

Updated: July 29, 2023

Reginald Bain | University of SouthCarolina | School of Music