BAIN MUSC 726G
Geometrical Music Theory

MUSIC AND MATHEMATICS

Bibliography


See also: MUSC 726G Articles


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

Andreatta, Moreno, Emmanuel Amiot, and Jason Yust. 2024. Geometry and Topology in Music. New York: CRC Press. {GB; CRC}

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

Alexander, Stephon. 2016. The Jazz of Physics: The Secret Link Between Music and the Structure of the Universe. New York: Basic Books. {GB}

Amiot, Emmanuel. 2016. Music Through Fourier Space: Discrete Fourier Transform in Music Theory. New York: Springer. {GB; Review: Yust 2017}

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

Ashton, Anthony. 2003. Harmonograph: A Visual Guide to the Mathematics of Music. New York: Walker Publishing Company. {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; Full text: Ebook Central}

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

Bendich, et al. 2016. "Geometric Models for Musical Audio Data." 32nd International Symposium on Computational Geometry (SoCG 2016): 65:1–65:4. {Ctralie.com}

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

Boethius, Anicius Manlius Severinus. 1989. Fundamental of Music. Translated by Calvin Bower. New Haven: Yale University Press. {Internet Archive}

Braguinsky, Nikita. 2022. Mathematical Music: From Antiquity to Music AI. New York: Boca Raton: FL: CRC Press. {GB}

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

Burstein, L. Poundie and Joseph N. Straus. 2020. Concise Introduction to Tonal Harmony, 2nd ed. New York: Oxford. {GB; 3/e: Norton}

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

Carter, Elliott. 2002. The Harmony Book. Edited by Nicholas Hopkins and John F. Link. New York: Carl Fischer. {GB}

Castine, Peter. 1994. Set Theory Objects: Abstractions for Computer-Aided Analysis and Composition of Serial and Atonal Music. Berlin, Peter Lang.

Chew, Elaine, ed.. 2016. Mathematical and Computational Modeling of Tonality: Theory and Applications. London: Springer. {GB}

Chew, Elaine, Gerard Assayag, and Jordan B. L. Smith. 2016. Mathemusical Conversations: Mathematics and Computation in Music Performance and Composition. Singapore: World Scientific. {GB}

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

Cohn, Richard. 2012. Audacious Euphony: Chromatic Harmony and the Triad's Second Nature. New York: Oxford. {GB}

Cooper, Grosvenor W. and Leonard B. Meyer. 1963. The Rhythmic Structure of Music. Chicago: University of Chicago Press. - R

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

De Souza, Jonathan. 2017. Music at Hand: Instruments, Bodies, and Cognition. New York: Oxford University Press. {GB}

Deutsch, Diana. 2019. Musical Illusions and Phantom Words: How Music and Speech Unlock Mysteries of the Brain. New York: Oxford University Press. {GB; Website}

Deutsch, Diana, ed. 2013. Psychology of Music, 3rd ed. Waltham, MA: Academic 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; Archive.org}


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}

duSautoy, Marcus. 2008. Symmetry: A Journey in to the Patterns of Nature. New York: Harper Collins. {GB}

______________. 2004. The Music of the Primes. New York: Harper Collins. {GB}

Elkins, James. 2000. How to Use Your Eyes. New York: Routledge. {GB}

Eerola, Tuomas. Music and Science: A Guide to Empirical Music Research. New York: Routledge. {GB}

Fitzpatrick, Richard. 2008. Euclid's Elements of Geometry. Available online at: <https://farside.ph.utexas.edu/Books/Euclid/Elements.pdf>.

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. {GB}

Frame, Michael and Amelia Urry. 2016. Fractal Worlds: Grown, Built, and Imagined. New Haven: Yale University Press. {GB}

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

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

Ghyka, Matila. 1977. The Geometry of Art and Life. Mineola, NY: Dover. {GB}

Gjerdingen, Robert. 2007. Music in the Galant Style. New York: Oxford University Press. {GB; Ebook Central}

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

Guedj, Denis. 1997. Numbers: The Universal Language. New York: Harry N. Abrams, Inc. {GB; WP}

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

Hanninen, Dora A. 2012. A Theory of Music Analysis: On Segmentation and Associative Organization. New York: University Rochester Press. {GB}

Hanson, Howard. 1960. Harmonic Materials of Modern Music: Resources of the Tempered Scale. New York: Appleton-Century Crofts. {GBd; Archive.org}

Hasty, Christopher. 2020/1997. Meter As Rhythm, 20th Anniversary Edition. New York: Oxford. {GB; Review: Roeder 1998} - R

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

Hofstadter, Douglas. 1999/1979. Gödel, Escher, Bach: An Eternal Golden Braid, 20th Anniversary Edition. New York: Basic Books. {GBd; WP}

________________. 1985. Metamagical Themas: Questing for the Essence of Mind and Pattern. New York: Basic Books. {GB}

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

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

Huron, David. 2016. Voice Leading: The Science Behind a Musical Art. Cambridge, MA: MIT 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}

Kandinsky, Wassily. 1977/1911. Concerning the Spiritual in Art, translated by T. H. Sadler. Mineola, NY: Dover {GB; Project Gutenberg}

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

Kopp, David. 2002. "Chromatic Transformations in Nineteenth-Century Music." Cambridge: Cambridge University Press. {GB} - NRT

Kramer, Jonathan D. 1988. The Time of Music: New Meanings, New Temporalities, New Listening Strategies. New York: Schirmer. {GB}

Krumhansl, Carol L.2001. Cognitive Foundations of Musical Pitch. New York: Oxford University Press. {GB}

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

Laitz, Steven G. The Complete Musician: An Integrated Approach to Theory, Analysis, and Listening, 4th Edition. New York: Oxford. {GB; 5th ed.: Oxford}

Larson, Steve. 2012. Musical Forces: Motion, Metaphor, and Meaning in Music. Bloomington: Indiana University Press. {GB}

Lakoff, George and Mark Johnson. 1980. Metaphors We Live By. Chicago: University of Chicago Press. {GB}

Lakoff, George and Rafael E. Nunez. 2000. Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being. New York: Basic Books. {GB}

Lehman, Frank. 2018. Hollywood Harmony: Musical Wonder and the Sound of Cinema. New York: Oxford University Press. {GB} - NRT

Lendvai, Ernö. 1971. Béla Bartók: An Analysis of His Music. New York: Kahn & Averill. {GB}

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} - R

Levy, Ernst. 1985. A Theory of Harmony. Albany: SUNY Press. {GB}

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

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

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

London, Justin. 2004. Hearing in Time: Psychological Aspects of Musical Meter. New York: Oxford. {GB} - R

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

Lumsden, Rachel and Jeffrey Swinkin, eds. The Norton Guide to Teaching Music Theory. New York: Norton, pp. 147–160. {GB}

Margulis, Elizabeth Hellmuth. 2013. On Repeat: How Music Plays the Mind. New York: Oxford University Press. {GB}

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

Mandelbrot, Benoit B. 1983. The Fractal Geometry of Nature. New York: Holt. {GBd}

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

Margulis, Elizabeth Hellmuth. 2013. On Repeat: How Music Plays the Mind. New York: Oxford University Press. {GB} - R

Martineau, John, ed. 2010. Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, and Cosmology. New York: Wooden Books. {GB}

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}

McClain, Ernest. 1977. The Pythagorean Plato: Prelude to the Song Itself. York Beach, Maine: Nicolas-Hays, Inc. {GB; Internet Archive}

Mermikides, Milton. 2025. Hidden Music: The Composer's Guide to Sonification. London: Cambridge University Press. {GB}

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

Meyer, Leonard. 1989. Style in Music. Chicago: University of Chicago Press. {GB}

____________. 1956. Emotion and Meaning in Music. Chicago: University of Chicago Press. {GB}

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: TCL}

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: TCL}

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}

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


Parncutt, Richard. 2024. Psychoacoustic Foundations of Major-Minor Tonality. Cambridge, MA: The MIT Press. {Full Text: DOAB}

Persichetti, Vincent. 1961. Twentieth-Century Harmony: Creative Aspects and Practice. New York: Norton. {GB}

Pesic, Peter. 2022. Sounding Bodies: Music and the Making of Biomedical Science. Cambridge, MA: MIT Press. {Full Text: DOAB}

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

__________. 1980. An Introduction to Information Theory: Symbols, Signals & Noise. Mineola, NY: Dover. {GB}

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

Pizŕ, Antoni. 2023. Listening to The World: A Brief Survey of World Music. CUNY Pressbooks. Available online at: <https://pressbooks.cuny.edu/apiza/>.

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}

Rosen, Joe. 2012/1975. Symmetry Discovered: Concepts and Applications in Nature and Science. Mineola, NY: Dover. {GB}

Rossing, Thomas, F. Richard Moore and Paul Wheeler. 2002. The Science of Sound, Third Edition. New York: Addison Wesley. {GB}

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

Russell, George. 1953. The Lydian Chromatic Concept of Tonal Organization for Improvisation. New York: Concept Publishing Company. {GB; Website}

Sautoy, Marcus du. 2003. The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics. New York: Harper Collins. {GB}

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; Archive.org}

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

Sethares, William. 2007. Rhythms and Transforms. New York: Springer. {GB; Website}

Stewart, Ian. 1992. Another Fine Math You've Got Me Into. New York: W.H. Freeman. {GB}

Slonimsky, Nicolas. 1986/1947. Thesaurus of Scales and Melodic Patterns. New York: Amsco Publications. {GB; Archive.org}

Straus, Joseph N. 2022. The Art of Post-Tonal Analysis: Thirty-Three Graphic Music Analyses. New York: Oxford University Press. {GB; Oxford; Companion Website;  Videos: JosephStraus.com; Reviews: Lopez 2023, Wente 2022, McGartland 2022}.

______________. 2018. Broken Beauty: Musical Modernism and the Representation of Disability. New York: Norton. {GB; Full Text: EBSCOhost; Videos: JosephStraus.com}

______________. 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; Full text: Ebook Central; Reviews: Yust et al. 2022; Gómez-Martín 2022; Gotham 2013} - R

Tufte, Edward R. 1983. The Visual Display of Quantitative Information. New York: Graphic Press. {GB}

Tymoczko, Dmitri. 2023. Tonality: An Owner's Manual. New York: Oxford University Press. {GB; Full text: Oxford Academic}

______________. 2011. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. New York: Oxford University Press. {GB; Full text: Ebook Central; See also: Companion Website | Author's Website; Review: Hook 2011}

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

Weyl, Hermann. 1952. Symmetry. Princeton, NJ: Princeton University Press. {GB}

White, Christopher. 2022. The Music in the Data: Corpus Analysis, Music Analysis, and Tonal Traditions. New York: Routledge. {Routledge}

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

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

Yust, Jason. 2018. Organized Time: Rhythm, Tonality, and Form. New York: Oxford University Press. {GB} - R

LEGEND
R - Rhythm & Meter
 NRT - Neo-Riemannian Theory

See also:
Post-Tonal Theory Bibliography {BAIN MUSC 525}
Teaching Post-Tonal Theory {BAIN MUSC 525}
Tuning Theory Bibliography {BAIN MUSC 726T}



Updated: February 22, 2025

Reginald Bain | University of SouthCarolina | School of Music
https://reginaldbain.com/vc/musc726g/