BAIN MUSC 726G
Geometrical Music Theory

Articles

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Andreatta, Moreno, Emmanuel Amiot, and Jason Yust. 2020. "Introduction." Journal of Mathematics and Music 14/2: 107–13. {Issue: JoMM}

Balzano, Gerald J. "The Group-Theoretic Description of 12-Fold and Microtonal Pitch Systems." Computer Music Journal 4/4 (Winter 1980): 66–88. {JSTOR}

Cuthbert, Michael Scott and Christopher Ariza. "music21: A Toolkit for Computer-Aided Musicology and Symbolic Music Data," in J. Stephen Downie and Remco C. Veltkamp (Eds.). 11th International Society for Music Information Retrieval Conference (ISMIR 2010), August 9-13, 2010, Utrecht, Netherlands: 637–642. {DSpace@MIT; Review: Tymoczko 2013}

Bamberger, Jeanne and Andrea Disessa. 2003. "Music as Embodied Mathematics: A Study of Mutually Informing Affinity." International Journal of Computers for Mathematical Learning 8: 123–160. {ResearchGate}

Bergomi, Mattia G. and Adriano Baratč. 2020. "Homological persistence in time series: an application to music classification." Journal of Mathematics and Music 14/2: 204–221. {Issue: JoMM}

Blot, Guillaume, Fracis Rousseaux, and Pierre Saurel. 2017. "Melody and Rhythm Through Network Visualization Techniques. International Symposium on Computer Music Multidisciplinary Research. {ResearchGate}

Callender, Clifton, Ian Quinn and Dmitri Tymoczko. 2008. "Generalized Voice-Leading Spaces." Science 320/587: 346-348. {Science; JSTOR}

Capuzzo, Guy. 2004. "Neo-Riemannian Theory and the Analysis of Pop-Rock Music." Music Theory Spectrum 26/2: 177–199. {JSTOR}

Clough, John and Gerald Myerson. 1986. "Musical Scales and the Generalized Circle of Fifths." The American Mathematical Monthly, 93/9: 695–701. {JSTOR}

Cohn, Richard. 2016. "A Platonic Model of Funky Rhythms." Music Theory Online 22/2 (June 2016). {MTO}

___________. 1998. "Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective." Journal of Music Theory 42/2 (1998): 167–180. {JSTOR}

___________. 1997. "Neo-Riemannian Operations, Parsimonious Trichords, and Their 'Tonnetz' Representations." Journal of Music Theory 41/1 (Spring 1997): 1–66. {JSTOR}

___________. 1996. "Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions." Music Analysis 15/1 (1996): 9-40. {JSTOR}

Collins, Nick. 2019. "Sonification of the Riemann Zeta Function." The 25th International Conference on Auditory Display (ICAD 2019). {ICAD}

Coxeter, H. S. M. "Music and Mathematics." The Mathematics Teacher 61/3 (March 1968): 312–320. {JSTOR}

Crans, Alissa, Thomas M. Fiore, and Ramon Satyendra. 2009. "Musical Actions of Dihedral Groups." American Mathematical Monthly 116/6: 479-495. {JSTOR}

Demaine, Erik D., Francisco Gomez-Martin, Henk Meijer, David Rappaport, Perouz Taslakian, Godfried T. Toussaint, Terry Winograd, David R. Wood. "The distance geometry of music." Computational Geometry 42/5 (July 2009): 429-454. {Science Direct}

Douthett, Jack, & Krantz, Richard J. 2008. "Dinner Tables and Concentric Circles: A Harmony of Mathematics, Music, and Physics." The College Mathematics Journal, 39/3: 203–211. {JSTOR}

Engebretsen, Nora and Per F. Broman. 2007. "Transformational Theory in the Undergraduate Curriculum - A Case for Teaching the Neo-Riemannian Approach." Journal of Music Theory Pedagogy 21 (2007). {JMTP}

Frederick, Leah. 2023. "Diatonic Voice-Leading Transformations." Music Theory Spectrum 46/1 (Spring 2024): 37–69. {Oxford Academic}

Gjerdingen, Robert and Janet Bourne. 2015. "Schema Theory as a Construction Grammar." Music Theory Online 21.2. {MTO}

Gollin, Edward. 2004. "On David Lewin's 'Projective Geometry' and the Aesthetic of Variety." Perspectives of New Music, 42/2 (Summer 2004): 6–10. {JSTOR}

Hall, Rachel W. 2008a. Geometrical Music Theory. Science 320/5874 (2008): 328-329. {Science; JSTOR}

____________. 2008b. "Math for Poets and Drummers." Math Horizons 15/3 (February 2008): 10–11, 24. {JSTOR}

Hall, Rachel W. and Paul Klingsberg. 2004. "Asymmetric Rhythms and Tiling Canons." The American Mathematical Monthly 113/10 (December 2006): 887–896. {JSTOR; See also: Bridges 2004}

Himpel, Benjamin. 2022. "Geometry of Music Perception." Mathematics 10/24 (4793). {MDPI}

Hook, Julian. 2018. "Teaching Mathematical Techniques in Music Theory." In The Norton Guide to Teaching Music Theory, edited by Rachel Lumsden and Jeffrey Swinkin. New York: Norton, pp. 88–104. {GB}

__________. 2007. "Why Are There Twenty-Nine Tetrachords? A Tutorial on Combinatorics and Enumeration in Music Theory.* Music Theory Online 13/4 (December 2007). {MTO; Examples}

__________. 2007b. "Review: David Lewin and the Complexity of the Beautiful." Intégral 21 (2007): 155–190. {Intégral}

__________. 2006. "Exploring Musical Space." Science 313/5783: 49–50. {Science; JSTOR}

__________. 2002. "Hearing With Our Eyes: The Geometry of Musical Space." In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, ed. Reza Sarhangi: 123 – 34. {Bridges Archive}

Howat, Roy. 1994. "Symmetry: Art & Science: Debussy, Bartok and Nature Forms." Symmetry: Culture and Science 5/3: 269–285.

_________. 1983b. "Bartók, Lendvai and the Principles of Proportional Analysis." Music Analysis 2/1 (Mar., 1983): 69–95. {JSTOR}

Hughes, Bryn. 2023. "Neo-Riemannian Triadic Progressions," in Mark Gotham, et al. Open Music Theory, Version 2. {OMT2}

Hsü, Kenneth J. and Andreas J. Hsü. 1990. "Fractal Geometry of Music." Proceedings of the National Academy of Sciences of the United States of America, 87/3 (1990): 938-941. {JSTOR}

Hunter, David J. and Paul T. von Hippel. 2003. "How Rare Is Symmetry in Musical 12-Tone Rows?" The American Mathematical Monthly 110/2: 124–132. {JSTOR}

Hyer, Brian. 1995. "Reimag(in)ing Riemann." Journal of Music Theory 39: 101–138.

Kramer, Jonathan. 1973. "The Fibonacci Series in Twentieth-Century Music." Journal of Music Theory 17/1 (Spring 1973): 110–48. {JSTOR}

Liu, Yang and Godfried T. Toussaint. 2010. "Mathematical Notation, Representation, and Visualization of Musical Rhythm: A Comparative Perspective." International Conference on Computer and Computational Intelligence (ICCCI 2010): pp. 28–32. {cgm.cs.mcgill.sc}

London, Justin. 2002. "Some Non-Isomorphisms between Pitch and Time." Journal of Music Theory 46/1-2 (Spring - Autumn 2002): 127–151.

McCartin, Brian J. 1998. "Prelude to Musical Geometry." The College Mathematics Journal 29/5 (Nov. 1998): 354–370. {JSTOR}

McDonough, John and Andrzej Herczyński. 2023. Fractal patterns in music. Chaos, Solitons & Fractals 170 (May 2023). {Science Direct}

Milne, Andrew J. and Steffen A. Herff. 2016. "How a little mathematics can help create some beautiful music." The Conversation (July 17, 2016). Available online at: <https://theconversation.com/how-a-little-mathematics-can-help-create-some-beautiful-music-61812>.

Milne, Andrew J. et al. 2016. "XronoMorph: Algorithmic generation of perfectly balanced and well-formed rhythms." {ResearchGate}

_________________. 2015. "Perfect Balance: A Novel Principle for the Construction of Musical Scales and Meters." {ResearchGate}

Morris, Robert. 2007. "Mathematics and the Twelve-Tone System: Past, Present, and Future." Perspectives of New Music 45/2:: 76–107. {JSTOR}

____________. 1998. "Voice-Leading Spaces." Music Theory Spectrum 20/2 (Fall 1998): 175–208. {JSTOR}

Moss, Fabian C., Markus Neuwirth, and Martin Rohrmeier. 2023. "The line of fifths and the co-evolution of tonal pitch-classes." Journal of Mathematics and Music 17/2. {JoMM}

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

Pesic, Peter. 2013. "Euler's Musical Mathematics." Spring Science+Business Media New York 35/2. {Academia.edu}

Pressing, Jeff. 1983. "Cognitive Isomorphisms Between Pitch and Rhythm in World Musics: West Africa, the Balkans, and Western Tonality." Studies in Music (Aus-
tralia): 38–61.

Reed Jacob and Matthew Bain. 2007. "A Tetrahelix Animates Bach: Revisualization of David Lewin’s Analysis of the Opening of the F# Minor Fugue from WTC I."  Music Theory Online 13/4 (December 2007). {MTO}

Roeder, John. 2014. "Transformation in Post-Tonal Music." The Oxford Handbook Topics in Music. {Oxford Academic}

___________. 2009a. "Beat-Class Modulation in Steve Reich's Music." Music Theory Spectrum 25/2: 275-304. {JSTOR}

___________. 2009b. "Constructing Transformational Signification: Gesture and Agency in Bartók’s Scherzo, Op. 14, No. 2, measures 1–32." Music Theory Online (March 2009) 15/1. {MTO}

Rothstein, Edward. 1995. "The Inner Life of Music and Mathematics." Math Horizons 3/2 (November 1995): 6–8. {JSTOR}

Shepard, Roger N. 1982. "Geometrical Approximations to the Structure of Musical Pitch." Psychological Review 89/4 (July 1982): 305–333. {APA PsycNet}

Steinitz, Richard. 1996. "Music, Maths & Chaos." The Musical Times 137/1837 (March 1996): 14–20. {JSTOR}

Straus, Joseph N. 2013. "Total Voice Leading." Music Theory Online 20/2 (June 2014). {MTO}

Temperley, David. "The Line of Fifths." Music Analysis 19/3 (October 2000): pp. 289–319. {JSTOR}

Toussaint, Godfried T. 2011. "The Rhythm that Conquered the World: What Makes a “Good” Rhythm Good?" Percussive Notes (November 2011): 52–59. {Pre-Print}

_________________. 2002. "A Mathematical Analysis of African, Brazilian and Cuban Clave Rhythms." Proceedings of Bridges: Mathematical Connections in Art, Music and Science (July 27-29, 2002): 157-168. {Bridges}

Temperley, David. 2000. "The Line of Fifths." Music Analysis 19/3 (October 2000). {JSTOR}

Thomson, David. "Musical Polygons." Mathematics Today (Apring 2021): 50-51. {IMA}

Tymoczko, Dmitri. "Why Topology? Journal of Mathematics and Music 14/2 14/2: 114-169. {Issue: JoMM}

2012. "The Generalized Tonnetz." Journal of Music Theory 56/1 (Spring 2012): 1–52. {JSTOR}

______________. 2010. "Geometrical Methods in Recent Music Theory." Music Theory Online 16/1 (March 2010). {MTO}

______________. 2009a. "Generalizing Musical Intervals." Journal of Music Theory 53/2 (Fall 2009): 227-254. {Princeton.edu}

______________. 2009b. "Three Conceptions of Musical Distance." International Conference on Mathematics and Computation in Music (June 2009). {Princeton.edu}

Tymoczko, Dmitri. 2008. "Scale Theory, Serial Theory and Voice Leading." Music Analysis, 27/1 (March 2008): 1–49. {JSTOR}

______________. 2006. "The Geometry of Musical Chords." Science 313/5793 (2006): 72–74. {JSTOR}

Wen, Olivia Xin and Carol Krumhansl. 2019. "Perception of Pitch and Time in the Structurally Isomorphic Standard Rhythmic and Diatonic Scale Patterns." Music and Science (September 24, 2019). Available online at: <https://journals.sagepub.com/doi/full/10.1177/2059204319873308>.

Westergaard, Peter. 1996. "Geometries of Sounds in Time." Music Theory Spectrum, 18/1 (Spring 1996): 1–21. {JSTOR}

Yust, Jason. 2020. "Generalized Tonnetze and Zeitnetze, and the Topology of Music Concepts." Journal of Mathematics and Music 14/2: 170–203. {Issue: JoMM}

Zbikowski, Lawrence. 2008. "Metaphor and Music." In Raymond W. Gibbs, Jr., ed., The Cambridge Handbook of Metaphor and Thought. Cambridge: Cambridge University Press. {GB}


Music and Mathematics Journals and Conference Proceedings
Bridges: Mathematics, Art, Music, Architecture, Culture {The Bridges Archive}

Journal of Music and Mathematics {Taylor & Francis}

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

MusMat: Brazilian Journal of Music and Mathematics {musmat.org}

Proceedings of the Mathematics and Computation in Music (MCM) Conference: 2007 | 2009 | 2011 | 2013 | 2015 | 2017 | 2019 | 2022 | 2024

Music Theory Journals

Music Theory Online {MTO}

Music Theory Spectrum
{Oxford Academic}

Perspectives of New Music {PNM}

Intégral: The Journal of Applied Musical Thought {Eastman}



Updated: December 21, 2024

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