References
- Brown, Matthew. 2005. Explaining Tonality. Rochester: University of Rochester Press.
- Callender, Clifton. 2004. “Continuous Transformations.” Music Theory Online 10 (3).
- Callender, Clifton, Ian Quinn, and Dmitri Tymoczko. 2008. “Generalized Voice Leading Spaces.” Science 320: 346–348. doi: 10.1126/science.1153021
- Cohn, Richard. 1996. “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions.” Music Analysis 15 (1): 9–40. doi: 10.2307/854168
- Cohn, Richard. 1997. “Neo-Riemannian Operations, Parsimonious Trichords, and their ‘Tonnetz’ Representations.” Journal of Music Theory 41 (1): 1–66. doi: 10.2307/843761
- Cohn, Richard. 2003. “A Tetrahedral Model of Tetrachordal Voice Leading Space.” Music Theory Online 9 (4).
- Cohn, Richard. 2011a. Audacious Euphony. New York: Oxford.
- Cohn, Richard. 2011b. “Tonal Pitch Space and the (Neo-)Riemannian Tonnetz.” In The Oxford Handbook of Neo-Riemannian Music Theories, edited by Alex Rehding, and Ed Gollin, 322–348. New York: Oxford University Press.
- Douthett, Jack, and Peter Steinbach. 1998. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal of Music Theory 42 (2): 241–263. doi: 10.2307/843877
- Fiore, Thomas M., and Ramon Satyendra. 2005. “Generalized Contextual Groups.” Music Theory Online 11 (3).
- Genuys, Grégoire. 2019. “Pseudo-distances Between Chords of Different Cardinality on Generalized Voice-Leading Spaces.” Journal of Mathematics and Music 13 (3): 193–206. doi: 10.1080/17459737.2019.1622809
- Haimo, Ethan. 1996. “Atonality, Analysis, and the Intentional Fallacy.” Music Theory Spectrum 18 (2): 167–199. doi: 10.2307/746023
- Hook, Julian. 2008. “Signature Transformations.” In Music Theory and Mathematics: Chords, Collections, and Transformations, edited by Jack Douthett, Martha M. Hyde, and Charles J. Smith, 137–160. Rochester: University of Rochester Press.
- Hook, Julian. 2011. “Spelled Heptachords.” In Mathematics and Computation in Music, Proceedings of the Third International Conference of the Society for Mathematics and Computation in Music, edited by Carlos Agon, Emmanuel Amiot, Moreno Andreatta, Gérard Assayag, Jean Bresson, and John Mandereau, 84–97. New York: Springer.
- Hughes, James. 2015. “Using Fundamental Groups and Groupoids of Chord Spaces to Model Voice Leading.” In Mathematics and Computation in Music, Proceedings of the 5th International Conference, edited by Tom Collins, David Meredith, and Anja Volk, 267–278. New York: Springer.
- Hyer, Brian. 1989. “Tonal Intuitions in Tristan und Isolde.” Ph. D. dissertation, Yale University.
- Lerdahl, Fred. 2001. Tonal Pitch Space. New York: Oxford University Press.
- Lerdahl, Fred. 2020. Composition and Cognition. Berkeley: University of California Press.
- Lewin, David. 1987. Generalized Musical Intervals and Transformations. New Haven: Yale University Press.
- Meyer, Leonard. 1989. Style and Music. Chicago: University of Chicago Press.
- Morris, Robert. 1998. “Voice-Leading Spaces.” Music Theory Spectrum 20 (2): 175–208. doi: 10.2307/746047
- Regener, Eric. 1974. “On Allen Forte’s Theory of Chords.” Perspectives of New Music 13 (1): 191–212. doi: 10.2307/832374
- Roeder, John. 1984. “A Theory of Voice Leading for Atonal Music.” Ph. D. dissertation, Yale University.
- Roeder, John. 1987. “A Geometric Representation of Pitch-Class Series.” Perspectives of New Music 25 (1–2): 362–409.
- Russell, Jonathan. 2018. “Harmony and Voice Leading in the Rite of Spring.” Ph. D dissertation, Princeton University.
- Schoenberg, Arnold. 1975. Style and Idea: Selected Writings of Arnold Schoenberg. Edited by Leonard Stein, Translated by Leo Black. New York: St. Martins Press.
- Siciliano, Michael. 2002. “Neo-Riemannian Transformations and the Harmony of Franz Schubert.” Ph.D. dissertation, The University of Chicago.
- Simon, Herbert. 1956. “Rational Choice and the Structure of the Environment.” Psychological Review 63 (2): 129–138. doi: 10.1037/h0042769
- Straus, Joseph. 2003. “Uniformity, Balance, and Smoothness in Atonal Voice Leading.” Music Theory Spectrum 25 (2): 305–352. doi: 10.1525/mts.2003.25.2.305
- Straus, Joseph. 2007. “Voice Leading in Set-Class Space.” Journal of Music Theory 49: 45–108. doi: 10.1215/00222909-2007-002
- Straus, Joseph. 2011. “Contextual Inversion Spaces.” Journal of Music Theory 55 (1): 43–88. doi: 10.1215/00222909-1219196
- Stuckenschmidt, Hans Heinz. 1965. “Debussy or Berg? The Mystery of a Chord Progression.” The Musical Quarterly 51 (3): 453–459. doi: 10.1093/mq/LI.3.453
- Tymoczko, Dmitri. 2006. “The Geometry of Musical Chords.” Science 313: 72–74. doi: 10.1126/science.1126287
- Tymoczko, Dmitri. 2008. “Scale Theory, Serial Theory, and Voice Leading.” Music Analysis 27 (1): 1–49. doi: 10.1111/j.1468-2249.2008.00257.x
- Tymoczko, Dmitri. 2009. “Generalizing Musical Intervals.” Journal of Music Theory 53 (2): 227–254. doi: 10.1215/00222909-2010-003
- Tymoczko, Dmitri. 2010. “Geometrical Methods in Recent Music Theory.” Music Theory Online 16 (1). doi: 10.30535/mto.16.1.7
- Tymoczko, Dmitri. 2011. A Geometry of Music. New York: Oxford University Press.
- Tymoczko, Dmitri. 2012. “The Generalized Tonnetz.” Journal of Music Theory 56 (1): 1–52. doi: 10.1215/00222909-1546958
- Tymoczko, Dmitri. 2016. “In Quest of Musical Vectors.” In Mathemusical Conversations: Mathematics and Computation in Performance and Composition, edited by Elaine Chew, Gérard Assayag, and Jordan Smith, 256–282. Singapore: Imperial College Press/World Scientific.
- Tymoczko, Dmitri, and Aditya Sivakumar. 2018. “Intuitive Musical Homotopy.” In Mathematical Music Theory, edited by Robert Peck, and Maria Montiel, 233–252. Singapore: World Scientific.