Relational poly-Klumpenhouwer networks for transformational and voice-leading analysis

Journal of Mathematics and Music

Volumn 12, Issue 1, 2018, Pages 35-55

  Popoff, Alexandre ^a   Andreatta, Moreno ^b   Ehresmann, Andrée ^c  

^a Université de Strasbourg ^*  (France)

^b UNIVERSITÉ DE STRASBOURG   (France)

^c UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

category theory; Klumpenhouwer network; parsimonious voice leading; PK net; relation; transformational analysis

Indexed keywords

EID: 85052059859     PISSN: 17459737     EISSN: 17459745     Source Type: Journal    
DOI: 10.1080/17459737.2017.1406011     Document Type: Article

References (15)

1. Clifton, Callender., 1998. “Voice-Leading Parsimony in the Music of Alexander Scriabin.” Journal of Music Theory 42 (2): 219–233. doi: 10.2307/843875
2. Cohn, Richard., 2012. Audacious Euphony: Chromaticism and the Triad's Second Nature. New York: Oxford University Press.
3. 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
4. Fiore, Thomas M., and Thomas, Noll. 2011. Commuting Groups and the Topos of Triads, 69–83. Vol. 6726 of Lecture Notes in Artificial Intelligence, edited by Carlos Agon, Moreno Andreatta, Gérard Assayag, Emmanuel Amiot, Jean Bresson, and John Mandereau. Berlin: Springer-Verlag.
5. GAP. 2016. GAP–Groups, Algorithms, and Programming, Version 4.8.6, The GAP Group. http://www.gap-system.org.
6. Klumpenhouwer, Henry., 1991. “A Generalized Model of Voice-Leading for Atonal Music.” PhD thesis, Harvard University.
7. Klumpenhouwer, Henry., 1998. “The Inner and Outer Automorphisms of Pitch-Class Inversion and Transposition: Some Implications for Analysis with Klumpenhouwer Networks.” Intégral 12, 81–93.
8. Lewin, David., 1982. “Transformational Techniques in Atonal and Other Music Theories.” Perspectives of New Music 21 (1-2): 312–381. doi: 10.2307/832879
9. Lewin, David., 1987. Generalized Music Intervals and Transformations. New Haven, CT: Yale University Press.
10. Lewin, David., 1990. “Klumpenhouwer Networks and Some Isographies that Involve Them.” Music Theory Spectrum 12 (1): 83–120. doi: 10.2307/746147
11. Mazzola, Guerino, and Moreno, Andreatta. 2006. “From a Categorical Point of View: K-Nets as Limit Denotators.” Perspectives of New Music 44 (2): 88–113.
12. Nolan, Catherine., 2007. “Thoughts on Klumpenhouwer Networks and Mathematical Models: The Synergy of Sets and Graphs.” Music Theory Online 13 (3): http://www.mtosmt.org/issues/mto.07.13.3/mto.07.13.3.nolan.pdf.
13. Noll, Thomas., 2005. “The Topos of Triads.” In Proceedings of the Colloquium on Mathematical Music Theory, 103–135. Vol. 347 of Grazer mathematische Berichte, edited by Harald Fripertinger and Ludwig Reich, Karl-Franzens-Universität, Graz, Austria.
14. Popoff, Alexandre, Carlos, Agon, Moreno, Andreatta, and Andrée, Ehresmann. 2016. “From K-Nets to PK-Nets: A Categorical Approach.” Perspectives of New Music 54 (2): 5–63. doi: 10.7757/persnewmusi.54.2.0005
15. Popoff, Alexandre, Moreno, Andreatta, and Andrée, Ehresmann. 2015. “A Categorical Generalization of Klumpenhouwer Networks.” In Proceedings of the 5th International Conference on Mathematics and Computation in Music (MCM 2015), London, UK, 22–25 June 2015, 303–314, Vol. 9110 of Lecture Notes in Computer Science, edited by Tom Collins, David Meredith, and Anja Volk. Cham, Switzerland: Springer International Publishing.