Groupoids and Wreath Products of Musical Transformations: A Categorical Approach from poly-Klumpenhouwer Networks

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 11502 LNAI, Issue , 2019, Pages 33-45

  Popoff, Alexandre ^a   Andreatta, Moreno ^c   Ehresmann, André e ^d  

^a

^b France

^c SORBONNE UNIVERSITÉ   (France)

^d UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

Category theory; Groupoid; Klumpenhouwer network; Transformational music theory; Wreath product

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

CATEGORY THEORY; GROUPOID; MUSIC THEORY; MUSICAL TRANSFORMATION; NETWORK STRUCTURES; ORDINARY SET; SWITZERLAND; WREATH PRODUCTS;

COMPUTATION THEORY;

EID: 85067877442     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-030-21392-3_3     Document Type: Conference Paper

References (18)

1. Ehresmann, C.: Catégories topologiques et catégories différentiables. In: Colloque de Géométrie Différentielle Globale. C.B.R.M. pp. 137–150. Librairie Universitaire, Louvain (1959)
2. Ehresmann, C.: Categories topologiques. iii. Indagationes Mathematicae (Proceed-ings) 69, 161–175 (1966). https://doi.org/10.1016/S1385-7258(66)50023-3
3. Fiore, T.M., Noll, T.: Commuting groups and the topos of triads. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS (LNAI), vol. 6726, pp. 69–83. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21590-2 6
4. Hook, J.: Uniform triadic transformations. J. Music Theory 46(1/2), 57–126 (2002). http://www.jstor.org/stable/4147678
5. Klumpenhouwer, H.: A Generalized Model of Voice-Leading for Atonal Music. Ph.D. thesis, Harvard University (1991)
6. Klumpenhouwer, H.: The inner and outer automorphisms of pitch-class inversion and transposition: some implications for analysis with Klumpenhouwer networks. Intégral 12, 81–93 (1998). http://www.jstor.org/stable/40213985
7. Lewin, D.: Transformational techniques in atonal and other music theories. Persp. New Music 21(1–2), 312–381 (1982)
8. Lewin, D.: Generalized Music Intervals and Transformations. Yale University Press (1987)
9. Lewin, D.: Klumpenhouwer networks and some isographies that involve them. Music Theory Spectr. 12(1), 83–120 (1990)
10. Mackenzie, K.C.: General theory of Lie groupoids and Lie algebroids, London Mathematical Society Lecture Note Series, vol. 213. Cambridge University Press (2005). http://www.ams.org/mathscinet-getitem?mr=2157566
11. Mazzola, G., Andreatta, M.: From a categorical point of view: K-nets as limit denotators. Persp. New Music 44(2), 88–113 (2006). http://www.jstor.org/stable/25164629
12. Nolan, C.: Thoughts on Klumpenhouwer networks and mathematical models: the synergy of sets and graphs. Music Theory Online 13(3) (2007)
13. Peck, R.: Generalized commuting groups. J. Music Theory 54(2), 143–177 (2010). http://www.jstor.org/stable/41300116
14. Peck, R.W.: Wreath products in transformational music theory. Persp. New Music 47(1), 193–210 (2009). http://www.jstor.org/stable/25652406
15. Popoff, A.: Opycleid: a Python package for transformational music theory. J. Open Source Softw. 3(32), 981 (2018). https://doi.org/10.21105/joss.00981
16. Popoff, A., Agon, C., Andreatta, M., Ehresmann, A.: From K-nets to PK-nets: a categorical approach. Persp. New Music 54(2), 5–63 (2016). http://www.jstor. org/stable/10.7757/persnewmusi.54.2.0005
17. Popoff, A., Andreatta, M., Ehresmann, A.: A categorical generalization of Klumpenhouwer networks. In: Collins, T., Meredith, D., Volk, A. (eds.) MCM 2015. LNCS (LNAI), vol. 9110, pp. 303–314. Springer, Cham (2015). https://doi. org/10.1007/978-3-319-20603-5 31
18. Popoff, A., Andreatta, M., Ehresmann, A.: Relational poly-Klumpenhouwer networks for transformational and voice-leading analysis. J. Math. Music 12(1), 35–55 (2018). https://doi.org/10.1080/17459737.2017.1406011