A categorical generalization of klumpenhouwer networks

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

Volumn 9110, Issue , 2015, Pages 303-314

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

^a IRCAM   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

Category theory; K nets; PK nets; Transformational theory

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTERS;

CATEGORY THEORY; MORPHISMS; PK-NETS; SET-VALUED; TRANSFORMATIONAL THEORY;

COMPUTATION THEORY;

EID: 84949035933     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-319-20603-5_31     Document Type: Conference Paper

References (19)

1. Lewin, D.: Transformational techniques in atonal and other music theories. Perspect. New Music 21(1–2), 312–371 (1982)
2. Lewin, D.: Generalized Music Intervals and Transformations. Yale University Press, New Haven (1987)
3. Mazzola, G.: Gruppen und Kategorien in der Musik: Entwurf einer mathematischen Musiktheorie. Heldermann, Lemgo (1985)
4. Mazzola, G.: Geometrie der Töne. Birkhäuser, Basel (1990)
5. Mazzola, G.: The Topos of Music: Geometric Logic of Concepts, Theory, and Performance. Birkhäuser, Basel (2002)
6. 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, vol. 6726, pp. 69–83. Springer, Heidelberg (2011)
7. Popoff, A.: Towards A Categorical Approach of Transformational Music Theory. Submitted
8. Kolman, O.: Transfer principles for generalized interval systems. Perspect. New Music 42(1), 150–189 (2004)
9. Fiore, T.M., Noll, T., Satyendra, R.: Morphisms of generalized interval systems and PR-groups. J. Math. Music 7(1), 3–27 (2013)
10. Nolan, C.: Thoughts on Klumpenhouwer networks and mathematical models: the synergy of sets and graphs. Music Theory Online 13(3), 1–6 (2007)
11. Lewin, D.: Klumpenhouwer networks and some isographies that involve them. Music Theory Spectr. 12(1), 83–120 (1990)
12. Klumpenhouwer, H.: A generalized model of voice-leading for atonal music. Ph.D. Dissertation, Harvard University (1991)
13. Klumpenhouwer, H.: The inner and outer automorphisms of pitch-class inversion and transposition. Intégral 12, 25–52 (1998)
14. Mazzola, G., Andreatta, M.: From a categorical point of view: K-nets as limit denotators. Perspect. New Music 44(2), 88–113 (2006)
15. Ehresmann, C.: Gattungen von lokalen Strukturen. Jahresber. Dtsch. Math. Ver. 60, 49–77 (1957)
16. Vuza, D.: Some mathematical aspects of David Lewin’s book generalized musical intervals and transformations. Perspect. New Music 26(1), 258–287 (1988)
17. Kan, D.M.: Adjoint functors. Trans. Am. Math. Soc. 87, 294–329 (1958)
18. Agon, C., Assayag, G., Bresson, J.: The OM Composer’s Book. Collection “Musique/Sciences”. IRCAM-Delatour France, Sampzon (2006)
19. Andreatta, M., Ehresmann, A., Guitart, R., Mazzola, G.: Towards a categorical theory of creativity for music, discourse, and cognition. In: Yust, J., Wild, J., Burgoyne, J.A. (eds.) MCM 2013. LNCS, vol. 7937, pp. 19–37. Springer, Heidelberg (2013)