Introduction. (English) Zbl 1466.00030

From the text: This special issue focuses on some geometrical and topological aspects of the representation and formalisation of musical structures and processes.


00B15 Collections of articles of miscellaneous specific interest
00A65 Mathematics and music


Full Text: DOI


[1] Amiot, Emmanuel. 2013. “The Torii of Phases.” In Mathematics and Computation in Music. MCM 2013, edited by Jason Yust, Jonathan Wild, and John Ashley Burgoyne, 1-18. Berlin, Heidelberg: Springer. · Zbl 1270.00023
[2] Amiot, Emmanuel. 2016. Music through Fourier Space: Discrete Fourier Transform in Music Theory. Heidelberg: Springer. · Zbl 1356.00006
[3] Andreatta, Moreno. 2003. “Méthodes algébriques dans la musique et musicologie du \(XX^e\) siècle: aspects théoriques, analytiques et compositionnels.” PhD thesis, Ecole des hautes études en sciences sociales, IRCAM, Paris.
[4] Andreatta, Moreno. 2018. “From Music to Mathematics and Backwards: Introducing Algebra, Topology and Category Theory into Computational Musicology.” In Imagine Math 6 - Mathematics and Culture, edited by M. Emmer, and M. Abate, 77-88. Berlin: Springer.
[5] Bergomi, Mattia G. 2015. “Dynamical and Topological Tools for (Modern) Music Analysis.” Ph.D. thesis, Université Pierre et Marie Curie, Paris.
[6] Bergomi, Mattia G., Adriano Baratè, and Barbara Di Fabio. 2016. “Towards a Topological Fingerprint of Music.” In Topology in Image Context, edited by A. Bac and J.-L. Mari, 88-100. Switzerland: Springer international Publishing. · Zbl 1339.00005
[7] Bergomi, Mattia G., Massimo Ferri, Pietro Vertechi, and Lorenzo Zuffi. 2019. “Beyond Topological Persistence: Starting from Networks.” arXiv preprint https://arxiv.org/abs/1901.08051. · Zbl 1479.55011
[8] Bigo, Louis. 2013. “Représentation symboliques musicales et calcul spatial.” PhD Thesis, université Paris Est Créteil / IRCAM.
[9] Bigo, Louis, Moreno Andreatta, Jean-Louis Giavitto, Olivier Michel, and Antoine Spicher. 2013. “Computation and Visualization of Musical Structures in Chord-Based Simplicial Complexes.” In Mathematics and Computation in Music, MCM 2013, edited by Jason Yust, Jonathan Wild, and John Ashley Burgoyne, 38-51. Heidelberg: Springer. · Zbl 1270.00025
[10] Bigo, Louis, Jean-Louis Giavitto, and Antoine Spicher. 2011. “Building Topological Spaces for Musical Objects.” In Mathematics and Computation in Music. MCM 2011, edited by Carlos Agon, Moreno Andreatta, Gérard Assayag, Emmanuel Amiot, Jean Bresson, and John Mandereau, 13-28. Berlin, Heidelberg: Springer. · Zbl 1335.00117
[11] Buteau, C., and G. Mazzola. 2008. “Motivic Analysis According to Rudolph Réti: Formalization by a Topological Model.” Journal of Mathematics and Music 2 (3): 117-134. doi: 10.1080/17459730802518292 · Zbl 1155.00308
[12] Callender, Clifton, Ian Quinn, and Dmitri Tymoczko. 2008. “Generalized Voice-Leading Spaces.” Science 320 (5874): 346-348. doi: 10.1126/science.1153021 · Zbl 1226.00016
[13] Catanzaro, Michael. 2011. “Generalized Tonnetze.” Journal of Mathematics and Music 5 (2): 117-139. doi: 10.1080/17459737.2011.614448 · Zbl 1226.00017
[14] Granger, Gilles-Gaston. 1947. “Pygmalion. Réflexions sur la pensée formelle.” Revue Philosophique (7-9): 282-300. Reprinted in Formes, opérations, objets. Paris: Librairie Philosophique J. Vrin, 1994.
[15] Hilbert, David. 1899. Grundlagen der Geometrie. Stuttgart: Teubner. · Zbl 1321.01034
[16] Klein, Felix. 1893. “A Comparative Review of Recent Researches in Geometry.” Bulletin of the American Mathematical Society 2 (10): 215-250. doi: 10.1090/S0002-9904-1893-00147-X · JFM 25.0871.02
[17] Krenek, Ernst. 1937. Über Neue Musik. Sechs Vorlesungen zur Einführung in die theoretischen Grundlagen. Vienna: Universal Edition. Wien (English translation as Music here and now, New York. Norton, 1939).
[18] Marquis, Jean-Pierre. 2009. From a Geometrical Point of View. A Study of the History and Philosophy of Category Theory. Berlin, Heidelberg: Springer. · Zbl 1165.18002
[19] Mazzola, Guerino. 1990. Geometrie der Toene. Zürich: Birkhäuser. · Zbl 0729.00008
[20] Mazzola, Guerino, R. Guitart, J. Ho, A. Lubet, M. Mannone, M. Rahaim, and F. Thalmann 2017. The Topos of Music III: Gestures. Musical Multiverse Ontologies. Berlin, Heidelberg: Springer. · Zbl 1384.00043
[21] Netske, Andreas. 2004. “Paradigmatic Motivic Analysis.” In Perspectives in Mathematical and Computational Music Theory, edited by Guerino Mazzola, Thomas Noll, and Emilio Lluis-Puebla, 343-365. Osnabrück: Osnabrück Series on Music and Computation.
[22] Noll, Thomas, and Robert Peck. 2007. “Welcome.” Journal of Mathematics and Music 1 (1): 1-6. doi: 10.1080/17459730701267843
[23] Papadopoulos, Athanase. 2020. “Mathématiques, musique et cosmologie: à partir du Timée de Platon.” forthcoming in Les jeux subtils de la poétique, des nombres et de la philosophie : Autour de la musique de Walter Zimmermann, edited by Pierre Michel, Moreno Andreatta, and José Luis Besada. Paris: Hermann.
[24] Plato. 1997. Complete Works. Edited by John M. Cooper and Douglas S. Hutchinson. Indianapolis/Cambridge: Hackett Publishing Company.
[25] Pressing, Jeff. 1983. “Cognitive Isomorphisms Between Pitch and Rhythm in World Musics: West Africa, the Balkans, and Western Tonality.” Studies in Music, 17: 38-61.
[26] Schoenberg, Arnold. 1911. Harmonielehre. Vienna: Universal Edition.
[27] Tymoczko, Dmitri. 2011. Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. New York: Oxford University Press. · Zbl 1339.00022
[28] Volk, Anja, and Aline Honingh. 2012. “Mathematical and Computational Approaches to Music: Challenges in an Interdisciplinary Enterprise.” Journal of Mathematics and Music 6 (2): 73-81. doi: 10.1080/17459737.2012.704154 · Zbl 1264.00029
[29] Yust, Jason. 2018. “Geometric Generalizations of the Tonnetz and their Relation to Fourier Phase Spaces.” In Mathematical Music Theory: Algebraic, Combinatorial, Topological and Applied Approaches to Understanding Musical Phenomena, edited by Mariana Montiel, and Robert Peck, 253-278. Singapore: World Scientific.
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