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Musical Descriptions Based on Formal Concept Analysis and Mathematical Morphology

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Musical_descriptions.pdf (1.618Mb)
Date
2018
Notes
Lecture Notes in Computer Science book series (LNCS, volume 10872)
Dewey
Algèbre
Sujet
Musical Information Research; Computational music analysis; Formal concept analysis; Mathematical morphology; Congruences; Quotient lattices; Harmonico-morphological descriptors
DOI
http://dx.doi.org/10.1007/978-3-319-91379-7_9
Conference name
23rd International Conference on Conceptual Structures, ICCS 2018
Conference date
06-2018
Conference city
Edinburgh, UK
Conference country
United Kingdom
Book title
Graph-Based Representation and Reasoning
Author
Chapman, Peter; Endres, Dominik; Pernelle, Nathalie
Publisher
Springer
Publisher city
Cham
Pages number
201
ISBN
978-3-319-91379-7
Book URL
10.1007/978-3-319-91379-7
URI
https://basepub.dauphine.fr/handle/123456789/20699
Collections
  • LAMSADE : Publications
Metadata
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Author
Agon, Carlos
1374 Sciences et Technologies de la Musique et du Son [STMS]
Andreatta, Moreno
93707 Institut de Recherche Mathématique Avancée [IRMA]
Atif, Jamal
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Bloch, Isabelle
162010 Laboratoire Traitement et Communication de l'Information [LTCI]
Mascarade, Pierre
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Type
Communication / Conférence
Item number of pages
105-119
Abstract (EN)
In the context of mathematical and computational representations of musical structures, we propose algebraic models for formalizing and understanding the harmonic forms underlying musical compositions. These models make use of ideas and notions belonging to two algebraic approaches: Formal Concept Analysis (FCA) and Mathematical Morphology (MM). Concept lattices are built from interval structures whereas mathematical morphology operators are subsequently defined upon them. Special equivalence relations preserving the ordering structure of the lattice are introduced in order to define musically relevant quotient lattices modulo congruences. We show that the derived descriptors are well adapted for music analysis by taking as a case study Ligeti’s String Quartet No. 2.

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