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Chapitre D'ouvrage Année : 2018

Musical Descriptions Based on Formal Concept Analysis and Mathematical Morphology

Résumé

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 descrip-tors are well adapted for music analysis by taking as a case study Ligeti's String Quartet No. 2.
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Dates et versions

hal-02021857 , version 1 (10-12-2019)

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Carlos Agon, Moreno Andreatta, Jamal Atif, Isabelle Bloch, Pierre Mascarade. Musical Descriptions Based on Formal Concept Analysis and Mathematical Morphology. Graph-Based Representation and Reasoning, Proceedings of the 23rd International Conference on Conceptual Structures, ICCS 2018, Springer, pp.105-119, 2018, ⟨10.1007/978-3-319-91379-7_9⟩. ⟨hal-02021857⟩
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