A formal concept analysis of harmonic forms and interval structures

Authors:
Tobias Schlemmer;Stefan E. Schmidt
Affiliations:
FR Mathematik, Institut für Algebra, Technische Universität Dresden, Dresden, Germany 01062;FR Mathematik, Institut für Algebra, Technische Universität Dresden, Dresden, Germany 01062
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2010

Citing 3
Cited 0

Formal Concept Analysis: Mathematical Foundations

Formal Concept Analysis: Mathematical Foundations
Towards a Semantology of Music

ICCS '07 Proceedings of the 15th international conference on Conceptual Structures: Knowledge Architectures for Smart Applications
Concept Lattice Orbifolds --- First Steps

ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

While small concept lattices are often represented by line diagrams to better understand their full structure, large diagrams may be too complex to do this. However, such a diagram may still be used to receive new ideas about the inherent structure of a concept lattice. This will be demonstrated for a certain family of formal contexts arising from mathematical musicology. In particular, we investigate how chord patterns can be characterised by their interval structure. For such contexts of pattern structures, it turns out that each corresponding concept lattice incorporates two competing building principles, one emanating from the top the other from the bottom of the lattice.