Using Formal Concept Analysisto Represent Chroma Systems

The article discusses the application of Formal Concept Analysis to the algebraic enumeration, classification and representation of musical structures. It focuses on the music-theoretical notion of the Tone System and its equivalent classes obtained either via an action of a given finite group on the collection of subsets of it or via an identification of Forte’s corresponding interval vector and Lewin’s interval function. The use of concept lattices, applied to a simple case such as the division of the octave into five equal parts and the associated Chroma System, clearly shows that these approaches are conceptually different. The same result is obtained for a given subsystem of the traditional Tone System, as we will show by analysing the case of the pentatonic system. This opens a window towards generic tone systems that can be used as starting point for the structural analysis of other finite chroma systems.