Theme with Variations as Mathematical Representation of Fuzzy Sets

Abstract

Artistic representations follow, at a closer look, formal and structural archetypes, which often have a physical and mathematical basis, even if the inspiration frequently transcends the scientific dimension of the construction of the musical discourse. Aware or not, the composers personify in their art archetypal structures which are general and embody the ideals of their expression in one way or another. The organization of musical forms constitutes no exception from this phenomenon which has never been investigated in Romanian musicology: the compatibility between physical and mathematical concepts and significant musical realities. Among the great musical genres and forms, the theme and variations are the closest to one of the elements present in the mathematics of the 20th century: the logic of fuzzy sets (or systems).