Between Mind and Mathematics. Different Kinds of Computational Representations of Music

In this article we analyse different types of representations of music, both from a cognitive and a computational point of view. Whereas mental representations of music are the objects of the musical mind, and are therefore by definition a subject of cognitive psychology and philosophy, it can be argued that mathematical representations of music also have some cognitive correlates enabling the understanding of non-tonal music. Amongst the many typologies of mathematical representations of music, we will analyse in detail some examples belonging to the transformational paradigm, which is a formalized subfield of computational musicology coming from the American set-theoretical tradition. Transformational music analysis also raises new questions about the cognitive and philosophical ramifications of algebraic and category-theory approaches in music theory, analysis and composition.