Motivic analysis according to rudolph réti: Formalization by a topological model

This paper proposes a formalization of the neutral niveau of Rudolph Réti's approach to motivic analysis within our mathematical model based on topological spaces of motives. Réti developed a substantial approach favouring melodic relationships below the musical surface. However, his approach has been much criticized for reasons such as an evident lack of methodology. This paper suggests that, when Réti's terminology is redefined in a precise mathematical setup, his approach can fit a computer-aided motivic analysis, and a topological solution to his problematic identity concept and limitation of transformations can be proposed. Our mathematical model, based on motif, contour, gestalt, and motif similarity, involves neighbourhoods of a motif that include similar motives of different cardinalities. It yields a topological space on the set of all motives of a composition, and in which Réti's concepts of shape, imitation, variation, and transformation are naturally formalized. The ‘germinal motif’ corresponds to the ‘most dense’ motif in the space.