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

Chantal Buteau, Guerino Mazzola

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)117-134
Number of pages18
JournalJournal of Mathematics and Music
Volume2
Issue number3
DOIs
StatePublished - Nov 2008

Keywords

  • Motivic space of a score
  • Motivic structure formalization
  • Réti’s approach
  • Topological model

Fingerprint Dive into the research topics of 'Motivic analysis according to rudolph réti: Formalization by a topological model'. Together they form a unique fingerprint.

Cite this