Between mind and mathematics. Different kinds of computational representations of music

Mathématiques et sciences humaines. Mathematics and social sciences

Andreatta, Moreno¹  Acotto, Edoardo¹ 

关键词: mental representations;    music;    conceptual spaces;    generative theory of tonal music;    phenomenological structuralism;    sound object;    transformational analysis;   

DOI  :  10.4000/msh.12254

学科分类：数学（综合）

来源: College de France * Ecole des Hautes Etudes en Sciences Sociales (E H E S S)

【 摘 要 】

In this article we analyse different types of representation 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 matter of cognitive psychology and philosophy, it can be argued that also mathematical representations of music have some cognitive correlates enabling the understanding of non-tonal music. Amongst the many typologies of mathematical representations of music, we will analyse in details 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 opens new questions about the cognitive and philosophical ramifications of algebraic and category-theory approaches in music theory, analysis and composition.

【 授权许可】

Unknown