P aradoxes of P itch S pace

Abstract

ABSTRACT Parallels between the mathematics of tiling, which describes geometries of visual space, and neo‐Riemannian theory, which describes geometries of musical space, make it possible to show that certain paradoxes featured in the visual artworks of M. C. Escher also appear in the pitch space modelled by the neo‐RiemannianTonnetz. This article makes these paradoxes visually apparent by constructing an embodied model of triadic pitch space in accordance with principles drawn from the mathematics of tiling, on the one hand, and from cognitive science, on the other – specifically, the notion that our experience of pitch relationships is governed in part by the metaphorical projection of patterns abstracted from embodied experience known as image schemas. These paradoxes are illustrated with reference to passages drawn from four compositions to whose expressive character such paradoxes contribute: the fifteenth‐century motet ‘Absalon fili mi’; the finale of Haydn's String Quartet in G major, Op. 76 No. 1; Brahms's Intermezzo in B minor, Op. 119 No. 1; and Wagner'sParsifal.

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