Analysing harmony – at the borders of tonality

Abstract

Geometric representations in networks, initiated by Euler and taken over first by
Riemann, then by the neo-Riemannian theories, form a useful tool to visualize
harmonic features linked to tonality. The aim here is to show that they are useful
also for illustrating non tonal harmony, as shown of the basis of the example of
Catacombae, from Mussorgsky’s Pictures at an Exhibition, of 1874. Catacombae is
not atonal properly speaking, but it evidences harmonic logics that answer other
criteria than strict traditional tonality. The paper proposes a concrete method of
analysis, usable by students, allowing a rigorous description of the harmonic
phenomena at play, without having to recourse to a theory of tonality as such