I ENCONTRO INTERNACIONAL DE ANÁLISE MUSICAL
UNESP–USP–UNICAMP
Perspectivas Analíticas para as Músicas dos Séculos XX e XXI
São Paulo, 20 de Agosto de 2009
Harmonic vectors: A Work in Progress
Nicolas MEEÙS, University Paris-Sorbonne
Summary:
THE THEORY OF HARMONIC VECTORS is a transformational approach of triadic harmony
analogous to neo-Riemannian theory. Although first concerned with tonal harmony, the
theory of harmonic vectors proved able to deal with marginal usages of triadic harmony,
either pre- or post-tonal. The presentation is divided in three parts: the first is devoted to
theoretical considerations; the second proposes a few examples of practical application; and
the third reports on researches conducted by colleagues and students in Paris.
• From a theoretical point of view, it must be stressed that descriptions of the movements of
harmony in terms of the fundamental bass or in terms of parsimonious voice leading (as in
neo-Riemannian theory) are equivalent. A closer consideration of tonal processes shows that
the relations are not symmetrical: the privileged direction is “flatwards” in the case of fifths or
thirds (neo-Riemannian relations R and L), “sharpwards” in the case of the change of mode
(neo-Riemannian relation P). These directions are dubbed “dominant vectors”.
• A statistical application to some of Bach’s chorales shows that dominant vector there
represent more than 90% of the progressions.
• The researches discussed, based on software developed in the Sorbonne, include:
– The PhD thesis (in progress) of Christophe Guillotel-Nothmann on the link between
harmonic progressions and the preparation and resolution of dissonances;
– The thesis of Claire Meyer on the Sacri concentus of Leonard Hodemont (1630-1631)
evidencing differences in the harmonic treatment of “major” and “minor” modes;
– The work of Philippe Cathé, Maître de conferences, on the harmonic style of the Beatles.