Harmonic vectors

Abstract

The theory of Harmonic vectors is a theory of root motion. It considers tonality as
resulting from chord progressions rather than as an a priori of musical composition.
It classifies the root progressions in two classes, “dominant vectors” and “subdominant
vectors”, to which all root motions can be reduced on the basis of the usual theories
of chord substitution. It can be shown that well formed tonal phrases are made
up of a majority of dominant vectors, of which at least one involves a substitution.
The application of the theory to music analysis is illustrated by graphic analyses of
three chorals by Bach. One ascertains a very strong asymmetry in the distribution of
dominant vs subdominant vectors and in the successions of vectors. The statistic data
seem to allow an original approach of modal harmony.