The theory of Harmonic vectors is a theory of root motion. It considers tonality as resulting from chord progressions instead of being 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.