While the theoretical recognition of keys must be credited to the middle baroque period, the honor of having realized their harmonic implications goes unquestionably to Rameau. His Traité de I'harmonie reduite à ses principes naturelles and later treatises, in which the author fundamentally amended his view, laid the foundation for modern harmonic theory by the recognition of a tonal center (centre harmonique), the discovery of the chord inversions, and the postulate that chords must be built up in thirds. By reducing all chords to three functions, the tonic, dominant, and subdominant, he designed a system of chordal relations that prescribed the progression of chords by a "fundamental bass." This bass reduced all harmonic progressions to a theoretical line that was independent of the actually sounding bass. With the functional determination of chord progressions and the emancipation of the fundamental bass from the thorough-bass Rameau actually exploded the continuo system, which recognized neither inversions nor the third structure of chords, and which knew of no harmonic direction of chords. It is strange that in the presentation of his system Rameau fell into inconsistencies which show him still imprisoned in continuo thinking. His manner of figuring the fundamental bass and that of "adding" tones to triads (Sixte ajoutée) represent vestiges of the continue practice which have survived even to the present day in such terms as sixth chord. In spite of its inner contradictions, however, Rameau's system of functional harmony represents the beginning of a era of harmonic thought. His emphatic subordination of melody to harmony, which cannot be reconciled with contrapuntal music, forms the transition to the theory of the classic period.
Manfred Bukofzer. Music in the Baroque Era, página 387.