Rameau theorized the Subdominant-Tonic-Dominant (S-T-D) relations as the central structure of tonality – which underlined the relationship between the diatonic scale and the key in a symmetric arrangement of chords and pitches (1737) – derived from cadential chords studied in Traité de l’harmonie (1722). These were the same chords formed in Renaissance, when the voices in modal counterpoint formed “modal triads”. A set of these modal triads from psalm- tones adopted in 17th century’s instrumental music created the tonal practice by transpositions in all pitches [Barnett 1998; Powers 1998].
Major and minor triads, first theorized by Zarlino (1558), are the “cores” of harmony. This topic was the central one of Riemannian harmonic-dualism theory, which bears harmonic functions linked to Rameau’s S-T-D relation and perception/imagination of triads distances [Tonvorstellung] [Riemann 1895; 1915].
These theories were formally demonstrated by Lewin with a mathematical manipulation of triad’s intervals which is based on a palindromic arrangement of intervals replaced above and below the starting triad – something very similar to palindromic structures allowed in modal music when the diatonic set, with an added Bb, formed a palindromic disposition of pitches’ intervals (G-A-B-C-D-E-F-G-A-Bb). This new point of view links the ancient logic of triadic relation to the post-tonal logic, and underlines the importance of studying the triadic relations’ syntax and their birth.