ABSTRACT
Moving beyond triads, Chapter 4 considers Riemann's attitude to seventh chords and outlines common critiques of his position, especially from the NRT perspective: this involves his claims that diminished and augmented triads are not a separate ‘species’ of chord, and that sevenths are necessarily extensions of triads, as opposed to being special musical objects with their own properties. The representation of a total network of smooth voice-leading connection in a post-Tristan world, offered by Cohn as a counter to these claims, is invaluable. But the authors attempt to reinject functional energy into his representation of tetrachordal pitch space by re-conceptualising its harmonic nodes as belonging to a field of ‘submoons’ that orbit the triadic functional moons hypothesised in Chapter 2. This allows them to explain the functional significations of chords that move ‘smoothly’ (as in Chopin's Op. 28, No. 4) and those which are highly disjunct but still acutely chromatic (the ‘Hagen Chords’ motif as it appears in Act 1, Scene 3 of Götterdämmerung) while avoiding some of the pitfalls of a purely Riemannian approach: e.g. the excessive number of possible functional labels that can result if a seventh is understood as being derived from one of many possible triadic formations.
