ABSTRACT
Chapter 2 lays out the book's essential argument: namely, that some chromatic events can be understood as ‘determinate negations’ of tonality. To adapt the words of Andrew Bowie, late tonal music is ‘limited to the refusal to follow the direction given by [traditional, diatonic tonality], while yet depending on it as what it has to leave behind to make any sense at all’ (2022, 98). In other words, marked chromatic events challenge traditional harmonic-functional frameworks without creating new patterns that suggest the existence of a fully worked-out, competing framework. Riemann's function theory provides a wonderfully clear means of representing this negative-dialectical relationship. (‘Negative’ because it does not give rise to a new framework, but forces us inventively to exhaust the existing one.) To make their point, the authors leap into one of the most complex passages of chromatic music in Wagner's opera, Götterdämmerung: namely, Waltraute's Plaint. In response to this scene's idiosyncrasies, they develop a theory of functional ‘moons’, adapting Richard Cohn's original conception of hexatonic ‘space’ to their Riemannian functional paradigm. They call the resultant model lunar tonality, and they discuss individual chords and their composite trajectories in terms of ‘light-side’ and ‘dark-side’ functions.
