In the analysis of late tonal music, analytical approaches which attempt to understand tonal function on the one hand, and harmonic transformation viewed through a neo-Riemannian lens on the other, often stand in an uneasy relation. Through analysis of Act 1, Scene 3 of Götterdämmerung, this chapter attempts to bring neo-Riemannian theory closer to its origin in Hugo Riemann’s functional theory, and so to point the way towards a new theoretical frame for understanding the tonal function of chromatic music. We urge this return to Riemann because it enables twenty-first-century listeners and theorists to appreciate the complex power of tonality as a system which, like the great socio-economic, legal, religious and scientific systems that have endured into the twenty-first century, has an indefatigable ability to subsume anything that might seem to pose a challenge to it back into itself, as a source of further power.