With his taxonomy of harmonic function Riemann hoped to introduce systematic order to the boundless dualistic harmonic grid. Yet he still felt the need to employ an additional category: cadential succession. In fact, Riemann's use of the term ‘cadence’ differed significantly from contemporary Anglo-American usage and may need some words of clarification: a cadence for Riemann was not a momentary event but rather a succession of chords that establishes a tonic. He explained the relation between the two concepts as follows:

As with many aspects of Riemann's harmonic system, there is some controversy about the validity and significance of Riemann's notion of cadential succession: most critics either ignore it, or argue that it is self-contradictory. Moreover, the criticism that Riemann himself did not comply with the restrictions he set himself has also been levelled.

All these criticisms have a certain validity, especially when applying Riemann's theory to musical works for analytical purposes. Despite the tension between practice and theory, as we shall see, in Riemann's thought cadential order did serve a supremely important purpose. No less than the rigorous, scientific appeal of Riemann's musical thought rested on the notion of cadential order: it can tell us how music ought to work.