Jacques de Liège was the first theorist to use the word cadentia in relation to harmonic theory, preceding later such uses, as far as survivals attest, by a century and a half. The concept he developed under this term (set out in Speculum musicae, IV. l) has been connected in recent times to ideas in fourteenth- and fifteenth-century discant theory now related to the notion of directed progression. While there are linguistic similarities in Jacques's exposition to that of this (mostly later) theory, there are also important discrepancies in the concept's content; and there is an ideological anomaly in viewing Jacques as the exponent of an important idea of Ars nova harmonic theory. This article proposes a different reading of the concept, one congruent with Jacques's conservative intellectual stance. It identifies two contrasting, though complementary, aspects within it, and examines the role of an expression of approximation (ea, quae prope sunt, sunt quasi idem) whose ultimate significance remains uncertain. What emerges clearly, however, is that Jacques regarded cadentia as a process whereby imperfect concords were redeemed for perfection, so that their presence in polyphonic music might be tolerable in an aesthetics of retrospection. His account of polyphony draws upon an established idea in mensural theory dating back at least to John of Garland; and it contrasts significantly with the contemporaneous but more modern account of Marchetto of Padua's Lucidarium.