This paper provides a formal semantic analysis of past interpretation in Medumba, a graded tense language. Based on original fieldwork, the study explores the empirical behavior and meaning contribution of graded past morphemes in Medumba and relates these to the account of the phenomenon proposed in Cable for Gĩkũyũ. Investigation reveals that the behavior of Medumba gradedness markers differs from that of their Gĩkũyũ counterparts in meaningful ways and, more broadly, discourages an analysis as presuppositional eventuality or reference time modifiers. (...) Instead, the Medumba markers are most appropriately analyzed as quantificational tenses. It also turns out that Medumba, though belonging to the typological class of graded tense languages, shows intriguing similarities to genuinely tenseless languages in allowing for temporally unmarked sentences and exploiting aspectual and pragmatic cues for reference time resolution. The more general cross-linguistic implication of the study is that the set of languages often subsumed under the label “graded tense” does not in fact form a natural class and that more case-by-case research is needed to refine this category. (shrink)