The meanings of temporal adverbials seem easy to describe, but the compositional interaction with tense and aspect is notoriously difficult to analyse because we (more accurately: I) do not understand yet the principles governing the tense/aspect architecture of natural languages well enough. One of the most difficult areas of temporal structure is the perfect, and the literature quoted in this article shows that there is little agreement on its meaning(s). I believe that we will make progress only by a careful investigation of the meanings of temporal adverbials and by stating their formal semantics in a way which is precise enough to test empirical predictions. This is what the present article wants to do. It studies the interaction of the German durative temporal PP seit a ‘since a’ with tense, in particular with the perfect. The result will be that the German present perfect morphology is ambiguous in at least four ways: (a) it may denote a semantic PAST; (b) it may denote an Extended Now in the sense to be explained; (c) it may express a perfect of result; (d) it may express a PRESENT PERFECT in a sense to be explained.