This book contributes to the growing work on scale-based formal semantic approaches to verbal phenomena. It presents a new scale-based framework for both aspectual classes and grammatical aspect with the aim of offering an analysis of achievements in the progressive. In order to analyse these, the temporal trace function is relativised to a granularity parameter, and the semantics of the progressive operator is assumed to involve partitivity over scales of change. To this end, a novel concept of a scale of change is adopted, building on a bottom-up idea of associating scales with events and characterising verbal predicates via event-level scales. As a crucial departure from former scale-based approaches, predicates like arrive" are associated with both two-valued and multi-valued scales of change. The new framework can then capture fine-grained aspectual class differences and predict the interpretations of the progressive for different aspectual classes.