A major ecosystem effect of biodiversity is to stabilise assemblages that perform particular functions. However, diversity–stability relationships (DSRs) are analysed using a variety of different population and community properties, most of which are adopted from theory that makes several restrictive assumptions that are unlikely to be reflected in nature. Here, we construct a simple synthesis and generalisation of previous theory for the DSR. We show that community stability is a product of two quantities: the synchrony of population fluctuations, and an average species-level population stability that is weighted by relative abundance. Weighted average population stability can be decomposed to consider effects of the mean-variance scaling of abundance, changes in mean abundance with diversity and differences in species' mean abundance in monoculture. Our framework makes explicit how unevenness in the abundances of species in real communities influences the DSR, which occurs both through effects on community synchrony, and effects on weighted average population variability. This theory provides a more robust framework for analysing the results of empirical studies of the DSR, and facilitates the integration of findings from real and model communities.