Chuang and Rouquier [3] describe an action by perverse equivalences on the set of bases of a triangulated category of Calabi-Yau dimension −1. We develop an analogue of their theory for Calabi-Yau categories of dimension w < 0 and show it is equivalent to the mutation theory of w-simple-minded systems.Given a non-positively graded, finite-dimensional symmetric algebra A, we show that the differential graded stable category of A has negative Calabi-Yau dimension. When A is a Brauer tree algebra, we construct a combinatorial model of the dg-stable category and show that perverse equivalences act transitively on the set of |w|-bases.