We propose a novel high-level signature for continuous semantic description of 3D shapes. Given an approximately segmented and labeled 3D mesh, our descriptor consists of a set of geodesic distances to the different semantic labels. This local multidimensional signature effectively captures both the semantic information (and relationships between labels) and the underlying geometry and topology of the shape. We illustrate its benefits on two applications: automatic semantic labeling, seen as an inverse problem along with supervised-learning, and semantic-aware shape editing for which the isocurves of our harmonic description are particularly relevant.