A novel theory of primary olfactory reception is described. It proposes that olfactory receptors respond not to the shape of the molecules but to their vibrations. It differs from previous vibrational theories (Dyson, Wright) in providing a detailed and plausible mechanism for biological transduction of molecular vibrations: inelastic electron tunnelling. Elements of the tunnelling spectroscope are identified in putative olfactory receptors and their associated G-protein. Means of calculating electron tunnelling spectra of odorant molecules are described. Several examples are given of correlations between tunnelling spectrum and odour in structurally unrelated molecules. As predicted, molecules of very similar shape but differing in vibrations smell different. The most striking instance is that of pure acetophenone and its fully deuterated analogue acetophenone-d8, which smell different despite being identical in structure. This fact cannot, it seems, be explained by structure-based theories of odour. The evidence presented here suggests instead that olfaction, like colour vision and hearing, is a spectral sense.