The relationship between molecular structure and odor character is one of the most complex structure-activity problems in biology. Despite over a century of effort, it remains unsolved, and synthesis of new odorants still proceeds largely by trial and error. In previous work, I have argued that the reason for this failure lies in a mistaken assumption, namely that molecular shape determines odor character. Instead, I have taken up and extended an old idea (Dyson, 1938) according to which vertebrate olfactory receptors detect odorants by their molecular vibrations. I propose that the detection mechanism is inelastic electron tunnelling. If this is correct, there should be a correlation between the tunnelling vibrational spectra of odorants and their odor character. Here, using semi-empirical quantum chemistry methods and a simple calculation method for tunnelling mode intensities, I calculate the spectra of structurally diverse odorants belonging to various odor categories. With few exceptions, the calculated spectra of bitter almonds, musks, ambers, woods, sandalwoods and violets strongly correlate with odor character.