The synchronization index model of sensory dissonance and roughness accounts for the degree of phase-locking to a particular frequency that is present in the neural patterns. Sensory dissonance (roughness) is defined as the energy of the relevant beating frequencies in the auditory channels with respect to the total energy. The model takes rate-code patterns at the level of the auditory nerve as input and outputs a sensory dissonance (roughness) value. The synchronization index model entails a straightforward visualization of the principles underlying sensory dissonance and roughness, in particular in terms of (i) roughness contributions with respect to cochlear mechanical filtering (on a Critical Band scale), and (ii) roughness contributions with respect to phase-locking synchrony (=the synchronization index for the relevant beating frequencies on a frequency scale). This paper presents the concept, and implementation of the synchronization index model and its application to musical scales.