Pitch is a fundamental attribute of auditory perception. The interaction of concurrent pitches gives rise to a sensation that can be characterized by its degree of consonance or dissonance. In this work, we propose that human auditory cortex (AC) processes pitch and consonance through a common neural network mechanism operating at early cortical levels. First, we developed a new model of neural ensembles incorporating realistic neuronal and synaptic parameters to assess pitch processing mechanisms at early stages of AC. Next, we designed a magnetoencephalography (MEG) experiment to measure the neuromagnetic activity evoked by dyads with varying degrees of consonance or dissonance. MEG results show that dissonant dyads evoke a pitch onset response (POR) with a latency up to 36 ms longer than consonant dyads. Additionally, we used the model to predict the processing time of concurrent pitches, here, consonant pitch combinations were decoded faster than dissonant combinations, in line with the experimental observations. Specifically, we found a striking match between the predicted and the observed latency of the POR as elicited by the dyads. These novel results suggest that consonance processing starts early in human auditory cortex and may share the network mechanisms that are responsible for (single) pitch processing.