The practice of harmonic mixing is a technique used by DJs for the beat-synchronous and harmonic alignment of two or more pieces of music. In this paper, we present a new harmonic mixing method based on psychoacoustic principles. Unlike existing commercial DJ-mixing software which determine compatible matches between songs via key estimation and harmonic relationships in the circle of fifths, our approach is built around the measurement of musical consonance at the signal level. Given two tracks, we first extract a set of partials using a sinusoidal model and average this information over sixteenth note temporal frames. Then within each frame, we measure the consonance between all combinations of dyads according to psychoacoustic models of roughness and pitch commonality. By scaling the partials of one track over ± 6 semitones (in 1/8th semitone steps), we can determine the optimal pitch-shift which maximises the consonance of the resulting mix. Results of a listening test show that the most consonant alignments generated by our method were preferred to those suggested by an existing commercial DJ-mixing system.