We present a hierarchical harmonic mixing method for assisting users in the process of music mashup creation. Our main contributions are metrics for computing the harmonic compatibility between musical audio tracks at small- and large-scale structural levels, which combine and reassess existing perceptual relatedness (i.e., chroma vector similarity and key affinity) and dissonance-based approaches. Underpinning our harmonic compatibility metrics are harmonic indicators from the perceptually-motivated Tonal Interval Space, which we adapt to describe musical audio. An interactive visualization shows hierarchical harmonic compatibility viewpoints across all tracks in a large musical audio collection. An evaluation of our harmonic mixing method shows our adaption of the Tonal Interval Space robustly describes harmonic attributes of musical instrument sounds irrespective of timbral differences and demonstrates that the harmonic compatibility metrics comply with the principles embodied in Western tonal harmony to a greater extent than previous approaches.