When focusing upon vertical harmonics (rather than scalar lines), I work entirely with interval-classes. I consciously avoid traditional chordal structures. Each interval-class has a distinctive hue, and by combining them in stacks one may create a limitless palette of more or less contrasting harmonic colors. Using this approach with an ear for implicit tonal centers, the listener may be led into expectations and then “surprised” by atypical twists and turns that are just near enough to those expectations to suggest one tonality whilst being just odd enough to confound with an alternate tonal center at the same time.
Polytonality is generally difficult to balance in such a way that the multiple tonal centers are all heard, so careful arrangement of instrumentation is crucial to making this work as intended. When it does work, the effect is magical as the ear is baffled by the paradox of what seems vaguely familiar yet also strange. That paradoxical perception causes a distinctly characteristic neurological response. The waves intermodulate in the auditory processes of the brain in a way which excites a sense of discovery, like exploring a new landscape.
Placing these stacks of interval-classes over shifting bass lines brings a sense of harmonic motion, as the bass line moves nearer or farther from the tonality of the stack above it. When there is not any semblance of traditional “chords” and their incumbent functional progressions, there is a far greater freedom but also a somewhat greater challenge. Strong voice-leading with careful attention to overlapping suspensions becomes crucial. The instrumental arrangement must bring out the pitches which determine the distinctive chroma of the contrasting tonalities, without having one overshadow the rest.
If done carelessly the result can be an indistinct mush with no direction. So a good deal of time must be spent listening and searching for sounds that work in musically effective ways, and bringing those sounds into focus with clarity that listeners can easily grasp. The reward for that effort is the joy of discovery and the wonder of strange beauty.