In the '80s the UC Davis University Chorus sang a piece by Edwin Fissinger (Welcome Yule?). There was a passage where the women had 3 part harmony in triads moving against the men's part which had different triads. The effect was thrilling. It led me to investigate polychords further, and to adopt them as one of the typical traits of my musical idioms.
There are many devices in music (rhythm, melody, harmony, instrumentation, dynamics to name a few), and polychords are just one of them. However, they do sound new, and they have rarely been used in the past. There are exceptions, of course, and Charles Ives is the first which comes to mind, with his brash setting of Psalm 67, with them men starting on an F# minor chord and the women on B major, first inversion. Also in pop music the dominant chord IV/V probably should count. And there are certainly many examples in jazz without explicitly acknowledging the technique. (cf. composer Robert Wolff on extended tertial sonorities.)
In this brief treatise I will give examples of polychords where they seem effective. By extension, I will also include examples where dissonances are the point of the passage. The reader or listener will of course need to judge what works best, appeals most, and is most appropriate.
Many of the examples are from my own compositions due to the scarcity of examples and ease of access.
I would encourage composers to investigate these sounds further, and to tap these riches.
I will be posting examples as I have time, and start a blog on FaceBook where people can comment, and cite or contribute their own examples.
Thank you for your interest!
The use of polychords is not a black & white affair, since there is a large amount of overlap amongst styles: pop, jazz, gospel, and neo-classical pushing the envelope. Kirby Shaw uses the 7th in the bass part frequently, which evokes both the traditional 4-2 inversion of the 7th chord, as well as a common jazz flavor. William Mathias uses polychords somewhat randomly. I (Dwight Stone) tend to use polychords related by 4th, 5th & 2nd.
Inversions of chords frequently allude to polychords, as in Lauridsens' "Chansons des Roses", #5 Dirait-on, which has the tonic chord first inversion, sans 5th, with the dominant chord placed above it, yielding a tonic maj9 chord; the 3rd in the bass yields a mild and attractive dissonant rub against the 9th above it; the 9th rubs simultaneously against its neighboring tonic note.
The evolution of polychords encompasses whole-tone and pandiatonic idioms, with washes of sound with multiple neighboring tones clashing, but not organized into distinct chords. Composers from Claude Debussy to Eric Whitaker to Donald Fagen (Nightfly) have evoked this kind of dissonance.