Polychords may be built with materials from different tonalities, modes, synthetic scales, etc; and then such materials are explored according to musical context and intentions of the composer. But the provenance of materials for polychordal and polyharmonic technique is not exhausted there. When looking at the overtone and undertone series, we can see some chord formation possibilities that can be arranged from the generated partials:
The simplest chord formations from the overtone series based in C, and up to the 16th partial, are:
Chords like D+ or Bb+ were purposefully overlooked because when inverted they are enharmonic with F#+; although you could choose modes from different key centers to compose melodic material based on such chords – i.e. D Ionian #5 or Bb Lydian #5.
The basis for chord construction stems from the overtone series generated by a single tone but when we have a Cmaj chord with the notes C E and G, we have multiple tones generating their own overtone series. That said, overtones from C have the chord options presented above, and E should have the same but transposed a major 3rd up. The same applies to G, with chords transposed a perfect 5th up as well. So, a polychord based in the overtones from Cmaj could be a C|G#m; Em|D or Bm|G#+:
And you can use different chord formations like a Csus4 to provide variety in the chord materials that stem from the overtone series:
To further expand our possibilities, we can also explore the undertone series:
As previously mentioned, inverted or mirrored augmented and diminished chords produce enharmonic chord tones and thus, the only major difference will the mode of choice to be used over such chord inversions.
So, for the same C major chord we can use chord materials derived either from the overtone or undertone series and build polychords like D⁰|Am or Fm|Gb+:
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