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In music, a cyclic set is a set, "whose alternate elements unfold complementary cycles of a single interval." Those cycles are ascending and descending, being related by inversion since complementary:
In the above example, as explained, one interval and its complement , creates two series of pitches starting from the same note :
According to George Perle, "a Klumpenhouwer network is a chord analyzed in terms of its dyadic sums and differences," and, "this kind of analysis of triadic combinations was implicit in," his, "concept of the cyclic set from the beginning".
A cognate set is a set created from joining two sets related through inversion such that they share a single series of dyads.
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