A complementary chord, also called an opposite chord, is a chord located a tritone apart from another chord of the same type.
In the case of the sigma chord, two complementary chords are two sigmas whose notes correspond at a tritone distance. For example, to the D sigma:
D–E–A–C–D♭
corresponds the complementary sigma of A♭:
A♭–B♭–E♭–G♭–G
The two chords are structures placed on opposite poles of the chromatic total. Their relationship depends on the tritone distance that separates each note of the first chord from the corresponding note of the second.
Complementary chord and opposite chord can be used as synonyms, but the term complementary indicates structural completion in the fulfilled world, while the term opposite instead emphasizes the symbolic polarity between the two forms in the unfulfilled world.