A complementary chord, also called an opposite chord, is a chord placed at a tritone distance from another chord of the same type.
In the case of the sigma chord, two complementary chords are two sigmas whose notes correspond to each other at a tritone distance. For example, corresponding to the sigma of D:
D–E–A–C–D♭
is the complementary sigma of A♭:
A♭–B♭–E♭–G♭–G
The two chords are two 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 may be used as synonyms, but the term complementary indicates the structural completion in the complete world, while the term opposite emphasises instead the symbolic polarity between the two forms in the incomplete world.