Many aspects of Elliott Carter's pitch language are well understood by music theorists, including his use of all-interval series, his technique of distributing intervals among instruments, and his use of the all-interval tetrachords and all-trichord hexachord.1 One feature of Carter's music that has not been widely discussed involves a situation where the union of any member of sc X with any non-intersecting member of se Y is always a member of sc Z.2 As an illustration, Example 1 shows mm. 84-96 of Carter's Gra (1993) for Bb clarinet. The multiphonic dyad {E4, B5} (mm. 85-86) recurs along with the pitches {Bl4, F5} (m. 85) at a variety of dynamics as members of sc 2-4[04] swirl around them: first (mm. 87-88), (mm. 92-94). The recurring pitches {E4, B5, Bb4, F5} form a member of sc 4-9[0167], and these pitches combine with any of the 2-^[04] members to form a member of se ATH, the all-triehord hexa chord 6-Z17[012478].3 The opening ATH member {9AB145} is labeled To(Z); the remaining ATH members, which complete the aggregate in tandem with T0(Z), are labeled T0K(Z), T6(Z), and T6K(Z). K is a con textual inversion4 that maps a given ATH member Z to the unique ATH