Generalized Contextual Groups

There is a neo-Riemannian-type group, the generalized contextual group, that can be constructed for the set of transpositions and inversions of any pitch-class segment, provided the segment contains at least two distinct pitch classes which span an interval other than a tritone. The generalized contextual group is dual to the T/I group for any pitch-class segment satisfying the condition above. This article shows how one can construct a generalized contextual group with symmetrical as well as asymmetrical pitchclass segments (previous work in this area has required asymmetry as a precondition to the construction of neo-Riemannian-type groups). The group is “generalized” in that there is a generalized contextual group for any Zm, so Z12 is just one subtype. We apply a mod 12 generalized contextual group (and its dual relation) in a network analysis of Hindemith, Ludus Tonalis, Fugue in E. We close with an application of a mod 3 generalized contextual group in an analysis of a chorale's chord voicings. Submission received April 2005 GENERALIZED CONTEXTUAL GROUPS THOMAS M. FIORE AND RAMON SATYENDRA