Furthermore, the formalism of neo-Riemannian theory treats voice leading in a somewhat oblique manner: "neo-Riemannian transformations," as defined above, are purely harmonic relationships that do not necessarily involve any particular mapping between the chords' notes. Neo-Riemannian transformations can be modeled with several interrelated geometric structures. The Riemannian Tonnetz ("tonal grid," shown on the right) is a planar array of pitches along three simplicial axes, corresponding to the three consonant intervals. Major and minor triads are represented by triangles which tile the plane of the Tonnetz. Edge-adjacent triads share two common pitches, and so the principal transformations are expressed as minimal motion of the Tonnetz. Unlike the historical theorist for which it is named, neo-Riemannian theory typically assumes enharmonic equivalence (G = A), which wraps the planar graph into a torus. Alternate tonal geometries have been described in neo-Riemannian theory that isolate or expand upon certain features of the classical Tonnetz. Richard Cohn developed the Hyper Hexatonic system to describe motion within and between separate major third cycles, all of which exhibit what he formulates as "maximal smoothness." (Cohn, 1996). Another geometric figure, Cube Dance, was invented by Jack Douthett; it features the geometric dual of the Tonnetz, where triads are vertices instead of triangles (Douthett and Steinbach, 1998) and are interspersed with augmented triads, allowing smoother voice-leadings. Many of the geometrical representations associated with neo-Riemannian theory are unified into a more general framework by the continuous voice-leading spaces explored by Clifton Callender, Ian Quinn, and Dmitri Tymoczko. This work originates in 2004, when Callender described a continuous space in which points represented three-note "chord types" (such as "major triad"), using the space to model "continuous transformations" in which voices slid continuously from one note to another. Later, Tymoczko showed that paths in Callender's space were isomorphic to certain classes of voice leadings (the "individually T related" voice leadings discussed in Tymoczko 2008) and developed a family of spaces more closely analogous to those of neo-Riemannian theory. In Tymoczko's spaces, points represent particular chords of any size (such as "C major") rather than more general chord types (such as "major triad").