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After reviewing some features of the traditional two-dimensional (2D) Tonnetz, we will explore features of a 3-D Tonnetz based on the familiar dominant-seventh/Tristan tetrachord 0258. We will then generalize the 3-D Tonnetz to accommodate relations among members of any tetrachord class. Lastly, we will investigate the relation of a Tonnetz's geometry to the group structure of the transforms relating its elements.
Edward Gollin (Thu,) studied this question.