1998/01/01 by Edward Gollin · 5 citations
Mathematics · #Mathematics and Applications
paper · doi:10.2307/843873
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.