Other theorists, such as Leonhard Euler (1739), Hermann von Helmholtz (1863/1885), Arthur von Oettingen (1866), Hugo Riemann (who should not be confused with mathematician Bernhard Riemann), and Christopher Longuet-Higgins (1978) have modeled pitch relationships using two-dimensional (or higher-dimensional) lattices, under the name of Tonnetz.
All of these models attempt to capture the fact that intervals separated by acoustically pure intervals such as octaves, perfect fifths, and major thirds are thought to be perceptually closely related.