V19 Interval Lattice
Carl Lumma reminded me (1999jun26) about a way to use a lattice to show interval connections: each node in the lattice represents a pitch class, and the direction of movement from one node to another indicates the interval between those nodes.
For example, this lattice shows the perfect fifth, major third and minor third:
From a given node, movement to the right is a perfect fifth up (and thus movement to the left is a perfect fifth down), movement diagonally up to the right is a major third up, and movement diagonally down to the right is a minor third up.
This kind of chart has been done before; the things I added (1999jul01) are: