Neo-Riemannian Transformation Theory is a way of looking at the harmonic progressions with more attention placed on the relationships between chord members (each, individual note in the chord) instead of between roots and the overall key. For that reason, it’s a helpful theory to use when analyzing music that uses triadic harmony (chords built from 3rds) and is sort of in a key and also sort of not in a key.
The Tonnetz is a geometrical representation of these relationships. Each triangle represents a triad, and the goal when creating chord progressions from the Tonnetz is to move from chord to chord with the least amount of movement. Change only one chord member when possible!
More on the theory coming soon!