The diagrams remind me of performing a Dehn twist. Perhaps what you're doing at each grouping corresponds to a Dehn twist on the Tonnetz? Of course, since the T

The diagrams remind me of performing a Dehn twist. Perhaps what you're doing at each grouping corresponds to a Dehn twist on the Tonnetz? Of course, since the Tonnetz is a particular subdivision of the torus, only certain groupings that satisfy some divisibility relations will correspond to Dehn twists.