TonnetzAnalysis sheetThomas Posen, Ph.D.
Progression

Directions. → up a perfect fifth (+7). ↗ up a major third (+4). ↘ up a minor third (+3). The opposite way goes down.

Triangles. ▲ is a major triad, ▼ is minor. The root is at the left end of the horizontal edge, the fifth at the right.

Moves. P flips a triangle across its → edge, L across its ↘ edge, R across its ↗ edge. Every note repeats, so use whichever copy is nearest.

Drawing a path. Shade the first chord’s triangle. Draw an arrow from each triangle’s center to the next, and label it P, L, R or a chain such as LP. Write the chords in the boxes below the grid with the moves in the circles.