Tonnetz
A map of harmony. Every major triad is an upward triangle and every minor triad a downward one, and neighbouring triangles share two notes. The trail shows the fewest flips from one chord to the next, which is the smoothest way the voices could have moved.
Connect the minichord, or try a test progression below.
Play a chord
- Move
- –
- Voices
-
Moved– Smoothest–
- So far
- –
The three flips
- P
- Parallel. Same root and fifth, the third moves a semitone: C to C minor.
- L
- Leading-tone. The root moves a semitone: C to E minor, where C slips down to B.
- R
- Relative. The fifth moves a whole step: C to A minor, where G rises to A.
Each flip moves one voice by a step or less, so a short trail means smooth voice leading is possible. Whether you took it shows in the bars: voices that leap around move far more than the trail needs.
Test progressions
Play the same progression both ways: the trail stays the same, but root position moves the voices much further. These only draw; the minichord makes its own sound.
Reading the map
Across the map notes step by fifths; up and to the right by major thirds; down and to the right by minor thirds. The same note appears many times because the map wraps around like a doughnut; the view quietly re-centres when the trail wanders far. In just intonation those copies would differ by a comma, and equal temperament is what makes them one note.