One of the things that distinguishes The Harmonic Lattice from other tonnetz or hex-keyboards apps is the way it handles voice leading.
Voice leading is the way that musical parts, or voices, set up and achieve melodic, harmonic, and formal goals using pitch and rhythm.
The notes in The Harmonic Lattice correspond to "pitch classes" (C, C#, etc.) but they do not specify which octave the pitch should be played in. This means that there is an inherent ambiguity in when playing notes on The Harmonic Lattice. One common way of resolving this ambiguity is to simply force all the notes to be in the same octave. This can lead to unnatural sounding chord progressions.
Instead The Harmonic Lattice uses an algorithm developed by Princeton music theorist Dmitry Tymoczko. This algorithm was originally described in a paper that appeared in the journal Science. It calculates the smoothest way to move from one chord to another. By tapping notes and triads on the lattice you select the pitch classes of a chord and the voice leading algorithm chooses the octaves. It is also possible to manually control the voice leading using the gestures described on the Interface page.