Notes on a piano are arranged in order of increasing pitch from left to right. This makes composing melodies intuitive. If you want a higher note move to the right. If you want a lower note move to the left. The piano keyboard is essentially a "melodic space". But playing chords and chord progressions is much less intuitive on a traditional keyboard. Why does one group of notes sound so good together while another group sounds so bad? On The Harmonic Lattice notes are arranged on a triangular grid with harmonically similar notes lying close to one another. Commonly used chords have an easily recognizable shape on the lattice and chord progressions can be thought of as paths through this "harmonic space".
When playing a chord progression on The Harmonic Lattice the individual voices that make up each chord are animated as they change pitches. This type of visualization provides a view into the intersection of harmony and melody. Music theorists call this voice leading.
As you play chords on the The Harmonic Lattice an algorithm calculates the smoothest way for the voices to transition from chord to chord. This results in natural and intuitive sounding chord progressions.
The Harmonic Lattice is a tool for exploring micro-tunings. Western music is typically played using a tuning system known as equal temperament. The Harmonic Lattice is a tool for exploring alternate tuning systems. There is a deep connection between the position of a note on the lattice and its tuning.
It is currently only available for the iPad. It can be downloaded from the app store here.
Be sure to check out the blog for an introduction to the app, a demo of some of the more advanced features, and an exploration of some of the underlying music theory concepts.
I highly recommend you pick up a copy of Harmonic Experience by W.A. Mathieu. It was hugely influential in my development as a musician and in the creation of this app.