This is a complement to my original post (couldn't fit everything in the allowed number of characters):
RELATIONSHIPS AND COLOR SCHEME
. On the isomorphic square grid, all C notes are lightly highlighted. This is just to provide some visual reference as to where each key and octave is. White keys are white and black keys are black, but this means nothing on an isomorphic keyboard - again, this is just to provide visual references, so you can find your way quickly when performing on the isomorphic grid.
. The mini-keyboard on top will activate the corresponding note(s) on the isomorphic grid when any key or set of keys are pressed. This is a nice touch in order to provide reference to those of us used to a traditional keyboard. Play any note or chord on the mini-keyboard while watching the corresponding keys light up on the grid.
The screenshot below illustrates playing a C-Major chord on the mini-keyboard, and the corresponding chord lights up on the iso grid:

Above you can see that the same chord is highlighted in three different places on the iso grid. Almost always, you will find that there are alternative positions on the grid where you can play a given melody or chord. Just pick one that suits your playing style the best! Of course, you can also play directly on the iso grid, avoiding the mini-keyboard completely. When playing directly on the iso grid, whenever one note is pressed, all squares containing that same note will light up. This is both a visual reference, and a quick way for making it easy to find an efficient way to play different sequences of notes and chords.
THE POWER OF ISOMORPHISM
So far, so good, but you could be wondering why the hell go through the process of learning how to play on the iso grid, instead of using an on-screen traditional keyboard. Well, now that you learned above how to play a C-Major chord on the iso grid, congratulations - you can play ANY and ALL major chords using exactly the same relative square positions, and therefore exactly the same finger position! This is true for all the different chords, intervals and scales - once you've learned one, you've learned them all. The screenshot below illustrates one of the "difficult" chords, the A-flat major. On the traditional keyboard, this is not so easy to play, especially on the iPad; the finger positioning is different from the C-Major. On the iso grid, the chord is easy and simple to play; the finger positioning, spacing and format are exactly the same as for the C-Major.

So you see that the iso grid has some advantages over the traditional keyboard:
. Chords and intervals are always played using exactly the same finger position, regardless of the key;
. The finger position on the iso grid often is a lot easier to perform on the iPad, compared to a traditional keyboard;
. Often, there are alternative positions on the grid for playing a given chord or melody, which helps in finding a way to perform with speed and precision.
Hope this helps - have fun!