Alternate keyboard input methods for a digital touchscreen piano?

Question

Typical digital touchscreen pianos I've seen mimic a physical keyboard, i.e. a series of vertical keys rising in pitch from left to right.

My question is: are there alternative digital touchscreen keyboards that use slightly or radically different interfaces?

(For a loose analogy of my thinking behind this question, think of the QWERTY versus Dvorak computer keyboard layouts. QWERTY is based on mechanical typewriters which arranged keys to have common sequences of letters separated, to minimize mechanical jams. Dvorak gets rid of that requirement and optimizes for keying speed. Similarly, I'm wondering if there are more "optimal" ways of inputing notes/chords in a digital touch-screen setting than the standard left-to-right piano layout.)

Answer 1

There is a lot of interest in isomorphic keyboards, where the same musical intervals are represented by the same 'shape' on the keyboard. Many of these are based on a two dimensional tiled layout of keys, where each direction represents an interval. Layouts include:

Janko, where one key to the 'East' goes up two semitones, 'North East' is down a semitone, and 'South West' is down another semitone;

Harmonic, where 'North' is 7 semitones, 'South East' is down 3, and 'South West' is down 4;

Wicki-Hayden, where one key to the 'East' goes up two semitones, 'North East' is up five a semitone, and 'South West' is down seven;

(These all from http://www.slideshare.net/dbgerhard/smc13)

A couple of iPad apps :

Hex OSC:

Musix: