Well, Jack...

If it had a bar for each note - you would need 12 for a chromatic system - it would release each octave of the named note when depressed.

All you gotta figure out is some way of arranging them so that with 4 fingers - it may be difficult to use the thumb, especially if the instrument is held at some angles - you could get most reasonable chords... you may have to be satisfied with having a 'base' key like C Major...