How fast are these LEDs able to strobe?
You could create a pattern match game that works to a beat (played on the phone). Use the android to play a beat, display simple images on all four of the LED quadrants, two of which match. The phone would have a 4 quadrant touch area. The player simple touches the matching pair of images displayed on the LEDs or slides between them, pinches them, double tap, etc. When the action is on beat (or close) and the match is correct there is a cool drum solo (to indicate success and give the player a break) and increases the beat. The player needs to make the match as fast as possible but on beat (ideally a match per beat), but each level could dictate how fast the player must make the match (i.e. lvl1=every 12 beats, lvl10=every 4 beats, etc) The different gestures play different sounds so the player has a sense of creativity in creating a song. If the player makes a mismatch they get a record scratch and the beat slows back down again. If the player is on beat but not making matches they still progress with a new collection of sounds for the gestures if they are off beat they return to previous sounds. I would use a reasonable level progression system so the player has to really work for new and interesting sounds for the gestures. The images the player must match could also dictate which gesture the player should do if you wanted to add more structure to the gameplay (like bop it) with images that look more and more like the dictating matching pair (if that makes any sense at all).
Spose this doesn't really need the LEDs and could all be done on the phone, buuuuut, ah well. That's one idea. The reason I asked about strobe speed is because the LED's displayed images could strobe off to the beat as well thus making matching more difficult as the beat speeds up.