An idea I had -- perhaps it's been already thought by lots of people:
Use the binary system to give access to tons (well, at least 128 or 256) notes to a musical instrument design.
You just need like 8 buttons (compared to over a dozen for a flute or 88 for a piano), so you can make it quite compact.
I'm thinking of some digital controller like instrument, but if they could pull off an analog one, that would be interesting too.