I want to put this out here before I forget the idea. An interesting single button game design would be to create a song one instrument at a time. Let's start of with something easy: a marching band drum cadence. The game would start with the bass drum. A series of points would come scrolling across the screen. When the points hit a certain line, the play would tap the button to play the beat. If they hit the point dead on, they get lots of points, if they miss it by a slight amount, then get get fewer points. At the end of the round, if they have enough points, they can progress to the next instrument. The next instrument would be played on top of the newly made bass line. For a snare drum, a roll would be played by holding the button. This would be represented as a line for the length of the roll. After all the instuments were done you would have what finally sounded like a full drum cadence. Comments?

I had a very similar idea to this a while ago, only with taiko drums. Instead of just slowly building up a song, I envisioned that you would get all four or five drums going, and then loop around to the first one, and change its pattern. So, you could have a constantly evolving piece of drum music with different simple drum patterns interacting in complex ways.

Kind of like "drum machine" on tokyoplastic.com.

http://www.gamasutra.com/features/20050602/green_01.shtml

thought this was a relevant link. Are you thinking just one button ever? or one button and a d-pad?