Love the idea. Also always likes rythm games, so thats a point for you :D
I think one improvement would be to have the button presses/rythm not only be on beat. Right now its always on the first beat. Some offbeat variations/other rythms would give variety to the gameplay (at least I think so :D)
Great visuals, good music: fitting the sleep theme very good.
I liked it. I got 2:39 minutes asleep ;)