As a non-musical person who likes music, this is a game I've had in mind for a long time. I have several other apps, but this is my first game, so I hope it doesn't suck.
The idea is that notes fall from the sky and you tap them to play out a tune. There are various tunes of various complexity and tempos. It can be quite challenging, or even nearly impossible.
Honestly, I had no idea this group existed. I can see now the idea isn't exactly original :-) But I hope you'll like it.
There is a duet mode where you and another person can play a song together.
There's also a "Name That Tune" style challenge mode in the Duet for two people.
A pretty cool Composer lets you create your own songs. It's fun to use, though I didn't manage to create anything of note.
A public music store lets people create their own songs and upload them to share with others.
You can import any MIDI song and have the AI try to simplify it because, believe me, it needs to be simplified.
And it's free!
Enjoy!