Now I want to watch K-On again!
Like taleweaver said, we don't understand if you are looking for a rhythm game with a specific element, or any rhythm game.
Or maybe you want only PSP games?
or maybe just "picking one instrument" and playing that part on the song. I don't remember playing game where you can pick only one instrument from the scores.
If you want a general rhythm game, I don't know about PSP, but I played few of them on other consoles.
First,
Osu Tatakae Ouendan series on NDS. that's like a classic in rhythm games. The series got a western version named "Elite Beat Agent" (less good but interesting).
That series even served as base for the PC open source version
OSU
If you want to stay in the anime world, you can find
Nodame Cantabile, very short and not that interesting, but that's Nodame cantabile, if you liked the anime/drama, then you'll want to play it.
Taiko no tatsujin, too. though, it's only drum music (2 touch mode only).
On NDS, there's also this very good game :
Maestro! Jump in music, easy in easy mode, too hard in normal.
there's also an old one, less known :
Daigasso, Band brothers. there's a
3DS version too.
On 3DS, you can find 3
Theatrhythm games : 2 Final fantasy and 1 Dragon quest.
I liked better the first Final fantasy game, even though it has less musics. But both are very good.
I don't have Dragon quest game, but I'm sure it's as good.
On Wii and other consoles, you have games like guitar hero, or Rock band, where you play with a instruments instead of the console's main controller.
I probably forgot a lot of other game series.
