So it's not exactly that, but if you want a rhythm game with some more nuance, Before the Echo is awesome.

You've got 3 different screens (mana gathering, spell casting, and enemy attacks) and you need to balance which you're prioritizing at any time. Mana is needed to cast spells, spells are needed to defeat the enemy, but you need to block their attacks to not lose all your HP. Each one goes different parts of he music, and as a bonus all the music is from Ronald Jenkees.

It's old, and while funny is also sometimes very cringey, but still a terrific bit of fun.