It's an Arena Shooter with elements of plenty of shmups and a hint of Asteroids etc..
It's major difference is that the level structure (and dynamic elements in the current game such as supplemental shot power) are decided based on what music track you choose to play - the track essentially IS the level.. So you'll get different formations of enemies, 'boss' ships appear at different times etc.. the background is also reactive to the music and gets extremely busy, though the powerups and enemy fire are just visible enough that you don't get many deaths where you just couldn't see something..
You'll get to dread the quiet bits in songs as your shot power drains down to nearly nothing, some careful manouvering is required until the beat picks up again..
Powerups take the form of damage, volume (which also seems to increase fire rate) and score multipliers (which are plentiful, you often end up with over 50x bonuses - you can also increase this by not shooting - this increases your 'daredevil' meter - but you can't usually do that for long..
http://www.youtube.com/watch?v=ASusmLRreXw
Worth a look
