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The music of Vice City is perhaps as important as anything in the game. It provides the personality and backdrop to the action. To hear the wide variety of music that GTA: VC has to offer, get into a vehicle and flip stations with the L1 button. This will take you through everything Vice City has to offer, including two talk channels: KCHAT and VCPR.
If you want to groove out to the tunes you hear in the game while you're at work or in your own real car, you can snag a boxed-set of most of the tracks. Just like in the game, they're split up into stations. The soundtrack for each disc/station is listed here (there are some songs that appear in the game that aren't on the discs):