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You know what's kinda awesome to think about? What happens when two really good song mages battle each other with their music.
Because think about it. They often can't just both sing their own songs at each other. That doesn't tend to work very well. Instead, they are better off trying to improvise off each other in such a way that they can twist the music into the theme they want while the other mage loses track of what they are doing.
Basically, they fight with jazz. :3
Well the thing you have to remember is, and I admit the video I linked is not a example of this, there is absolutely no reason why they would calmly take turns. Instead it would be more like melodies and counter melodies as they both reacted to each other's song, focusing on directing the over all feeling of the piece as a whole, tripping up each other with complex rhythmic patterns, and so on. Rap is just not anywhere near complex enough. Heck at that level using meaningful words at all is basically impossible. You have to just let the music flow chaotically while doing your best to shape it in a general direction. Doing stuff like that is basically what jazz is all about. I mean music based magic typically isn't used in direct combat exactly because it can be easy to disrupt, counter, or cause to go wild. But it sounds hella fun to watch/listen to a battle like that!
Well, I can think of six non-jazz songs that accomplish this well...
But they're all from one game series so...
They're all Guitar Battles, three from Guitar Hero III: Legends of Rock, one from GH Aerosmith and the other two from Guitar Hero World Tour (though those are in-game functionally different)
Guitar Battle vs. Lou (Metal cover of The Devil Went Down To Georgia as performed by Stephen Ouimette)
There was supposed to be a Bass Duel vs. Sting, but that was cut (Guitar Hero World Tour).
(the video this links to is the song you play along with Sting - he's in the vocalist's placement while playing bass and it is the original version of Demolition Man before studio fading and rendering)