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Although if the music is on your computer exactly as it is on your phone nothing will happen other than a regular sync, but I think you meant the NEW music is on your computer. So here's your options
1- You could jailbreak and download swaptunes, which allows you to sync with multiple librarys.
2- without jailbreaking
You could download "senuti" on your computer, which does the opposite of iTunes, hence senuti is iTunes spelled backwards. What it does is allows you to take the music, videos/movies off you iPhone, and put them on your computer. Then just add them to iTunes and sync your new music, and Viola! Your done 😀
*hope I could help, good luck
-Any questions please ask-