How to back up my stuff on my iphone 4s to my new computer?

So I got a brand new computer and i'm trying to back up all my stuff onto the iTunes and everything is backed up except my music, can I even back that up? Cause when I press the back up button it doesn't back up my music, help?

Backup will not back up music, this is because if you lose your music, you can simply re-download it all from iTunes, all you would need to do is sign in with your Apple ID and click on Purchased.

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