How to sync my iPhone's songs to my new computer?

Six months ago I got a Mac and it got stolen just recently and it had all my songs on there. Some of the songs weren't purchased because I got it off of CDs. And once I downloaded all of the CD songs, I thought that I didn't need to use it anymore so I gave the CDs away. And now i got a new computer but when I try to sync my iPhone to the new computer, the songs don't transfer to the computer! I wanted to have my songs on my computer so when I do things on my computer, I don't have to plug in my earphones to my phone and plug in another earphones into my computer.

Use senuti app

Usually If I down load songs on one computer and want to put them on my laptop there's an actual 'sync' button that does the trick, so I have no idea how to help you.

sorry this was probably no help at all But it's all I could think of

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