A music app that will save your music?

Ok so I was wondering if there's a app in the apple store that will save your music so that you can play it lik on a different device. For ex. If you download a bunch of music on a specific app on lik a iPhone 4s it could lik save it by an account or email on the app so that in the future if your phone breaks or you get a new phone lik a iphone 5 you could redownload the app n enter in your email or account n your music you downloaded on the phone before is now on your new phone so you don't hav to waste your time redownloadin everything. Thanks so much for those who will answer the question!

Spotify and Pandora are good music apps, but they both cost money for the monthly membership stuff.

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