Q: is there a way to sync music between devices?

Settings > iTunes & App Store > Automatic Downloads > Music/Apps

How To  >  http://support.apple.com/kb/ht4539

Troubleshoot  >  http://support.apple.com/kb/ts3688

Download Past Purchases

1. Sign in with the Apple ID that you used for the original purchase. See which Apple ID you used to download an item.

2) See if the content is available for redownload. Previously purchased items might not be available if they're no longer on the iTunes Store.

From >  http://support.apple.com/kb/HT2519