Can't sync TO the computer from iPhone so going to lose 30 albums! Help!

Question

I have an old iPhone 4 which I used to sync with my old Acer laptop.  The laptop died and I bought a new Macbook Air (love it!).  I copied music from the old laptop to the Macbook but for some reason lots of albums didn't copy across.  It's mainly albums that I had uploaded from CD.  It didn't matter as I only listened to music via the phone but I now have an iPhone 6 and I need to get all these albums on to that.  However when I try to sync the iPhone 4 with the macbook it tells me I will lose everything on the iPhone 4 as it will only sync one way i.e. macbook to phone, not phone to macbook.
The problem is that I no longer have the CDs (got rid of them in a house clear out as i thought they were happily on my computer) and the old Acer has died completely so I can't get the albums off there.  Therefore they now only exist on the old phone.
I wondered if anyone knows any ways of getting round the syncing problem to get the music off the iPhone 4 and onto the Macbook?  Otherwise I'm going to lose around 30 albums!
Thanks so much
Claire C

Answer 1

When you got rid of your CDs you also got rid of the right to have a copy of the music.  And, as you can see, there are reasons for keeping the CDs as a backup.
You obviously did not do the correct process to transfer the iTunes library from the old computer to the new one.  If you still have the old computer your question would best be addressed from that perspective.  If you do not you will have to buy third party software to do a less-than-ideal transfer of non-iTunes purchases from the iPhone before wiping it so it will sync with the new computer.
Your i-device was not designed for unique storage of your media. It is not a backup device and media transfer was planned with you maintaining a master copy of your media on a computer which is itself independently backed up against loss.  To use a device with a a different setup you transfer the old library from a computer or a backup directly to the new setup, not the device to the library. Media syncing is one way, computer to device, updating the device content to the content on the computer, not updating or restoring content on a computer. The exception is iTunes Store purchases which can be transferred to a computer.
iTunes Store: Transferring purchases from your iOS device or iPod to a computer - http://support.apple.com/kb/HT1848 - only purchases from iTunes Store
For transferring other items from an i-device to a computer you will have to use third party commercial software.  See this document by turingtest2: Recovering your iTunes library from your iPod or iOS device - https://discussions.apple.com/docs/DOC-3991