iOS devices(iPods, iPads and iPhones) aren't designed for that feature. You can only transfer purchased music to a computer, everything that was downloaded elsewhere or ripped from CD's can't be transferred back to a computer.
This has everything to do with the entertainment industry and laws Apple has to follow. It's designed to prevent spreading of illegally downloaded media.
Yes you can transfer the non purchased music to your computer but you will need to purchase a third party application to do it.
Here is one application that will do it. You can try it in a limited basis for free.
thanks, but when i got a new iphone 2 years ago, the music transferred to the "ipod" on the phone. this time, with a new computer AND a new iphone 5, the music did not move. these are songs from old albums that i own, so no scheming inolved to defraud the music industry...just want my old tunes on my new devices.
i have a new computer. how do i save my music (not purchased) from my ipad onto my itunes library?
From your OLD computer...
Copy your ENTIRE iTunes FOLDER to an External Drive... and then from the External Drive to your New Computer..
Full Details Here > http://support.apple.com/kb/HT1751