This may be one of the easiest things to do in an Apple Expert's eyes but everything that I googled on transferring music from my iPhone to another computer was saying...too bad. So I called Apple this morning to figure out the answer to my problem: How do I transfer music that I purchased on my iPhone to my new computer that I don't currently have my iPhone synced...without erasing my music!
I'm glad I called and am doing my part to keep the Apple Experts employed.
Here are the steps in case you don't want to go through the trouble of talking to those lovely people:
In iTunes, pull down the iTunes menu -->select Preferences-->select Devices-->click box next to "Disable automatic syncing for iPhones and iPods" --> Click OK
Here's what it looks like:
In the iTunes window, find your iPhone (mine's allielune) under Devices and right click (hold the control button and click the mouse at the same time); this will produce a pull down menu. Click on "Transfer Purchases."
TA DA! That's it. I knew Apple couldn't be so evil to deny me a way to move my music that I already paid for with my hard earned money!