How to transfer music from an old iPhone to a new one?

Is there a way to transfer music from an old iPhone to a new one without using iTunes or a computer?
I've registered my iTunes account to the max amount of devices. I've gone through many phones, iPods, etc. I don't even use my computer any more.
I'd like to know how to move the songs on my old phone to my new one if its even possible.

I think the only way to move the songs is by computer

You could clear out that registered devices cache if you want. Then you could add whatever newer devices & go from there.

Check the Account Information in iTunes you'd see the option.

You can use the iCloud, dropbox, and the other online storage.
I suggest to use iCloud.