Is it possible to download music on your iTunes music library without a computer?

I do not own a computer and I was wondering if there was a way to transfer music on my iPad or iPhone on the default music app without iTunes.

I'm a little confused… Surely if you don't have a computer the only way you could have got any music onto your iPhone or ipad would be via downloading it from iTunes, thus if you have iTunes open on the other device it should give you the option to download a song that is purchased in your account onto the other device that doesn't have it on? It would either be in 'purchased' or go onto the iTunes store and try to download whichever song and it should already show its on your account and let you get it this way. Hope that's right.