How do I transfer music from my Ipad to my Iphone?

The same way you got it on your iPad, sync it to your phone from your iTunes library. If not in your iTunes library, you can download it directly to your phone: iTunes app>More>Purchased...iTunes purchased music only.

If it was music purchased on the iPad just go to the iTunes store app on your iPhone, tap More, then Purchased, then Music, then Not on this phone.

If it was music from other sources (MP3s, CDs) they should still be in iTunes on your computer; just sync them to the iPhone.

If it was music from other sources (MP3s, CDs) they should still be in iTunes on your computer; just sync them to the iPhone.----

Well, that computer is no longer around, so Ipad is the last resort - how to deal with it then?

Take a look at TouchCopy.