I'm learning and practicing with the E-R model trying to design a music industry database.
I suppose an album can be had by an artist and a band, not necessary by only one of these. How can I represent this relationship?
ALBUM but add a "many to many" relationship between the two.
There are still a lot of complexities you are missing (eg "Artist formerly known as Prince" vs "Prince", cover songs, etc)
Aside from a learning example, if you want to actually do this I suggest checking out MusicBrainz which is an open source project to document the worlds music collection with one schema. It's pretty complex, but it has to be to get the job done.
You can find more information in their schema document.