Autoincrementing fields are meant to identify unique rows in a table. Since the second table you mentioned was for CDs, then its autoincement field should be used to identify each CD, not the artist on said CD.
So, let's say the artist table is something like:
create table artists (fullname text, id serial, yada text);
Then the CD table should be something like this:
create table artwork (fullname text, id serial, artistid int constraint artwork_owner references artists(id));
Now, when you insert into the artwork table, there has to already be an artist in the artist table with the id you are putting into artwork.artistid.
Further, if you try to delete the row from the artist table for an artist who has artwork listed in the artwork table, you will be told that there are records in the artwork table that refer to it and you have to delete those before you can delete that artist.