Table: music

ID      Artist
1       Jimmy Barnes
2       Elvis
3       Jimmy Bob Junior Jnr

Table: music_existing
ID      Computer_ID     Music_ID
1       1               1
2       1               2

(pschulz01)
  select m.artist
   from music as m, music_existing as me
   where m.id left join me.Music_ID
     and me.Computer_ID != 1