I thought for your purpose a hash of hashes might be better? For example:

my %hash = ( artistsong1 => { 1 => 1, 3 => 1, 5 => 1 },
             artistsong2 => { 2 => 1, 4 => 1 } );
# to find  for ArtistSong1, does 1 exist?
if($hash{artistsong1}->{1})
{
  print "yes, 1 does exist for artistsong1!\n";
}
[download]

If in fact, your set for song1, song2, song3 are always mutually exclusive, then it might make sense to reverse the data structure to:

my %hash = 
( 1 => artistsong1,
  3 => artistsong1,
  5 => artistsong1,
  2 => artistsong2,
  4 => artistsong2,
  6 => artistsong3,
  7 => artistsong3
);
# to find where 1 is?
my $artistsong = $hash{1};
[download]

Or of course you could also make hashes of hashes of hashes like $hash{$artist}->{$song}->{1}) && print "yes, for $artist, $song, there's 1!\n";