add.pl

$dbentry = "BPM-$info.txt"; #add DB prefix
if (-e $dbentry) { #check if file already exists (it should't)
    open(DBENTRY, ">>$dbentry") || die "cannot open file $dbentry\n"; 
+#open w/ error handling
    print DBENTRY "$info\n "; #append Album info (shouldn't have to ap
+pend)
    close(DBENTRY); #make sure we're all neat
} else { #we should be creating a new file
    open(DBENTRY, ">$dbentry") || die "cannot create file $dbentry\n";
+ #open w/ error handling
    print DBENTRY "$info\n "; #add the Album info
    close(DBENTRY); #make sure we're all neat
}
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You do realize that append mode will create the file if it does not already exist? So that should simply be:

$dbentry = "BPM-$info.txt"; #add DB prefix
open(DBENTRY, ">>$dbentry") || die "cannot open file $dbentry: $!"; #o
+pen w/ error handling
print DBENTRY "$info\n "; #append Album info
close(DBENTRY); #make sure we're all neat
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bpm.pl

        @files = (@files, $name); #add it!
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Using push would be more efficient (and idiomatic.)

        push @files, $name; #add it!
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You should at least test your code with warnings enabled!

$ perl -Wc bpm.pl
Found = in conditional, should be == at bpm.pl line 33.
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That line should be:

    if ($flag eq "yes") { #if the flag is on
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But you could simplify that a lot and there is no need to store all of the files lines in an array, just store the ones that match /$bpm/:

foreach my $filename ( @files ) { #for each filename in the array
    open(PHILE, '<', $filename) || die "cannot open $filename: $!"; #o
+pen file w/ error handling
    my @lines = scalar <PHILE>; #get the Artist/Album info
    while ( <PHILE> ) {
        push @lines, $_ if /$bpm/;
    }
    if ( @lines > 1 ) {
        print @lines;
    }
    else {
        print "sorry, no matching BPMs found."; #deliver the bad news
    }
    close PHILE; #finish up
}
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