use List::Util qw(max sum);
use strict;
use warnings;

sub note2num {
	my ($n,$m) = split(//,uc(shift()));
	my %nums = qw(C 0 D 2 E 4 F 5 G 7 A 9 B 11);
	my $num = $nums{$n};
	$num++ if ($m eq 'S' || $m eq '#');
	$num-- if ($m eq 'F' || $m eq 'B');
	$num;

}
sub num2note {
	my $num = int(shift()) % 12;
	my %notes = (0,'C',1,'C#',2,'D',3,'D#',4,'E',5,'F',6,'F#',7,'G',8,'G#',9,'A',10,'A#',11,'B');
	$notes{$num};
}

sub root	{
	my @chord = @_;
	my @weights;
	my @rootWeights = (10,0,1,0,3,0,0,5,0,0,2,0); # weights of root-support intervals, similar to those in Parncutt (1988)
	my @notes;	$notes[$_] = 0 foreach (0..11);
	$notes[note2num($_)] = 1 foreach (@chord);
	
	foreach my $pc(0..11) {
		$weights[$pc] = sum(map{$notes[($pc+$_)%12]*$rootWeights[$_]} (0..11));
	}
	my $ambig=sqrt(sum(@weights)/max(@weights));
	my @final = map {num2note($_)} sort {$weights[$b] <=> $weights[$a]} (0..11);
	($ambig,@final);
}

my ($ambiguity, @roots) = root('b','d#','f','g#');
foreach (1..int($ambiguity)) {
	print "Root $_ = $roots[$_-1]\n";
}