Wow. This is simple, but oh so beautiful. From the keyboard of the mighty Ernst Terhardt comes this lovely little algorithm to calculate the root of a chord, given a bunch of notes.

What amazed me was that the root note doesn't have to be included! - as evidenced by the 'Tristan' example. I'll be playing with this for days! :)

Update - Now improved! Uses the full subharmonic range, and picks out all possible answers - eg. "a c e g" can be either C(6) or A(m7).

my %nums = qw(A 0 A# 1 BB 1 B 2 C 3 C# 4 DB 4 D 5 D# 6 EB 6 E 7 F 8 F#
+ 9 GB 9 G 10 G# 11 AB 11);
my %notes = qw(0 A 1 A# 2 B 3 C 4 C# 5 D 6 D# 7 E 8 F 9 F# 10 G 11 G#)
+;
use List::Util qw(max);

sub find_root {
    my @f;
    foreach my $n (map {$nums{uc($_)}} @_) {
        ++$f[($n+$_)%12] foreach (0,0,0,2,5,5,8,10);
    }
    my $max = max(@f);
    map {$notes{$_}} grep {$f[$_] == $max} (0..11);
}

print find_root(qw(c f a)),"\n";    # F - 2nd inversion
print find_root(qw(e g a# c)),"\n"; # C - 1st inversion 7th)
print find_root(qw(f b d# g#)),"\n";# C#(!)/G# - 'Tristan' chord, C#9(
+no bass) *or* G#m6

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In reply to Chord root by benn

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