This arrangement copyright © 2005 David Webber
The reason that harmonies cannot be satisfactorily generated by computer for any given melody, is essentially that different harmonies can be used with the same melody to produce different effects. (For example in a film score the same theme may recur with different harmonisations and orchestrations to create different moods.)
The example above of a well known tune is extremely simple. It can be "adequately" (if not excitingly) harmonised by just three major chords I, IV and V (or C, F, and G in the key of C-major) as shown in the first 12 bar statement of the theme. And every note of the melody is on the accompanying chord. This is part of what makes the piece so simple and (it may have to be said) uninteresting!
In attempting to follow this with a "less uninteresting" alternative harmonisation I have constrained myself deliberately in two ways, which are not typical of normal arrangements.
- I have not changed the melody in the slightest: neither in pitch nor in rhythm;
- I have only used chords which include the melody note.
Actually I cheated on the second, but only slightly. At one point I wanted an F chord under the melodic D, and so I called it F6 to put the D on the chord! [See also chord names.]
In the slow 4-bar interlude I have also avoided (as in the introduction) the use of any accidentals. But it is still very different from the
original. After that, in reharmonising the complete melody, I have avoided (in some places at least) repeating the same harmonisation of the
same melody, in order to emphasise the choice even more. I may also have used about 11 of the 12 possible notes of the chromatic scale.
Well there we are. It may not be Rachmaninov, but I hope it does illustrate the idea that there are always alternative harmonies, and that a computer, insensitive to the composer's mood, cannot easily guess them.