I think the answer is that is has to be the kind of tune that defies expectations and yet – after being heard a few times – implants itself in our minds.
A prime example of a haunting tune is Laura, composed by David Raskin in 1945.
For ease of discussion, let’s consider it in the key of C. The first thing we notice is that the opening bar involves the extremely unlikely combination of A, B and C. (A minor the harmony, B the note being played, C the key [and the chord we might normally expect]).
Having started in that weird way, the tune continues in the same vein. In its 32 bars, it gets through an astonishing range of chords. No matter how simple the version of chords you try to use, you are unlikely to get away without using at least Am7 (sometimes with flattened 5th), D7, G, Gdim, Gm7, C7, F7, Fdim, Fm7 (sometimes with flattened 5th), Bb7, Eb major 7, Eb7, Em7, Bm, E7, G7, and C (C - the home chord - surprisingly being used only with the final note).
How’s that for a tune of 32 bars? Can you think of any other popular song with such changes? No wonder the tune is VERY rarely attempted: it’s too difficult! It is almost as if Raskin set himself the task of writing a tune that used pretty well every possible chord in the chromatic scale.
Strangely, though, you find the chord changes – as you work through each sixteen bars – are based subtly on the familiar circle of 5ths – starting with A (in the form of minor 7th rather than usual 7th).
What makes it sound so ‘haunting’ is that the chords are not the conventional 7ths. Minors, diminisheds and major 7ths are preferred to normal 7ths and the melody note often adds a 9th to the chord, as indeed on the very first note.
Also, the second half copies the first only for 8 bars and then – although keeping the rhythmic pattern of the first sixteen bars, introduces a slightly different upward arpeggio and harmony.
FIRST SIXTEEN ENDING:
SECOND SIXTEEN ENDING:
You will not be surprised to hear that Raskin (who died in 2004) was a classically-trained composer. The son of an orchestral conductor, he studied composition at the University of Pennsylvania and later was tutored by Arnold Schoenberg. Raskin wrote over 100 film scores. Laura was based on the theme for the 1944 film of the same name. Lyrics for it were provided by the great Johnny Mercer.