Most melodies from the Western common practice period have a harmonic background, i.e., a succession of chords that fit the melody. In this paper we provide a novel approach to infer this harmonic background from the score notation of a melody. We first construct a pitch context vector for each note in the melody. This vector summarises the pitches that are in the preceding and following contexts of the note. Next, we use these pitch context vectors to generate a list of candidate chords for each note. The candidate chords fit the pitch context of a given note each with a computed strength. Finally, we find an optimal path through the chord candidates, employing a score function for the fitness of a given candidate chord. The algorithm chooses one chord for each note, optimizing the total score. A set of heuristics is incorporated in the score function. The system is heavily parameterised, extremely flexible, and does not need training. This creates a framework to experiment with harmonization of melodies. The output is evaluated by an expert survey, which yields convincing and positive results.

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