An Information-Theoretical Method for Comparing Completions of Contrapunctus XIV from Bach’s Art of Fugue

The unfinished final Contrapunctus from Bach’s posthumously-published Kunst der Fuge has received several dozen completions over the past century. Although the majority of these have been published and recorded, none has yet established themselves as the leading solution among performers, and this may have more to do with their perceived ‘Bach-ness’ than the undoubted contrapuntal skill and ingenuity that they each demonstrate. This study uses an established information-theoretical method drawn from mathematics to explore the extent to which it is possible to ‘measure’ the similarity of these reconstructions to the original, and so determine which are closest to the musical lines of Bach’s existing opening of Contrapunctus XIV.