J.S. Bach’s Contrapunctus XIV : a Zipf’s law-based computational study to analyse and classify attempted completions

J.S. Bach's Contrapunctus XIV from The Art of Fugue remained incomplete at his death. Over 70 completions of varying quality have been attempted to date. We apply a computational musicology approach based on Zipf’s Law to evaluate 18 prominent completions for alignment with Bach’s compositional style. Using 276 metrics and machine learning (both supervised and unsupervised), we demonstrate that we can distinguish Bach’s style from other composers and differentiate nuances in Bach’s own style (e.g. comparing The Art of Fugue and The Well-Tempered Clavier) with high accuracy. Four completions emerge with distinct stylistic alignments: Korsyn and Eskeland exhibit macro-stylistic similarity with The Art of Fugue corpus in both pitch-duration and bassline proportions, while Moroney and Hughes exhibit micro-stylistic similarity with Bach’s original fragment in terms of higher-order structural patterns. Consistent with earlier research, this framework appears capable of exploring macro- and micro-stylistic similarities across musical corpora. This study provides a quantitative framework for evaluating the stylistic alignment of Contrapunctus XIV completions and, potentially, for exploring similar musicological questions.