Effects of Temporal Position on Harmonic Succession in the Bach Chorale Corpus

Abstract

Recent computer-aided studies of harmony in various corpora of music (e.g., Bach and Lutheran chorales, late-twentieth-century rock music, etc.) have demonstrated how the treatment of various harmonies differs among repertoires. These differences are most often represented through transitional probability matrices showing the likelihood of any recognized sonority following any other sonority within a defined state space of possible sonorities. While such models of tonality are useful for demonstrating differences among genres, they tend to downplay the impact of temporal ordering and metric position on harmonic treatment. A potential source of this deficit is the difficulty in making meaningful temporal comparisons without a precise definition of phrase beginnings and endings and without a large collection of phrases of the same length. This paper mitigates these challenges by identifying 799 phrases from the Bach chorale corpus that are identical in length and cadence. It then creates a small state space of chord roots and functional categories and, further, demonstrates how the treatment of harmonies is conditioned by their location within phrases. In so doing, it is hoped that the paper will contribute to more refined models of tonalities that recognize music’s essential temporality.