A Model for Scale-Degree Reinterpretation: Melodic Structure, Modulation, and Cadence Choice in the Chorale Harmonizations of J. S. Bach

Abstract

This paper reports a corpus study of the 371 chorale harmonizations by J. S. Bach. Specifically, this study investigates what kinds of events are typical at phrase endings given various melodic conditions, i.e., how well melodic structure is a predictor of modulation and cadence choices. Each fermata event was analyzed by ear and encoded with regard to the local key area and the cadence type. The frequency of each cadence type was then tabulated with respect to categorizations of the melodic structure (in terms of the intervallic pattern and scale degree content) prior to the fermata. It is shown that most fermata events can be categorized by a small collection of event types. As a result, a simplified conceptual model of cadence choice is posited. This model proposes that a basic harmonization default is to (re-)interpret the soprano note at the fermata as scale-degree 1, 2, or 3 in some closely-related key area via an authentic or half cadence. The efficacy of this model is found to be very good, especially given certain conditions. Moreover, an overall success rate above 90% can be achieved through only four additional concepts.