A Computational Model That Generalises Schoenberg’s Guidelines for Favourable Chord Progressions

This paper presents a formal model of Schoenberg’s guidelines for convincing chord root progressions. This model has been implemented as part of a system that models a considerable part of Schoenberg’s Theory of Harmony. This system implements Schoenberg’s theory in a modular way: besides generating four-voice homophonic chord progressions, it can also be used for creating other textures that depend on harmony (e.g., polyphony). The proposed model generalises Schoenberg’s guidelines in order to make them applicable for more use cases. Instead of modelling his rules directly (as constraints on scale degree intervals between chord roots), we actually model his explanation of these rules (as constraints between chord pitch class sets and roots, e.g., whether the root pitch class of some chord is an element in the pitch class set of another chord). As a result, this model can not only be used for progressions of diatonic triads, but in addition also for chords with a large number of tones, and in particular also for microtonal music beyond 12-tone equal temperament and beyond 5-limit harmony.