Modal Pitch Space: A Computational Model of Melodic Pitch Attraction in Folk Music

We introduce a computational model that quantifies melodic pitch attraction in diatonic modal folk music, extending Lerdahl’s Tonal Pitch Space. The model incorporates four melodic pitch indicators: vertical embedding distance, horizontal step distance, semitone interval distance, and relative stability. Its scalability is exclusively achieved through prior mode and tonic information, eliminating the need in existing models for additional chordal context. Noteworthy contributions encompass the incorporation of empirically-driven folk music knowledge and the calculation of indicator weights. Empirical evaluation, spanning Dutch, Irish, and Spanish folk traditions across Ionian, Dorian, Mixolydian, and Aeolian modes, uncovers a robust linear relationship between melodic pitch transitions and the pitch attraction model infused with empirically-derived knowledge. Indicator weights demonstrate cross-tradition generalizability, highlighting the significance of vertical embedding distance and relative stability. In contrast, semitone and horizontal step distances assume residual and null functions, respectively.