Abstract
Extensive computational research has been dedicated to detecting keys and modes in tonal Western music within the major and minor modes. Little research has been dedicated to other modes and musical expressions, such as folk or non-Western music. This paper tackles this limitation by comparing traditional template-based with unsupervised machine-learning methods for diatonic mode detection within folk music. Template-based methods are grounded in music theory and cognition and use predefined profiles from which we compare a musical piece. Unsupervised machine learning autonomously discovers patterns embedded in the data. As a case study, the authors apply the methods to a dataset of Irish folk music called The Session on four diatonic modes: Ionian, Dorian, Mixolydian, and Aeolian. Our evaluation assesses the performance of template-based and unsupervised methods, reaching an average accuracy of about 80%. We discuss the applicability of the methods, namely the potential of unsupervised learning to process unknown musical sources beyond modes with predefined templates. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Abstract

Abstract
Expanding upon the potential of generative machine learning to create atemporal latent space representations of musical-theoretical and cognitive interest, we delve into their explainability by formulating and testing hypotheses on their alignment with DFT phase spaces from {0,1}12 pitch classes and {0,1}128 pitch distributions – capturing common-tone tonal functional harmony and parsimonious voice-leading principles, respectively. We use 371 J.S. Bach chorales as a benchmark to train a Variational Autoencoder on a representative piano roll encoding. The Spearman rank correlation between the latent space and the two before-mentioned DFT phase spaces exhibits a robust rank association of approximately .65±.05 for pitch classes and .61±.05 for pitch distributions, denoting an effective preservation of harmonic functional clusters per region and parsimonious voice-leading. Furthermore, our analysis prompts essential inquiries about the stylistic characteristics inferred from the rank deviations to the DFT phase space and the balance between the two DFT phase spaces. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Abstract
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. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.