Nádia Sousa Carvalho

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.

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.

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.

Abstract
We propose a method for computing the similarity of symbolically-encoded Portuguese folk melodies. The main novelty of our method is the use of a preprocessing melodic reduction at multiple hierarchies to filter the surface of folk melodies according to 1) pitch stability, 2) interval salience, 3) beat strength, 4) durational accents, and 5) the linear combination of all former criteria. Based on the salience of each note event per criteria, we create three melodic reductions with three different levels of note retention. We assess the degree to which six folk music similarity measures at multiple reduction hierarchies comply with collected ground truth from experts in Portuguese folk music. The results show that SIAM combined with 75th quantile reduction using the combined or durational accents best models the similarity for a corpus of Portuguese folk melodies by capturing approximately 84-90% of the variance observed in ground truth annotations.

Abstract
FluidHarmony is an algorithmic method for defining a hierarchical harmonic lexicon in equal temperaments. It utilizes an enharmonic weighted Fourier transform space to represent pitch class set (pcsets) relations. The method ranks pcsets based on user-defined constraints: the importance of interval classes (ICs) and a reference pcset. Evaluation of 5,184 Western musical pieces from the 16th to 20th centuries shows FluidHarmony captures 8% of the corpus's harmony in its top pcsets. This highlights the role of ICs and a reference pcset in regulating harmony in Western tonal music while enabling systematic approaches to define hierarchies and establish metrics beyond 12-TET.