Discovering Tonal Profiles with Latent Dirichlet Allocation

Music analysis, in particular harmonic analysis, is concerned with the way pitches are organized in pieces of music, and a range of empirical applications have been developed, for example, for chord recognition or key finding. Naturally, these approaches rely on some operationalization of the concepts they aim to investigate. In this study, we take a complementary approach and discover latent tonal structures in an unsupervised manner. We use the topic model Latent Dirichlet Allocation and apply it to a large historical corpus of musical pieces from the Western classical tradition. This method conceives topics as distributions of pitch classes without assuming a priori that they correspond to either chords, keys, or other harmonic phenomena. To illustrate the generative process assumed by the model, we create an artificial corpus with arbitrary parameter settings and compare the sampled pieces to real compositions. The results we obtain by applying the topic model to the musical corpus show that the inferred topics have music-theoretically meaningful interpretations. In particular, topics cover contiguous segments on the line of fifths and mostly correspond to diatonic sets. Moreover, tracing the prominence of topics over the course of music history over ∼600 years reflects changes in the ways pitch classes are employed in musical compositions and reveals particularly strong changes at the transition from common-practice to extended tonality in the 19th century.

Transitions of Tonality: A Model-Based Corpus Study

Fabian Claude Moss

Tonality has been the cornerstone of Western music-theoretical discourse for centuries. This study addresses the subject, using traditional music analysis, data-driven corpus methods, and computational models, concentrating on historical changes of tonality with a particular focus on the 19th century. The thesis engages three analytical levels of increasing scope - micro, meso, and macro - and is thus located between the poles of the particular and the general. The micro-level presents a detailed analysis of Franz Liszt's Sonetto 47 del Petrarca, S. 161, no. 4 (1858), in order to illustrate compositional innovations testifying to the radical changes in tonality within the 19th century. The analysis exemplifies how these novelties permeate musical compositions in that period, and also expose the benefits and limitations of manual music analysis. The meso-level examines a corpus of harmonic annotations of pieces by Beethoven, Schubert, Chopin, Liszt, Dvořák, Grieg, Tchaikovsky, Debussy, and Medtner, containing over 75,000 chord symbols. It presents a comprehensive model for the analysis of chord symbols in large corpora in order to study chords and the progressions between them. Whilst the individual composers' chord vocabularies vary considerably - paying tribute to idiomatic usages of harmony - it is shown that the overarching similarities of the chord distributions point to similarities in their harmonic language that surpass individual traits and that can be modeled by Zipf's and Heaps's laws. An entropy-based method is presented to systematically study the effect of certain features on chord prediction, revealing that suspensions are the strongest predictors. The study shows that chord progressions are largely asymmetrical and proceed mostly by fifths; however, third-based progressions become increasingly prevalent within the studied period. The macro-level explores a corpus of nearly 3 million notes in more than 2000 pieces created by 75 composers, comprising a historical range of approximately 600 years. The encoding of the data distinguishes enharmonically equivalent notes, hence providing a larger note vocabulary than most previous approaches in empirical music research. A Principal Component Analysis (PCA) shows that the line of fifths can be derived from the co-occurrence as well as the co-evolution of tonal pitch-classes. Moreover, the hierarchical topic model known as Latent Dirichlet Allocation (LDA) is used to discover latent tonal profiles. These largely correspond to distributions on contiguous line-of-fifths segments and moreover demonstrate the elevated roles of fifths as well as major and minor thirds as intervals between the most frequent notes. This motivates to model pieces as distributions on the Tonnetz. To that end, a new model, the Tonal Diffusion Model (TDM), is introduced. The results are obtained by fitting the model to the corpus and exhibit two trends. Over the entire historical period under consideration, notes are primarily distributed along the fifths axis of the Tonnetz. Furthermore, 19th-century composers also explore the major and minor thirds axes of the Tonnetz, extending their compositions in ever farther regions. The diverse methodology in this study provides quantitatively grounded insights from a range of perspectives, bridging the fields of music theory, computational musicology, mathematical modeling, and the digital humanities.

EPFL2019

Extracting Mobile Behavioral Patterns with the Distant N-Gram Topic Model

Katayoun Farrahi, Daniel Gatica-Perez

Mining patterns of human behavior from large-scale mobile phone data has potential to understand certain phenomena in society. The study of such human-centric massive datasets requires new mathematical models. In this paper, we propose a probabilistic topic model that we call the distant n-gram topic model (DNTM) to address the problem of learning long duration human location sequences. The DNTM is based on Latent Dirichlet Allocation (LDA). We define the generative process for the model, derive the inference procedure and evaluate our model on real mobile data. We consider two different real-life human datasets, collected by mobile phone locations, the first considering GPS locations and the second considering cell tower connections. The DNTM successfully discovers topics on the two datasets. Finally, the DNTM is compared to LDA by considering log-likelihood performance on unseen data, showing the predictive power of the model on unseen data. We find that the DNTM consistantly outperforms LDA as the sequence length increases.

2012

A Probabilistic Approach to Mining Mobile Phone Data Sequences

Katayoun Farrahi, Daniel Gatica-Perez

We present a new approach to address the problem of large sequence mining from big data. The particular problem of interest is the effective mining of long sequences from large-scale location data to be practical for Reality Mining applications, which suffer from large amounts of noise and lack of ground truth. To address this complex data, we propose an unsupervised probabilistic topic model called the distant n-gram topic model (DNTM). The DNTM is based on Latent Dirichlet Allocation (LDA), which is extended to integrate sequential information. We define the generative process for the model, derive the inference procedure, and evaluate our model on both synthetic data and real mobile phone data. We consider two different mobile phone datasets containing natural human mobility patterns obtained by location sensing, the first considering GPS/wifi locations and the second considering cell tower connections. The DNTM discovers meaningful topics on the synthetic data as well as the two mobile phone datasets. Finally, the DNTM is compared to LDA by considering log-likelihood performance on unseen data, showing the predictive power of the model. The results show that the DNTM consistently outperforms LDA as the sequence length increases.

2014

Transitions of Tonality: A Model-Based Corpus Study

Fabian Claude Moss

EPFL2019