Computational musicology | EPFL Graph Search

Computational musicology is an interdisciplinary research area between musicology and computer science. Computational musicology includes any disciplines that use computers in order to study music. It includes sub-disciplines such as mathematical music theory, computer music, systematic musicology, music information retrieval, computational musicology, digital musicology, sound and music computing, and music informatics. As this area of research is defined by the tools that it uses and its subject matter, research in computational musicology intersects with both the humanities and the sciences. The use of computers in order to study and analyze music generally began in the 1960s, although musicians have been using computers to assist them in the composition of music beginning in the 1950s. Today, computational musicology encompasses a wide range of research topics dealing with the multiple ways music can be represented. History This history of computational musicology gene

The Tonal Diffusion Model

Robert Lieck, Fabian Claude Moss, Martin Alois Rohrmeier

Pitch-class distributions are of central relevance in music information retrieval, computational musicology and various other fields, such as music perception and cognition. However, despite their structure being closely related to the cognitively and musically relevant properties of a piece, many existing approaches treat pitch-class distributions as fixed templates. In this paper, we introduce the Tonal Diffusion Model, which provides a more structured and interpretable statistical model of pitch-class distributions by incorporating geometric and algebraic structures known from music theory as well as insights from music cognition. Our model explains the pitch-class distributions of musical pieces by assuming tones to be generated through a latent cognitive process on the Tonnetz, a well-established representation for harmonic relations. Specifically, we assume that all tones in a piece are generated by taking a sequence of interval steps on the Tonnetz starting from a unique tonal origin. We provide a description in terms of a Bayesian generative model and show how the latent variables and parameters can be efficiently inferred. The model is quantitatively evaluated on a corpus of 248 pieces from the Baroque, Classical, and Romantic era and describes the empirical pitch-class distributions more accurately than conventional template-based models. On three concrete musical examples, we demonstrate that our model captures relevant harmonic characteristics of the pieces in a compact and interpretable way, also reflecting stylistic aspects of the respective epoch.

2020

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

Statistical characteristics of tonal harmony: A corpus study of Beethoven’s string quartets

Daniel Harasim, Fabian Claude Moss, Markus Franz Josef Neuwirth, Martin Alois Rohrmeier

Tonal harmony is one of the central organization systems of Western music. This article characterizes the statistical foundations of tonal harmony based on the computational analysis of expert annotations in a large corpus. Using resampling methods, this study shows that 1) the rank-frequency distribution of chords resembles a power law, i.e. few chords govern a large proportion of the data; 2) chord transitions are referential and chord predictability is significantly affected by distinguished chord features; 3) tonal harmony conveys directedness in time; and 4) tonal harmony operates differently at the hierarchical levels of chords and keys. These results serve to characterize tonal harmony on empirical grounds and advance the methodological state-of-the-art in digital musicology.

2019

Transitions of Tonality: A Model-Based Corpus Study

Fabian Claude Moss

EPFL2019