Music theory | EPFL Graph Search

Music theory is the study of the practices and possibilities of music. The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is the "rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built." Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. Because of the ever-expanding conception of what constitutes music, a more inclusive definition could be the consideration of any sonic phenomena, including

Music Cognition: The Complexity of Musical Structure

Christoph Finkensiep, Mathieu Giraud, Daniel Harasim, Martin Alois Rohrmeier

Music is highly complex and provides a rich variety of insights into the human mind, its mental structures, and processes. Experienced musicians are able to create complex structures in real time effortlessly, yet there is at present no successful model of full musical structure. The integration of different musical aspects such as melody, rhythm, voice leading, and form as well as the representation of long-term structure are particularly challenging. To open new possibilities for the study of higher-order structure in music and its perceptual correlates, cognitive music research would benefit from further mutual integration of theoretical, mathematical, computational, and psychological research, similar to advancements in linguistics. This symposium therefore focuses on the formal understanding and empirical investigation of music-theoretically motivated research questions in music cognition. It connects perspectives from music theory, behavioral research, corpus research, and computational modeling, and aims to initiate interdisciplinary discussions about the currently most challenging topics related to the cognition of higher-order structures in music.

2021

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

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