Tonality is one of the most central theoretical concepts for the analysis of Western classical music. This study presents a novel approach for the study of its historical development, exploring in particular the concept of mode. Based on a large dataset of approximately 13,000 musical pieces in MIDI format, we present two models to infer both the number and characteristics of modes of different historical periods from first principles: a geometric model of modes as clusters of musical pieces in a non-Euclidean space, and a cognitively plausible Bayesian model of modes as Dirichlet distributions. We use the geometric model to determine the optimal number of modes for five historical epochs via unsupervised learning and apply the probabilistic model to infer the characteristics of the modes. Our results show that the inference of four modes is most plausible in the Renaissance, that two modes–corresponding to major and minor–are most appropriate in the Baroque and Classical eras, whereas no clear separation into distinct modes is found for the 19th century.

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.

This corpus study constitutes the first quantitative style analysis of Choro, a primarily instrumental music genre that emerged in Brazil in the second half of the 19th century. We evaluate its description in the recent and comprehensive theoretical work A estrutura do Choro (Almada, 2006) by analyzing a set of representative pieces from the Choro Songbook (Chediak, 2009, 2011a,b), a central reference for this genre. We digitized this resource by transcribing the chord symbols and formal structure of all 295 pieces, and publish it as the freely available Choro Songbook Corpus. Our approach uncovers central stylistic traits of this musical idiom on empirical grounds. It thus advances data-driven musical style analysis by studying both harmony and form in a musical genre that lies outside the traditional canon.