Exploring the foundations of tonality: statistical cognitive modeling of modes in the history of Western classical music

Abstract

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.

Recursive Bayesian Networks: Generalising and Unifying Probabilistic Context-Free Grammars and Dynamic Bayesian Networks

“…Our first major finding is that the prior mean, shown in Figure 6(b), corresponds to a major pitch profile (as could be expected from the training data) and is in excellent agreement with recent Bayesian estimates from the literature [65]. The fact that the major profile appears in the prior (i.e.…”

Cultural evolution and music

“…For example, research on traditional and folk music have revealed that scales around the world have a tendency to converge towards similar patterns (McBride and Tlusty, 2019;Brown and Jordania, 2013;Kuroyanagi et al, 2019), musical variation is correlated with social complexity (Lomax, 1968;Wood et al, 2021) and sometimes population history (Brown et al, 2014; but see Matsumae et al, 2021), and that certain styles of music are reliably associated with particular behavioral contexts across cultures (Mehr et al, 2019) according to their acoustic features (Mehr et al, 2018;Hilton et al, 2021). Studies of classical music have found that melodic intervals are associated with particular historical periods (Rodriguez Zivic et al, 2013;Weiß et al, 2019;Harasim et al, 2021), and that tonal complexity and harmonic richness have increased over time ( Weiß et al, 2019;Serra-Peralta et al 2021). Studies of contemporary and popular music have tracked changes in a variety of music characteristics such as diversity, loudness, and the emotional valence of lyrics (Mauch et al, 2015;Serrà et al, 2012;Napier and Shamir, 2018;Brand et al, 2019), and have used detailed information on population structure and the distribution of cultural variants to try to understand the processes underlying such changes (Youngblood, 2019b;Klimek et al, 2019;Youngblood et al, 2021;Rosati et al, 2021).…”

“…Below, we will brie y review some of the most notable research on the cultural evolution of classical music. One of the most interesting and robust ndings from studies of classical music is that distributions of melodic intervals change over time and are clearly clustered into well-known historical periods (Rodriguez Zivic et al, 2013;Weiß et al, 2019;Harasim et al, 2021). For example, the transition between the classical and romantic periods is characterized by great intervallic diversity and fewer transitions between adjacent notes (Rodriguez Zivic et al, 2013).…”

Sequence alignment of folk song melodies reveals cross-cultural regularities of musical evolution

“…1,[24][25][26][27][28] However, attempts to test such proposals quantitatively have focused almost exclusively on Western music. [29][30][31][32][33][34][35][36][37] Whether such regularities are specific to Western music or more general features of human music remains unknown.…”

“…Previous analyses have also focused on population-level macro-scale evolution. For example, analyses of Western popular and classical music have demonstrated changes over time in the overall frequency of certain types of musical intervals, 30,34 harmonies, 36 or lyrics, 31 but do not address the micro-scale processes by which individual musical works change as they are transmitted between individuals. Such micro-level processes of oral transmission likely played important roles through most of our evolutionary history before the advent of musical notation and audio recording technology.…”