Arrow of time across five centuries of classical music

Abstract

The concept of time series irreversibility-the degree by which the statistics of signals are not invariant under time reversal-naturally appears in nonequilibrium physics in stationary systems which operate away from equilibrium and produce entropy. This concept has not been explored to date in the realm of musical scores as these are typically short sequences whose time reversibility estimation could suffer from strong finite size effects which preclude interpretability. Here we show that the so-called horizontal visibility graph method-which recently was shown to quantify such statistical property even in nonstationary signals-is a method that can estimate time reversibility of short symbolic sequences, thus unlocking the possibility of exploring such properties in the context of musical compositions. Accordingly, we analyze over 8000 musical pieces ranging from the Renaissance to the early Modern period and show that, indeed, most of them display clear signatures of time irreversibility. Since by construction stochastic processes with a linear correlation structure (such as 1/ f noise) are time reversible, we conclude that musical compositions have a considerably richer structure, that goes beyond the traditional properties retrieved by the power spectrum or similar approaches. We also show that musical compositions display strong signs of nonlinear correlations, that nonlinearity is correlated to irreversibility, and that these are also related to asymmetries in the abundance of musical intervals, which we associate to the narrative underpinning a musical composition. These findings provide tools for the study of musical periods and composers, as well as criteria related to music appreciation and cognition.

Cultural evolution and music

“…European "common practice" music since the 17th century is particularly richly documented (Taruskin, 2005). The Kunst der Fuge database, for example, has ~19,500 full MIDI transcriptions that have been used to investigate 4 everything from changes in harmonic richness (Serra-Peralta et al 2021) to statistical regularities in temporal structure ( González-Espinoza et al, 2020). Other databases, like the Classical Music Navigator and ArkivMusic , provide detailed 5 6…”

Cognitive Emotional Embedded Representations of Text to Predict Suicidal Ideation and Psychiatric Symptoms

“…To achieve this, further data to train the models with shall allow us to predict, in real-time with better accuracy, the emotional state of a person through his or her writing, in order to deploy effective protocols of helpful interventions. On the other hand, an alternative perspective is to investigate the sequential structure of our texts [77] by using techniques from statistical physics which could capture nontrivial interrelations between syntagmatic sequences, by means of entropy based measures or visibility graphs, that have been recently successfully applied to musical pieces [78].…”

Heaps’ law and vocabulary richness in the history of classical music harmony

“…We perform our study over the Kunstderfuge corpus [40], which, at the time of our analysis, consisted of 17,418 MIDI files corresponding to pieces of 79 classical composers, from the 12th to the 20th century (Ref. [41] has scrutinized the Kunstderfuge corpus looking for properties different than the ones we are interested in). Removing files that were not clearly labelled or corrupted (files that we are not able to process) and files for which we could not obtain the bar (and thefore could not determine the beat), yields a remainder of 9489 files and 76 composers, ranging from Guillaume Dufay (1397-1474) to Messiaen (1908Messiaen ( -1992.…”