Multiple scaling behaviour and nonlinear traits in music scores

González-Espinoza, Alfredo; Larralde, Hernán; Martı́nez-Mekler, Gustavo; Müller, Markus

doi:10.1098/rsos.171282

Cited by 14 publications

(14 citation statements)

References 27 publications

(63 reference statements)

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“…One attractive topic for further exploration is the scaling behavior of the rhythms observed here (He et al, 2010;Kello et al, 2010;Ville et al, 2010;Hardstone et al, 2012). Since frequency here has a novel definition, scaling behaviors would require a distinct test, a topic for future study [especially since music exhibits well-known scaling laws (Manaris et al, 2005;Lloyd, 2011;González-Espinoza et al, 2017)].…”

Section: The Music Of Thoughtmentioning

confidence: 99%

The Musical Structure of Time in the Brain: Repetition, Rhythm, and Harmony in fMRI During Rest and Passive Movie Viewing

Lloyd

2020

Front. Comput. Neurosci.

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Space generally overshadows time in the construction of theories in cognitive neuroscience. In this paper, we pivot from the spatial axes to the temporal, analyzing fMRI image series to reveal structures in time rather than space. To determine affinities among global brain patterns at different times, core concepts in network analysis (derived from graph theory) were applied temporally, as relations among brain images at every time point during an fMRI scanning epoch. To explore the temporal structures observed through this adaptation of network analysis, data from 180 subjects in the Human Connectome Project were examined, during two experimental conditions: passive movie viewing and rest. The temporal brain, like the spatial brain, exhibits a modular structure, where "modules" are intermittent (distributed in time). These temporal entities are here referred to as themes. Short sequences of themes -motifs -were studied in sequences from 4 to 11 s in length. Many motifs repeated at constant intervals, and are therefore rhythmic; rhythms, converted to frequencies, were often harmonic. We speculate that the structure and interaction of these global oscillations underwrites the capacity to experience and navigate a world which is both recognizably stable and noticeably changing at every moment -a temporal world. In its temporal structure, this brain-constituted world resembles music.

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Section: The Music Of Thoughtmentioning

confidence: 99%

The Musical Structure of Time in the Brain: Repetition, Rhythm, and Harmony in fMRI During Rest and Passive Movie Viewing

Lloyd

2020

Front. Comput. Neurosci.

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“…8 is suggestive. Note that though evidence for different profiles of nonlinear correlations in music scores has been reported previously [20], a specific index such as ξ , able to quantify the amount of nonlinearity in a signal, was lacking.…”

Section: B Nonlinearity Index ξmentioning

confidence: 91%

“…While it has been extensively certified that music evidences long-range temporal correlations with (typically) a heavy tailed power spectrum [1,3,7,8], less is known about nonlinear correlations. However, recent studies have reported evidence of nonlinear correlations in musical pieces and discussed their possible relevance in their structure [20].…”

Section: B Nonlinearity Index ξmentioning

confidence: 99%

“…It is nowadays widely accepted that music presents a so-called 1/ f power spectrum and that this is a fingerprint of "appealing sound" [14][15][16][17][18][19]. However, recent evidence has challenged this vision, as it has been suggested that pleasantness could be also related to nonlinearities present in music compositions, a property which by definition is not captured in the power spectra [20]. These findings motivate further exploration into quantitative ways of measuring structure in music compositions that goes beyond linear theories.…”

Section: Introductionmentioning

confidence: 99%

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Arrow of time across five centuries of classical music

González-Espinoza

Martı́nez-Mekler

Lacasa

2020

Phys. Rev. Research

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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.

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“…Analyses based on statistical methods can capture information about musical features, such as the style of a musical piece, the composer, and even the emotions conveyed [1,[3][4][5][6][7][8][9][12][13][14][15][16][17][18][19][20]. Several statistical analyses employ successive pitches as units of context.…”

Section: Introductionmentioning

confidence: 99%

Melodies as Maximally Disordered Systems under Macroscopic Constraints with Musical Meaning

Useche

Hurtado

2019

Entropy

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One of the most relevant features of musical pieces is the selection and utilization of musical elements by composers. For connecting the musical properties of a melodic line as a whole with those of its constituent elements, we propose a representation for musical intervals based on physical quantities and a statistical model based on the minimization of relative entropy. The representation contains information about the size, location in the register, and level of tonal consonance of musical intervals. The statistical model involves expected values of relevant physical quantities that can be adopted as macroscopic constraints with musical meaning. We studied the occurrences of musical intervals in 20 melodic lines from seven masterpieces of Western tonal music. We found that all melodic lines are strictly ordered in terms of the physical quantities of the representation and that the formalism is suitable for approximately reproducing the final selection of musical intervals made by the composers, as well as for describing musical features as the asymmetry in the use of ascending and descending intervals, transposition processes, and the mean dissonance of a melodic line.

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Multiple scaling behaviour and nonlinear traits in music scores

Cited by 14 publications

References 27 publications

The Musical Structure of Time in the Brain: Repetition, Rhythm, and Harmony in fMRI During Rest and Passive Movie Viewing

The Musical Structure of Time in the Brain: Repetition, Rhythm, and Harmony in fMRI During Rest and Passive Movie Viewing

Arrow of time across five centuries of classical music

Melodies as Maximally Disordered Systems under Macroscopic Constraints with Musical Meaning

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