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Multiple scaling behaviour and nonlinear traits in music scores
Alfredo González-Espinoza1,2,3, Hernán Larralde2, Gustavo Martínez-Mekler2,3,4
1Instituto de Investigación en Ciencias Básicas y Aplicadas, UAEM, Morelos, México.
Royal Society Open Science
|January 9, 2018
Summary
This study analyzes music scores using detrended fluctuation analysis (DFA), revealing composer-specific nonlinear correlations. These correlations significantly impact the aesthetic perception of music.
Area of Science:
- Musicology
- Statistical Analysis
- Acoustics
Background:
- Musical pieces exhibit complex structures.
- Understanding the statistical properties of music can reveal compositional patterns.
Purpose of the Study:
- To statistically analyze music scores from different composers.
- To investigate the presence and impact of nonlinear autocorrelations in music.
- To explore the role of these correlations in aesthetic perception.
Main Methods:
- Detrended Fluctuation Analysis (DFA) applied to music scores.
- Analysis of magnitude series to detect nonlinear autocorrelations.
- Validation using surrogate data.
- Acoustic pleasantness experiment comparing original music with surrogate pieces.
Main Results:
- Distinct fluctuation profiles identified for different composers, corresponding to unique autocorrelation structures.
- Evidence for nonlinear autocorrelations in musical pieces, varying in amount and character across composers.
- Surrogate music pieces with altered nonlinear correlations were found to differ in pleasantness.
Conclusions:
- Nonlinear correlations are a significant feature of musical structure.
- These correlations vary systematically between composers.
- Nonlinear correlations play a crucial role in the aesthetic perception and pleasantness of music.
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