We present a statistical analysis of music scores from different composers using detrended fluctuation analysis. We find different fluctuation profiles that correspond to distinct auto-correlation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear auto-correlations by estimating the detrended fluctuation analysis of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.
SI-master
Supporting Information, here are the graphs for the fluctuation functions.
The graphs are labeled as following:
Palestrina Motets: PalestrinaMo-#
Bach Musical Offering: BachMO-#
Bach Well Tempered Clavier: BachWTK-#
Haydn String Quartets: HaydnSQ-#
Mozart Piano Sonatas: MozartPS-#
Mozart String Quartets: MozartSQ-#
Beethoven Fugues: BeethovenF-#
Beethoven Early Quartets: BeethovenEQ-#
Beethoven Late Quartets: BeethovenLQ-#
Dvorak Humoresques: DvorakH-#
Dvorak Silhouettes: DvorakS-#
Dvorak Serenade for Strings: DvorakSt-#
Shostakovich Preludes and Fugues: ShostakovichPF-#
The number corresponds to the place in the full list of opus.
Files corresponding to a scaling behavior over all s boxes (profile 1) are in Scaling.pdf, files corresponding to the functions showing a crossover (profiles 1 and 2) are in Crossovers.pdf, the files with the graps of profiles 4 and 5 are in NoScaling.pdf
The values of the alpha's and R squared for the linear fitting in the fluctuations function are on the Tables: TableScaling.pdf corresponds to the functions following a power law and TableCrossovers.pdf to the functions with a crossover.
InfoSeries.jl-master
Repository for every calculation of the DFA and the construction of the time series from the .csv file. The repository can also be consulted in GitHub: https://github.com/spiralizing/InfoSeries.jl
Supplementary Material
Full list of opus analyzed, details for the construction of the time series, individual DFA functions and their relation with the power spectra. Description of the survey.
SupplementaryMaterial.pdf
SM-TimeSeries
All time series analyzed and the four tracks of the Survey. The time series were constructed as described in the Supplementary Material, from MIDIs downloaded from the web databases mentioned in references.
