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Analysis of temporal fluctuations in Bach’s sinfonias

Author

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  • Telesca, Luciano
  • Lovallo, Michele

Abstract

The correlation structures in 15 Bach’s sinfonias were analyzed. Each sinfonia is characterized by the superposition of three voices. Each voice is a sequence of pitches. Each voice was transformed in a time series, in which the sampling time was given by the smallest pitch duration in that voice. The scaling properties of the three voices of each sinfonia was quantified by means of the estimate of the scaling exponent, performed using the power spectral density (PSD) and the detrended fluctuation analysis (DFA). The results show that the voice time series are persistent. The DFA was applied not only to any single voice time series, but also to couples (2-DFA) of voices and to the triple (3-DFA) of voices. It was found that the first voice of each sinfonia modulates the scaling behavior of the whole sinfonia.

Suggested Citation

  • Telesca, Luciano & Lovallo, Michele, 2012. "Analysis of temporal fluctuations in Bach’s sinfonias," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3247-3256.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:11:p:3247-3256
    DOI: 10.1016/j.physa.2012.01.036
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    Cited by:

    1. Gulich, Damián & Zunino, Luciano, 2014. "A criterion for the determination of optimal scaling ranges in DFA and MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 17-30.
    2. Itami, A.S. & Antonio, F.J. & Mendes, R.S., 2015. "Very prolonged practice in block of trials: Scaling of fitness, universality and persistence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 82-89.

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