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A study on Improvisation in a Musical performance using Multifractal Detrended Cross Correlation Analysis

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  • Sanyal, Shankha
  • Banerjee, Archi
  • Patranabis, Anirban
  • Banerjee, Kaushik
  • Sengupta, Ranjan
  • Ghosh, Dipak

Abstract

MFDFA (the most rigorous technique to assess multifractality) was performed on four Hindustani music samples played on same ‘raga’ sung by the same performer. Each music sample was divided into six parts and ‘multifractal spectral width’ was determined for each part corresponding to the four samples. The results obtained reveal that different parts of all the four sound signals possess spectral width of widely varying values. This gives a cue of the so called ‘musical improvisation’ in all music samples, keeping in mind they belong to the bandish part of the same raga. Formal compositions in Hindustani raga are juxtaposed with the improvised portions, where an artist manoeuvers his/her own creativity to bring out a mood that is specific for that particular performance, which is known as ‘improvisation’. Further, this observation hints at the association of different emotions even in the same bandish of the same raga performed by the same artist, this interesting observation cannot be revealed unless rigorous non-linear technique explores the nature of musical structure. In the second part, we applied MFDXA technique to explore more in-depth about ‘improvisation’ and association with emotion. This technique is applied to find the degree of cross-correlation (γx) between the different parts of the samples. Pronounced correlation has been observed in the middle parts of the all the four samples evident from higher values of γx ​whereas the other parts show weak correlation. This gets further support from the values of spectral width from different parts of the sample — width of those parts is significantly different from other parts. This observation is extremely new both in respect of musical structure of so called improvisation and associated emotion. The importance of this study in application area of cognitive music therapy is immense.

Suggested Citation

  • Sanyal, Shankha & Banerjee, Archi & Patranabis, Anirban & Banerjee, Kaushik & Sengupta, Ranjan & Ghosh, Dipak, 2016. "A study on Improvisation in a Musical performance using Multifractal Detrended Cross Correlation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 67-83.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:67-83
    DOI: 10.1016/j.physa.2016.06.013
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    Cited by:

    1. Banerjee, Archi & Sanyal, Shankha & Roy, Souparno & Nag, Sayan & Sengupta, Ranjan & Ghosh, Dipak, 2021. "A novel study on perception–cognition scenario in music using deterministic and non-deterministic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    2. Schadner, Wolfgang, 2022. "U.S. Politics from a multifractal perspective," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. McDonough, John & Herczyński, Andrzej, 2023. "Fractal patterns in music," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Gündüz, Güngör, 2023. "Entropy, energy, and instability in music," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    5. Nag, Sayan & Basu, Medha & Sanyal, Shankha & Banerjee, Archi & Ghosh, Dipak, 2022. "On the application of deep learning and multifractal techniques to classify emotions and instruments using Indian Classical Music," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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