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The European Physical Journal Special Topics

, Volume 223, Issue 8, pp 1561–1577 | Cite as

Phase synchronization of instrumental music signals

  • Sayan Mukherjee
  • Sanjay Kumar Palit
  • Santo Banerjee
  • M.R.K. Ariffin
  • D.K. Bhattacharya
Regular Article Synchronization of Systems and Networks for Communication
Part of the following topical collections:
  1. Chaos, Cryptography and Communications

Abstract

Signal analysis is one of the finest scientific techniques in communication theory. Some quantitative and qualitative measures describe the pattern of a music signal, vary from one to another. Same musical recital, when played by different instrumentalists, generates different types of music patterns. The reason behind various patterns is the psycho-acoustic measures – Dynamics, Timber, Tonality and Rhythm, varies in each time. However, the psycho-acoustic study of the music signals does not reveal any idea about the similarity between the signals. For such cases, study of synchronization of long-term nonlinear dynamics may provide effective results. In this context, phase synchronization (PS) is one of the measures to show synchronization between two non-identical signals. In fact, it is very critical to investigate any other kind of synchronization for experimental condition, because those are completely non identical signals. Also, there exists equivalence between the phases and the distances of the diagonal line in Recurrence plot (RP) of the signals, which is quantifiable by the recurrence quantification measure τ-recurrence rate. This paper considers two nonlinear music signals based on same raga played by two eminent sitar instrumentalists as two non-identical sources. The psycho-acoustic study shows how the Dynamics, Timber, Tonality and Rhythm vary for the two music signals. Then, long term analysis in the form of phase space reconstruction is performed, which reveals the chaotic phase spaces for both the signals. From the RP of both the phase spaces, τ-recurrence rate is calculated. Finally by the correlation of normalized tau-recurrence rate of their 3D phase spaces and the PS of the two music signals has been established. The numerical results well support the analysis.

Keywords

Phase Space European Physical Journal Special Topic Phase Synchronization Average Mutual Information Surrogate Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  • Sayan Mukherjee
    • 1
  • Sanjay Kumar Palit
    • 2
  • Santo Banerjee
    • 3
  • M.R.K. Ariffin
    • 4
  • D.K. Bhattacharya
    • 5
  1. 1.Mathematics Department, Sivanath Sastri CollegeKolkataIndia
  2. 2.Basic Sciences & Humanities Department, Calcutta Institute of Engineering and ManagementKolkataIndia
  3. 3.Institute for Mathematical Research, Universiti Putra MalaysiaPutraMalaysia
  4. 4.Mathematics Department, Faculty of Science, Universiti Putra Malaysia, Malaysia Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra MalaysiaPutraMalaysia
  5. 5.Department of Instrumental MusicRabindra Bharati UniversityRabindra BharatiIndia

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