Mathematical Analysis of Hymns for Meditation

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-12
Year of Publication : 2020
Authors : Madhukar Krishnamurthy
  10.14445/22315373/IJMTT-V66I12P501

MLA

MLA Style: Madhukar Krishnamurthy  "Mathematical Analysis of Hymns for Meditation" International Journal of Mathematics Trends and Technology 66.12 (2020):1-9. 

APA Style: Madhukar Krishnamurthy(2020). Mathematical Analysis of Hymns for Meditation  International Journal of Mathematics Trends and Technology, 1-9.

Abstract
In this work we study the mantra and Vedic chants used for meditation and convert them to time series with the frequency of 44100 Hertz. We then perform the mathematical and statistical analysis of these chants and compare these results with few of the popular known songs in Hindi, Kannada and Spanish/English. We also consider the Tirumala temple bell sound for our analysis and study. We conclude that the meditation songs are lyapunov stable and in fact they are asumptotically stable. And hence are perfect for meditation.

Reference

[1] Hegger R, Kantz H and Schreiber T, Practical implementation of nonlinear time series methods: The TISEAN package, Chaos, 9, 413, 1999.
[2] A. Provenzale, L. A. Smith, R. Vio, and G. Murante, Distinguishing between low-dimensional dynamics and randomness in measured time series, Physica D 58, 31 (1992).
[3] M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A 45, 3403 (1992).
[4] F. Takens, ``Detecting Strange Attractors in Turbulence'', Lecture Notes in Math. Vol. 898, Springer, New York (1981).
[5] P Grassberger and I Procaccia, Measuring of strangeness in strange attractors, Physica D 9, 189 (1983).
[6] M. Sano and Y. Sawada, Measurement of the Lyapunov spectrum from a chaotic time series, Phys. Rev. Lett. 55, 1082 (1985).

Keywords : Correlation, Entropy, Lyapunov Spectrum, Power Spectrum, Time Series