Mathematical Analysis of Hymns for Meditation

Madhukar Krishnamurthy

doi:https://doi.org/10.14445/22315373/IJMTT-V66I12P501

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 12 | Year 2020 | Article Id. IJMTT-V66I12P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I12P501

Mathematical Analysis of Hymns for Meditation

Madhukar Krishnamurthy

Citation :

Madhukar Krishnamurthy, "Mathematical Analysis of Hymns for Meditation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 12, pp. 1-9, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I12P501

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.

Keywords

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

References

[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).