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Statistical analysis of melody lengths with a new formula for computing melodic weight of a note in a song: a case study

Author Affiliations

  • 1Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi-835215, India
  • 2Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi-835215, India

Res. J. Mathematical & Statistical Sci., Volume 6, Issue (8), Pages 1-6, December,12 (2018)


Melody is that part of music which is pleasant while rhythm is the part that is periodic. For research purpose, we may take melody more appropriately as a sequence of notes which is complete and hence can be taken as a single entity. For example, each line in a song is a melody. A sequential subset of a melody is called a segment. Length of a melody (or a segment) refers to the number of notes in it. Aye Mere Watan Ke Logo (O people of my country) is a Hindi patriotic song written by the lyricist Pradeep, the tune being composed by C. Ramchandra that was sung by the legendary playback singer Lata Mangeshkar. The present paper provides a statistical analysis of melody lengths of this popular patriotic song. A Chi-Square goodness of fit test reveals that the distribution of the melody lengths over the lines of the song is not uniform, a feature surprisingly found to be common with India’s national anthem Jana Gana Mana. A set of descriptive statistical summary measures are next calculated to compare these two songs. It may be noted that analysis of melody lengths is a neglected area in music research. From that angle, the paper provides some food for thought. Additionally, the paper also provides a new formula for calculation of melody weights in a song. The experimental results are encouraging.


  1. Beran Jan (2004)., Statistics in Musicology., Chapman and Hall. ISBN 978-1-584-88219-0
  2. Meredith, David (Ed.)(2016)., Computational Music Analysis., Springer. ISBN 978-3-319-25929-1
  3. Muller Meinard (2015)., Fundamentals of Music Processing., Springer. ISBN 978-3-319-21944-8
  4. Mazzola Guerino, Mannone Maria, Peng Yang, O’Brien Margaret and Torunsky Nathan (2016)., All About Music., Springer. ISBN 978-3-319-47333-8
  5. Chakraborty Soubhik, Mazzola Guerino, Tewari Swarima and Patra Moujhuri (2014)., Computational Musicology in Hindustani Music., Springer. ISBN 978-3-319-11471-2
  6. Rao S. and Rao P. (2014)., An Overview of Hindustani Musicin the context of Computational Musicology., Journal of New Music Research, 43(1), 24-33. https://www.tandfonline.com/doi/abs/10.1080/09298215.2013.831109
  7. Datta Asoke Kumar, Solanki Sandeep Singh, Sengupta Ranjan, Chakraborty Soubhik, Mahto Kartik and Patranabis Anirban (2017)., Signal Analysis of Hindustani Classical Music., Springer. ISBN978-981-10-3958-4
  8. Temperley David (2010)., Music and Probability., MIT Press. ISBN 978-0-262-515191
  9. Piano (2018)., Google Cloud Platform., http://www.synthesizernotes.com/aye-mere-watan-ke-logo.html accessed on 29.9.18
  10. Chakraborty Soubhik, Sarkar Saurabh, Tewari Swarima and Pal Mita (2012)., Modeling India’s National Anthem: A Statistical Approach., International Research Journal of Social Sciences, 1(2), 1-7. http://www.isca.in/IJSS/Archive/ v1/i2/4.ISCA-JSS-2012-035.pdf