Sri Muthuswami Dikshitar  - Update of Jan'2004

[Extract from an article by Prof.K.R.Rajagopalan that appeared in the Sangeet Natak Academy Journal]

Modern methods of using entropy to analyze Carnatic Music have already been used.The number of times each note occurs in a song is counted and then they are converted to proportions called P's.The entropy called H is calculated by the formula H = - �( p, ld p)
ld - logarithm to base 2.For example in the three songs the following are the proportions of notes from higher panchama (HP) to lower panchama.

Song1 - nAgalingam - Shankarabharanam
Song2 - sadAshivam upAsmahe - Shankarabharanam
Song3 - dharmasamvardhani - madhyamavati

If all the swaras have the same proportion of occurence ie maximum variation (at any stage one cannot say what the next swara would be as is the case with tosses of a coin or a roll of dice) then the values of H would be a maximum.Thus by comparing values of H for various songs one can find whether there is larger degree of freedom in the exploitation of the swaras than in the other songs.In the above table the notes in different octaves have been treated as being different.Since it is said that the swara is the same whatever the octave the next table would present calculations of H based on 7 swaras only for a number of compositions of the trinity in Kalyani and Shankarabharanam.

Shankarabharanam:

Dikshitar:

Tyagaraja:

Shyama Shastri:

Kalyani:

Dikshitar:

Tyagaraja:

Considering both ragas have all seven swaras they have a maximum H value of 2.80764.It is seen for all composers generally H values for Kalyani are higher than the ones in shankarabharanam.It would also be noted that the songs found toward the end of the list are more in vogue than those found toward the beginning of the list.Could we take this to indicate that easier pieces would have generally low H values?