Katapayadhi scheme for Melakarta raagas

Katapayadi scheme for Melakartha raaga :

St.Venkatamakhi, who lived in the 16th century, structured the Carnatic music ragas into a mathematical table based on a scientific classification of their swaras. He identified a total of 72 ragas as Melakarta ragas or Janaka (the parent) ragas. All other ragas must be born out of one of the 72 ragas and therefore, are children ragas or Janya ragas.

These 72 ragas each have a name and are classified into two major groups of 36 each. The first set of 36 ragas all have one common swaram, the Sudha Madhyamam and the second set of 36 ragas all have one common swaram, the Prathimadhyamam. With in these two sets of 36 ragas each, they are further sub-divided into groups of six ragas for each group.

From the names of the ragas, we will be able to identify the Melakarta to which it belongs. This is provided by the kaTapayadi scheme. According to this scheme, the first two letters of a raga will lead us to identify the melakarta to which it belongs.

The "ka-Ta-pa-ya" rule used by ancient Indian mathematicians and grammarians is a tool to map names to numbers. Writing the consonants of the Sanskrit alphabet as four groups with "ka, Ta, pa, ya" as the beginning letters of the groups we get

1 2 3 4 5 6 7 8 9 0
ka kha ga gha Nga Ca cha ja Jha nya
Ta Tha Da Dha Na Ta tha da dha na
pa pha ba bha ma
ya ra la va Sha Shha sa ha

For example, the first two letters of the raga nagaanandini are na and ga and from the above table, you can locate these two consonants in column 0 and column 3. When you reverse the numbers 0 and 3, you get 30 are Melakarta 30. You can verify this from the table of Melakarta ragas provided above.
For example:
"kharaharapriya" : kha = 2 and ra = 2 i.e 22 reversing the digits : 22
"shaNmukhapriya" : sha = 6 and mu = 5 i.e 65 reversing the digits : 56
"naThabhairavi" : na = 0 and Tha = 2 i.e 02 reversing the digits : 20
"divyamaNi" : di = 8 and va = 4 i.e 84 reversing the digits : 48

That is exactly what St. VenkaTamakhi of the 18th century is purported to have done. He applied the "kaTapaya" scheme to name the janaka raagas to fit their place in the mELakarta list. Some of these already had suitable names and some had unsuitable names that were in common use. He changed those names a little to fit the naming scheme. Thus "kalyANi" becomes "mEcha kalyANi","SankarAbharaNam" becomes "dheera SankarAbharaNam" etc. Under this naming scheme, the number of a janaka raaga is obtained by decoding the first two letters using the "kaTapaya" scheme. For the naming scheme used for the mELakarta raagas, apart from the decoding rules mentioned above for, conjoint consonants, in case one of the consonants is from the 'ya' group, the first consonant is to be considered instead of the last. And finally, to get back to our familiar western notation, reverse the decoded digits.