Agni Mantra

Agni Mantra

Wednesday, December 21, 2005

The "kaTapayaadi" scheme applied to Melakarta Ragas

The "kaTapayaadi" scheme applied to Melakarta Ragas
"The 'ka-Ta-pa-ya' scheme
and its application to
mELAkarta raagas of Carnatic music

The ka-Ta-pa-ya scheme:
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 ~ma cha Cha ja jha ~na
Ta Tha Da Dha Na ta tha da dha na
pa pha ba bha ma
ya ra la va Sa sha sa ha

Now, each letter of the group is numbered from 1 through 9 and 0 for the tenth
letter. Thus, ka is 1, sa is 7, ma is 5, na is 0 and so on. So to indicate
the number 356 for example one would try and come up with a word involving
the third, fifth and sixth letters of the groups like 'gaNitam' or 'lESaca'.
However, in the Indian tradition, the digits of a number are written left to
right in the increasing order of their place value - exactly opposite the way
we are used to writing in the western way. Therefore 356 would be indicated
using letters in the 6th, 5th, and 3rd positions of the group e.g. 'triSUlaM'.

There apparently were upto 4 flavors of this scheme in use in ancient
India. These differ in how to interpret the conjoint consonant. The popular
scheme was to use only the last consonant. And any consonant not attached
to a vowel is to be disregarded. These rules should be used while decoding
a phrase in 'katapayadi' scheme.

The following phrase found in 'sadratnamAla' a treatise on astronomy,
bhadram budhi siddha janma gaNita Sraddha@h mayadbhUpagi@h
when decoded yields
4 2 3 9 7 8 5 3 5 6 2 9 5 1 4 1 3
which when reversed gives
3 1 4 1 5 9 2 6 5 3 5 8 7 9 3 2 4
which is readily recognised as the digits in 'pi' (except that the 17th
digit is wrong - it should be 3) :-)!

(source: The article 'The Katapayadi Formula and Modern"
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