Before trying to understand Katapayādhi Sūtra, it is strongly recommended to know about Melakartha Rāgas. You can read about them here.
What is Katapayādhi Sūtra in Carnatic Music?
Katapayādhi Sūtra is an ancient numerical encoding system used to determine the number of a Melakartha rāga from its name, and through that number, its swarasthānas can also be determined.
Here’s how Katapayādhi Sutra table looks like:
The first (top) row has numbers from 1 to 0 for each column.
Second row has Ka, Kha, Ga, Gha, Ṅa, Cha, Chha, Ja, Jha, Ña
Third row has Ṭa, Ṭha, Ḍa, Ḍha, Ṇa, Ta, Tha, Da, Dha, Na
Fourth row has pa, Pha, ba, Bha, Ma
Fifth row has ya, ra, la, va, sha, Sha, sa, ha, La, Ksha.
The structure of the Katapayādhi table follows the traditional Sanskrit consonant arrangement (Vyanjanas). The consonants are grouped in the same order as they appear in the varga system — Ka-varga, Cha-varga, Ṭa-varga, Ta-varga, Pa-varga, and so on.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 |
|---|---|---|---|---|---|---|---|---|---|
| Ka | Kha | Ga | Gha | Ṅa | Cha | Chha | Ja | Jha | Ña |
| Ṭa | Ṭha | Ḍa | Ḍha | Ṇa | Ta | Tha | Da | Dha | Na |
| Pa | Pha | Ba | Bha | Ma | |||||
| Ya | Ra | La | Va | Śa | Sha | Sa | Ha | Ksha |
The Rule
- Take the first two meaningful consonants of the Melakartha rāga name (ignoring vowels).
- Convert them into numbers using the Katapayādhi table.
- Reverse the digits.
The resulting number is the Melakartha number.
The best way to explain how Katapayādhi Sutra works is by giving an example. So let’s take one.
Example: Let us consider a Melakartha Rāga – Māyāmālavagowla. Now, the first two syllables of the name of the rāga are Ma and Ya. If we were to find these syllables in the Katapayādhi Sutra table, we’ll find them in 5th and the 1st column respectively. 5 and 1.
Now, reverse the digits. That will be, 1 and 5.
And that is the answer. Māyāmālavagowla is the 15th Melakartha Rāga in the 72 Melakartha Rāga system.
Why Do We Reverse the Digits?
In the Katapayādhi system, numbers are read from right to left. So the first syllable gives the unit digit, and the second syllable gives the tens digit.
That is why 5–1 becomes 15.
For example, if a rāga begins with “Cha–Ra”, Cha corresponds to 6 and Ra corresponds to 2. Reversing the digits gives 26.
See the beauty of this framework. From the name alone, we can determine the Melakartha number. From the Melakartha number, we know its position among the 72 rāgas. And from that position, we know its swarasthānas.
[…] There is an ancient framework by which, from the name of the rāga alone, its Melakartha number and thereby its swarasthānas could be known. Read more about it (Katapayādhi Sutra) here. […]