Katapayadi Sankhya is a way of determining the Mela number from the name of a Melakarta raga. Given below is the Katapayadi Sankhya. Each value in the cell is a Sanskrit syllable.

The logic works like this.

• Take out the first two syllables from the name of any Melakarta raga [Note: There are some ragas that are exception to this rule]
• Find out the corresponding number of those syllables from the table given above
• Reverse the numbers. This will be the Mela number of that raga.

Lets take raga Harikambhoji

• First two syllables are Ha and Ri.
• From the table, Ha has the value 8 and Ri has the value 2 [Ri is a variation of Ra]
• We have 82 which when reversed gives us 28
• 28th Melakarta raga is Harikambhoji.

Deriving Swaras from Mela number:
Once we have the mela number, a simple set of rules are applied on this number and the swaras in the raga are derived.

{Ri,Ga} Rule:
Note the reminder from dividing the Mela number by 36

• {Ri1,Ga1} if reminder is > 0 and < 7
• {Ri1,Ga2} if reminder is > 6 and < 13
• {Ri1,Ga3} if reminder is > 12 and < 19
• {Ri2,Ga2} if reminder is > 18 and < 25
• {Ri2,Ga3} if reminder is > 24 and < 31
• {Ri3,Ga3} if reminder is > 30 or equal to zero

Ma Rule:

• Ma1 if Mela number < 37
• Ma2 if Mela number > 36

{Dha,Ni} Rule:
Note the reminder from dividing the Mela number by 6

• {Dha1,Ni1} if reminder is 1
• {Dha1,Ni2} if reminder is 2
• {Dha1,Ni3} if reminder is 3
• {Dha2,Ni2} if reminder is 4
• {Dha2,Ni3} if reminder is 5
• {Dha3,Ni3} if reminder is 0

This way we can find out the swaras in each Melakarta raga by applying these rules.

Consider the raga Harikambhoji

• Mela number is 28
• 28 mod 36 is 28. Since 28 is between 24 and 31, we get {Ri2,Ga3}
• 28 is less than 37, therefore Ma is Ma1
• 28 mod 6 is 4, therefore {Dha,Ni} is {Dha2,Ni2}
• Sa, Pa are always fixed for all Melakarta ragas

Thus swaras for Harikambhoji raga would be Sa, Ri2, Ga3, Ma1, Pa, Dha2, and Ni2.

Now you can go ahead and try finding out swaras for all Melakarta ragas!!

Melakarta ragas are Sampoorna ragas i.e. they have all the seven swaras in their aarohana and aavarohana. A Melakarta raga has the following properties.

• It should have the swaras Sa and Pa
• The swaras Ri and Ga should be present in such a way that
  • Ga is always preceded by Ri
  • The index value of Ga should always be greater than or equal to the index value of Ri i.e. A combination of {Ri2, Ga1}, or {Ri3, Ga2}, etc is not acceptable
• Previous rule applies for Dha and Ni
• The swara Ma is either Ma1 or Ma2

Applying the rules, the possible combinations of {Ri,Ga} would be

• { Ri1 , Ga1 }
• { Ri1 , Ga2 }
• { Ri1 , Ga3 }
• { Ri2 , Ga2 }
• { Ri2 , Ga3 }
• { Ri3 , Ga3 }

Similarly the possible combinations of {Dha,Ni} would be

• { Dha1 , Ni1 }
• { Dha1 , Ni2 }
• { Dha1 , Ni3 }
• { Dha2 , Ni2 }
• { Dha2 , Ni3 }
• { Dha3 , Ni3 }

This way, we have 1 Sa, 1 Pa, 6 {Ri,Ga}, 2 Ma, 6 {Dha, Ni}

1 X 1 X 6 X 2 X 6 = 72

There are 72 Melakarta ragas!

Each Melakarta raga has a fixed number mapped to it known as the Mela number. You can find the list of Melakarta ragas with its corresponding Mela numbers here.

In the next post, I’ll talk about how individual swaras are determined for each Melakartha raga.

To start with, this post gives a quick intro to the terms swara and raga.

Swara
Swaras are the basic atoms of music or what people call it as a note. There are seven swaras in Carnatic music. They are Sa, Ri Ga, Ma, Pa, Dha and Ni. Some properties of swaras are

• The swaras Sa and Pa are fixed and do not have any variants
• There are different variants for Ri, Ga, Ma, Dha and Ni
• The notes Ri, Ga, Dha and Ni have 3 variants each i.e. Ri1, Ri2, Ri3, Ga1, Ga2, Ga3, etc.
• The note Ma has 2 variants which are Ma1 and Ma2
• The following notes are equal
  • Ri2 = Ga1, Ri3 = Ga2, Dha2 = Ni1, Dha3 = Ni2. [These notes sound same when sung or played in an instrument.]

Raga
A Raga is made up of five or more swaras.

• Each raga has an ascending sequence of notes known as Aarohana and a descending sequence of notes known as Aavarohana
• A raga may contain variable number of swaras in Aarohana and Aavarohana. This way, there are thousands of possible combinations of swaras to form a raga
• Melakarta ragas are those ragas that have all the seven swaras in their ascending and descending sequence. The swaras that appear in the Aarohana are same as those in the Aavarohana.
• Melakarta ragas are the basic ‘parent’ ragas from which all other ragas are derived.

The next part of this post will talk about how Melakarta ragas are named and numbered.