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The Melekartha System is the most scientific system of creation and classification of ragas and forms the basic of the classical carnatic music system. It defines the rules to create the base ragas with 7 notes each using a combination of the 12 keys in an octave.

Melakartha system uses a powerful scientific algorithm to create the fundamental 72 ragas of the carnatic music system. All other ragas in the carnatic music system are derived from one/more of these 72 ragas. The derived ragas are called janya ragas.

## Introduction to 7 Swaras or Notes in Carnatic Music

In the Melakartha system we divide the 12 keys of an octave (in the keyboard) into 7 swaras as follows:

S = Shadjama = First key of the octave

2. Rishaba

R1 = Shudhdha Rishabha = Second key of the octave
R2 = Chathushruthi Rishabha = Third key of the octave
R3 = Sathshruthi Rishabha = Fourth key of the octave

3. Gandhara

G1 = Shudhdha Gandhara = Third key of the octave
G2 = Sadharana Gandhara = Fourth key of the octave
G3 = Anthara Gandhara= Fifth key of the octave

M1 = Shudhdha Madhyama = Sixth key of the octave
M2 = Prathi Madhyama = Seventh key of the octave

5. Panchama

P = Panchama = Eigth key of the octave

6. Daivatha

D1 = Shudhdha Daivatha = Nineth key of the octave
D2 = Chathushruthi Daivatha = Tenth key of the octave
D3 = Sathshruthi Daivatha = Eleventh key of the octave

N1 = Shudhdha Nishadha = Tenth key of the octave
N2 = Kaishika Nishadha = Eleventh key of the octave
N3 = Kaakali Nishadha = Twelveth key of the octave

You can see above that R2=G1, R3=G2, D2=N1 and D3=N2. The reason for this lies in the Melakartha algorithm.

## Melakarta Algorithm – maps 12 keys of octave to 7 swaras of a raga

The Melakartha algorithm is as follows:

• A Melakartha Raga has all the 7 swaras in it.
• A Melakartha Raga cannot have multiple entries for the same swara. For instance you cannot have both N1 and N2 in the same raga as they both are Nishadas.
• The same frequency cannot occupy more than one swara, for instance, if R2 is the Rishabha in a raga then G1 cannot be used as Gandhara in that raga as G1=R2.
• The swara order (increase in frequency called ArOhaNa) is Sa (Shadjama), Ri (Rishabha), Ga (Gandhara), Ma (Madhyama), Pa (Panchama), Dha (Daivatha), Ni (Nishadfha).

Based on the above algorithm we can form the Melakartha ragas as follows.

• Sa and Pa are the same in all ragas as they have only one entry.
• Ma has two entries so we can form two ragas for every given combination of all other swaras i.e. if we are given a sa,ri,ga,pa,da and ni combination we can form two melakartha ragas for that combination by using M1 as ma in one raga as M2 as ma in another raga.
• For instance, given S,R1,G2,P,D1,N1 we can form two Melakarthas as follows:
S,R1,G2,M1,P,D1,N1 and S,R1,G2,M2,P,D1,N1
• R1 has 3 entries and Ga has 3 entries where two entries are common to both (i.e. R2=G1 and R3=G2). Hence, considering the fact that frequency of Ga has to be always greater than Ri (i.e. the key for Ri cannot come after the key for Ga) ,we can have totally 6 combinations for Ri,Ga as follows:
R1G1, R1G2, R1G3, R2G2, R2G3 and R3G3
• Similarly we can have 6 entries for Dha,Ni combination as follows:
D1N1, D1N2, D1N3, D2N2, D2N3 and D3N3
• Thus we have unique 2 entries for Ma, 6 entries for Ri,Ga and 6 entries for Ni,Dha. This makes a total of 2x6x6 = 72 unique combinations of all the 7 swaras defined based on 12 keys in an octave. .
• Thus using the Melakartha algorithm we can create 72 Melakartha ragas. A mELakartha rAgA is also called a Sampoorna raga as it has all the 7 swaras in it.