Classification of ragas - the Melakartha system

The fundamental classification of ragas are as Melakartha ragas and Janya ragas. Melakartha are the fundamental ragas. For a raga to be termed as Melakartha raga, it has to be a sampoorna raga (i.e., has all the 7 swaras appearing once and only once and in the same order both in aarohana and avarohana). This begs a question, if there are only 7 notes (from our earlier lecture, we saw that there were 7 notes S R G M P D N) then how many melakartha can be there?
Well, the 7 notes are not just limited to 7 frequencies but to variations between them.



Consider one octave from the above image, that is from one C to another C. You will notice that there are 12 keys (7 white and 5 black). These 12 keys form the 12 swarasthanas. Each of the swarasthana is a variation of the 7 fundamental notes. M or madhyama has 2 variations, R, G, D, N have 3 variations each, S and P are fixed notes. We will denote the variations using subscripts 1,2 or 3. They are arranged on the 12 swarasthanas on a overlapping scale as follows.
1. S
2. R1
3. R2 = G1
4. R3 = G2
5. G3
6. M1
7. M2
8. P
9. D1
10. D2 = N1
11. D3 = N2
12. N3

Now this becomes a simple process of choosing 1 each of R G M D N to form a melakartha along with the S and P. We see that there are only 6 combinations of R and G that are possible - R1G1, R1G2, R1G3, R2G2, R2G3, R3G3 (The others are either meaningless because R2 is same as G1 etc or are one of the above six R2G2 == R3G1). Similarly D and N also have 6 combinations. Along with 2 variations of M, they give rise to a total of 6 X 6 X 2 = 72 Melakartha ragas. They start with Kanakangi as the 1st Melakartha with a scale of S R1 G1 M1 P D1 N1 S and end with Rasikapriya as the 72nd Melakartha with a scale of S R3 G3 M2 P D3 N3 S.
The Melakartha ragas are arranged in 12 groups of 6 ragas each. The first 6 groups have M1 and the last 6 groups have M2. The first group starts with R1G1 and the next group has R1G2 and so on. Within each group the order goes as D1N1, D1N2, D1N3, D2N2, D2N3, D3N3. That is the sort order is basically M, RG group, DN group.
Given the Melakartha number it is possible to find out it's scale and vice versa. For ex 56th Melakartha means, this is in M2 group (since 56 > 36), it is in the 10th group (that is the 4th of the M2 ragas) and it is the 2nd within the group. That is it's scale will be S (R2 G2) M2 P (D1 N2) (This is the famous Shanmukapriya).

Another example:
What is the Melakartha number of S R2 G3 M1 P D1 N2 S
R2 G3 is the 5th group and D1 N2 is the 2nd raga in that group which means the number will be 4*6+2 = 26 (This is the raga Charukesi).
Here's a link to the Melakartha classification and the scales of all the 72 ragas
http://en.wikipedia.org/wiki/Melakarta#Table_of_Melakarta_ragas

The ragas represented as piano keys can be seen at
http://commons.wikimedia.org/wiki/Melakarta_ragams_(svg)

A page with links to sample of ragas on the keyboard
http://www.carnaticindia.com/melakartha_ragas.html

Demos of various melakarthas
http://www.musicindiaonline.com/music/carnatic_vocal/s/artist.105/ Look for Melakartha in the title.