Interpreting Melakartha Chart

This post is heavily inspired and guided from my talk with my Flute Sir: Shri. Bhaskar. My talk with him on one of my flute classes about Raagas in Carnatic music has instilled tremendous reverence in me for Carnatic Music.

Let me get the terminologies right first:
Raaga - The progression of swaras in some specific order. Each Raaga has Arohanam and Avarohanam.

Swaram - The fundamental constituent of a Raaga. There are 7 Swarams. Sa Ri Ga Ma Pa Dha Ni. Sa and Pa are called Prakruthi Swaras, for there is only one type of Sa and Pa. (its equivalent of C and G in Western Music). The rest has that many variations represented in brackets.
Ri(3)
Ga(3)
Ma(2)
Dha(3)
Ni(3).
Note that Ri2 == Ga1, Ri3 == Ga2, Dha2 == Ni1, Dha3 == Ni2, where "==" is the Equivalence relation.

Arohanam and Avarohanam - A raaga can have musical notes that either ascend or descend relative to current position. When you are in a note and you want to ascend, you should look at your current position in the ascending table and continue to sing the next swaram in the ascending table. When you descend, you just follow the descending table and continue to descend along the swarams defined in that table. The ascending table is called Arohanam and the descending table is called Avarohanam. If there is an anomaly in ascending of an Arohanam and descending of an Avarohanam, its called Vakram.

Melakartha Raagas - There are over 2000+ note progressions forming Raagas. All of them can be derived from 72 raagas called Melakartha Raagas. What’s special about Melakartha Raagas:
They are symmetric, in the sense that Arohanam.reverse() == Avarohanam.
They are complete, in the sense that each of the 72 melakartha has at least and utmost one instance of the 7 swaras in their Arohanam and the rule holds good for Avarohanam too.

How did we arrive at 72?
Its basic combination: There is Sa(1) - Ri(3)- Ga(3) - Ma(2) Pa(1) Dha(3) Ni(3)
Ri2==Ga1
hence when Ri2 is there, Ga1 is not possible as part of melakartha scheme. Hence for Ri2 the Ga that can follow can be only Ga2 and Ga3.

It’s the same with Dha and Ni combo.

Hence,
Sa - 1
Ri Ga - (R1 G1, R1 G2, R1 G3, R2 G2, R2 G3, R3 G3) - 6
Ma - (Ma1, Ma2) - 2
Pa - 1
Dha Ni - (D1 N1, D1 N2, D1 N3, D2 N2, D2 N3, D3 N3) - 6

Multiply the possibilities to get the overall possibilities = 1 * 6 * 2 * 1 * 6 = 72.
Ok, so we now understood how Melakartha scheme is 72.

What is Janya?
A Janya is some raaga that is derived from Melakartha Raaga. The cookbook way of preparing a Janya from its melakartha raaga is : do a transformation (add, delete one or more swaras and change order) on the Melakartha. Note that when adding a new swara, that swara must exist on its Melakartha, you can't arbitrarily insert a swara that’s not in the melakartha.

We will now try to explore more about Melakarthas:
(Note: I have not devised them, I m just trying to spell out the requirements and trying to map the existing awesome solution to the requirements).

Now that we have the fundamentals, lets add some notation to Melakartha and make it systematic.

1. Lets put numbering from 1-72 to easily identify the Raaga.
2. Lets name them.
3. Lets devise a system to classify them easily so that given number, should be able to tell the Swaras in it (and hence the arohanam and avarohanam).

3rd can be achieved if 1st point is done correctly.

All Melakarthas already have names, so lets use them. For classifying, the chart below is going to help us tremendously:

ok,
Lets try to analyze the chart first and spell the notations in the chart. In the chart above you wont find Sa and Pa. The reason being it’s part of all the 72 Melakarthas and there is only one version of Sa and Pa. There are only 2 versions of Ma. Hence there should be 72/2=36 raagas with Ma1 and 36 raagas with Ma2. The remaining swaras are Ri Ga Dha Ni. (Sa Pa Ma are explored).
Each of these 36 raaga blocks should have Sa Ri* Ga* Ma1 Pa Dha* Ni*
(* denote raagas that can vary and non * are those that are fixed for those 36 Raagas).

Now, lets say we now break this 36 into blocks of combiations of Ri and Ga.
The Ri Ga combination (as we saw from the
Melakartha explanation) can be [R1 G1, R1 G2, R1 G3, R2 G2, R2 G3, R3 G3]. which is 6.
Hence the 36 is divided now it 36/6 = 6 blocks. Each of these blocks has one of the above combiations for Ri and Ga. Now for the third block of Ri Ga it is
Sa Ri1 G3 M1 P D* N*. In other words, the only variables now are Dha and Ni.
When we are in the 3rd block, 2 blocks each consisting of 6 raagas precede it. Hence the first raaga in this block should be numbered 13. Its swara signature is S R1 G3 M1 P D1 N1. (which is GayakaPriya).

This is found easily with the above chart this way. All melakartha raagas on the right hand side has Suddha Madhyamam (which is Ma1) and the raagas on left hand side has Pratha Madhyamam (Ma2). For Ri and Ga classification, we express different notation as:
R1 is denoted as Ra
R2 is denoted as Ri
R3 is denoted as Ru

G1 is denoted as Ga
G2 is denoted as Gi
G3 is denoted as Gu


The Dha and Ni combinations in order of [d1 n1, d1 n2, d1 n3, d2 n2, d2 n3, d3 n3] are the 6 raagas in each block.

Thus if you know the Swara signature, you can find the Raaga and vice versa with this chart.

So we have explored the combination of Swara Signature -> Raaga Number, Raaga Number -> Raaga Name (which is obvious with the chart) and Raaga Name -> Swara Signature, all with the help of this chart.

Lets say you don’t have this chart, how will you find the Raaga Number, given Raaga Name? This is also possible, but it’s not so direct though.

Take the first 2 letters of the Raaga.
Lets take Maya Malava Gaula.
first two letters as per sanskrit/tamil/kannada are Ma Ya.

Vallinam letters, with their chronology in brackets are : Ka(1) Sa(2) Da(3) Tha(4) Pa(5) Ra(6)
Mellinam letters, with their chronology in brackets are : Ga(1) Gya(2) Na(3) Na(4) Ma(5) Na(6)
Idaiyinam letters: Ya(1) Ra(2) La(3) Va (4) LA(5) Zha (6)

look at the chronology numbers for Ma and Ya. They are 5 and 1 respectively. Reverse them, so it becomes 15, which is the raaga number for Maya Maulava Gaula.

There are counter examples that don’t work with this. But, it seems that a similar grouping of letters in Sanskrit/Kannada seems to work to get the right number. (I need to find out what should be patched). In Tamil, each of vallinam, mellinam and idayinam have only 6 letters, where as the units digit of a raaga number can be from 1-9 and the tens digit can be from 1-7.
This has to be apparently fixed, after which it would be a perfect mapping :-).

In whatever case it is, the chart is useful at least to get swaras for a given melakartha raaga or to get the raaga give the swara and also to find the raaga number in both the above cases.
Hope my post was useful. Thanks a lot for reading till the end of the post.