Melakarta Raga Scheme

Raagas are mainly classified into Janka Raagas and Janya Raagas.
'Janaka Raaga' is the other name for Melakartha Raaga.

St.Venkatamukhi's classification of Raagas and its subsequent development and support by the trinity has had a decisive role in shaping Carnatic Music. Classification of Raagas was based on the scale used by a Raaga and thus, Venkatamukhi was in effect classifying various scales, called Melas. His system not only classified known Raagas but also introduced several new ones, based on the possibilities that the system of classification he used, threw up. All melas are full scales, having 7 notes.

Swara Name
-------------------------------------
Sa Shadjam
Re1 Shuddha Rishabam
Re2/Ga1 Chatushruti Rishabam/Shuddha Gandharam
Ga2/Re3 Sadharana Gandharam/Shatshruti Rishabam
Ga3 Anthara Gandharam
Ma1 Shuddha Madhyamam
Ma2 Prati Madhyamam
Pa Panchamam
Dha1 Shuddha Dhaivatham
Dha2/Ni1 Chatushruti Dhaivatam/Shuddha Nishidam
Ni2/Dha3 Kaishiki Nishadam/Shatshruti Dhaivatam
Ni3 Kakali Nishadam

As you can see, Sa and Pa are fixed swaras; Sa is the root, and Pa is its fifth.
The Melakartha ragas are the main or parent ragas that can be made from these swaras by including at least one of each swara.
(Note: you can't have a raaga with, say, Re3 and Ga1; Re must always be below Ga, Dha must always be below Ni, and so on).
Also, all Melakartha raagas must have the same swaras going up (arohana) and coming down (avarohana). There are hundreds of janya ragas (child ragas) made by removing up to 3 swaras and having differing arohana and avarohana, but there are only 72 Melakartha ragas.

CHARACTERISITICS OF A JANAKA RAAGA:

1. Janaka Raagas carry all the seven swaras (s r g m p d n) in the ascending order and the same seven swaras (s r g m p d n) in the descending order. The notes ascend and descend in exactly the same order.
2. Each swaram must occur only once in the Arohanam only once and only once in the Avarhonam.
3. Both the arohanam and the avarohanam must have the Tara Sthayi (upper s)
as one of the notes.

Although there are seven swaras, there are varieties with them (e.g. Antara Gandharam and Sadharana Gandharam, Sudha Dhaivatam, Chatussruthi Dhaviatam and so on; using one of these notes in combination with the other six swaras will create a new raaga).

MELAKARTA RAAGA SCHEME
In any given Melakartha raga, there are two parts: the upper half, Pa-Dha-Ni-Sa, known as the uttaranga, and the lower half, Sa-Re-Ga-Ma, known as the purvanga.

UTTRANGA RAAGAS
Let us examine the possible permutations of the uttaranga. Pa is fixed, Sa is fixed; Dha and Ni are the only variables. There are three Dha and three Ni, but no tone can be occupied by two swaras and Ni must always be above Dha; this leaves us with 6 combinations:

Pa-Dha1-Ni1-Sa
Pa-Dha1-Ni2-Sa
Pa-Dha1-Ni3-Sa
Pa-Dha2-Ni2-Sa
Pa-Dha2-Ni3-Sa
Pa-Dha3-Ni3-Sa

Each of the above uttarangas has a name: Pa, Sri, Go, Bhu, Ma, and Sha, respectively.

PURVANGA RAAGAS
Now let us examine the purvanga. In this, Sa is the only fixed swara and Re, Ga, and Ma are all variable. Let us disregard the variations in Ma for the moment and assume it is fixed: the same principles as above apply, and we get 6 combinations from 3 Re and 3 Ga. For each of those there are two Ma; therefore, there are 12 possible purvangas:

Sa-Re1-Ga1-Ma1
Sa-Re1-Ga2-Ma1
Sa-Re1-Ga3-Ma1
Sa-Re2-Ga2-Ma1
Sa-Re2-Ga3-Ma1
Sa-Re3-Ga3-Ma1
Sa-Re1-Ga1-Ma2
Sa-Re1-Ga2-Ma2
Sa-Re1-Ga3-Ma2
Sa-Re2-Ga2-Ma2
Sa-Re2-Ga3-Ma2
Sa-Re3-Ga3-Ma2

Each of the above purvangas (also called chakras), too, has a name: Indu, Netra, Agni, Veda, Bana, Ruthu, Rishi, Vasu, Brahma, Disi, Rudra, and Aditya, respectively. Combined with the 6 uttarangas, this makes 72 raagas.