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Explanation of the Melakarta Chart
Before looking onto the melakarta chart, it is useful to understand the arrangement of the melakarta ragas or parent scales. Mathematically speaking there are seventy-two scales that are possible. Considering the fact that sa and pa are fixed with ma as the variable note, the acceptable combinations of the first part of the scale, known as the purvanga, and the second half of the scale known as the uttaranga. Below, the purvanga is shown by #A and the purvanga is shown by #B.
Note that possibilities of S R2 G1, S R3 G2, and D2 N1 S, D3 N2 S are eliminated, because they are duplicates (R2 = G1, R3 = G2, D2 = N1, D3 = N2). In addition, note the possibilities of S R3 G1 and D3 N1 S are eliminated, because this pattern is nonsensical. The pitch of ga or ni must always be higher than re or dha, respectively. In other words, the R and D will limit on which G and N could be used. If R1 was used, then any of the three G can be used. If R2 was used, only G2 and G3 could be used. The number for G cannot be less than the number of R. Thus, G1 cannot be used for a raga using R2 (because 1 < 2). This rule also holds true for D vs. N. The number following N cannot be less than the number of D.
Since there were six possible combinations on the purvanga and six possible combinations in the uttaranga, there can be thirty-six overall combinations given that the ma is shuddha (M1). However, there is always the possibility that ma is augmented, also known as prati ma (M2). To account for M1 and M2 melakartas, thirty-six is multiplied by two to get seventy-two possible scales.
Classification of these melas is extremely intricate. Each mela is numbered from one to seventy-two. The first mela consists of all the flattened notes, while the last mela consists of the sharpest form of each note. As there are scales and points about them, they are usually referred to by their number, instead of their name. From this order, divisions are made possible.
MAJOR DIVISION: Divide them by which ma is used. (Suddha ma (36) vs. prati ma (36))
The first division is done by cutting the seventy-two into two halves of thirty-six melas. The first set of melas will be the ones with M1. The other half will be identical replications of first half, except it will be called M2. To get a M2 version of a certain M1 raga, you simply add thirty-six to the mela number. For instance, Mela 15 is (S R1 G3 M1 P D1 N3 S) known as Mela Mayamalavagoula. To find the mela number of its M2 form, you add thirty-six to get Mela 51 known as Mela Kamavardhini (S R1 G3 M2 P D1 N3 S). (15 + 36 = 51)
Likewise, if you want to find the suddha ma version of the same raga, you subtract thirty-six from the mela number.
SUBDIVISION: Six subdivisions per half major division. (36/6) Χ 2 = 12 cakrams
Within each half of thirty-six, the section is divided further into sixths. These sixth sections are known as the cakram (or cakra). There are twelve charkas and each charka has six melas within them in a particular order. The cakram is identified by the purvanga notes. Since there were six purvangas identified earlier, they were divided into six. Each mela of a particular charka will have the same purvanga. For instance, all purvangas with S R1 G1 with M1 is of the Indu Cakra, or the first cakram. The cakrams build from the lowest forms of the note to the highest. Therefore, Indu Cakram uses the lowest forms (S R1 G1 M1) while Aditya Cakram uses the highest forms possible for each note (S R3 G3 M2).
Indu Cakra has the purvanga: S R1 G1 M1 (lowest forms of every note)
Netra Cakra has the purvanga: S R1 G2 M1
Agni Cakra has the purvanga: S R1 G3 M1
Veda Cakra has the purvanga: S R2 G2 M1
Bana Cakra has the purvanga: S R2 G3 M1
Rtu Cakra has the purvanga: S R3 G3 M1 (highest forms of each note, but uses M1)
Rsi Cakra has the purvanga: S R1 G1 M2 (lowest forms of each note, but uses M2)
Vasu Cakra has the purvanga: S R1 G2 M2
Brahma Cakra has the purvanga: S R1 G3 M2
Disi Cakra has the purvanga: S R2 G2 M2
Rudra Cakra has the purvanga: S R2 G3 M2
Aditya Cakra has the purvanga: S R3 G3 M2 (highest form of each note)
If one were to exclude the Ma note in each of the cakras, then Indu (first) and Rsi (seventh) would be the same. Likewise, Netra (second) and Vasu (eighth) would be the same. The difference between the M1 cakra and the corresponding M2 cakra is six. Therefore, one would need to add six to get to the M2 cakra (or vice versa, subtract six from the M2 cakra to get the corresponding M1 cakra).
PRASTARAM: Six subdivisions per cakram.
Next, each cakram is further divided into six more parts. As mentioned above, there are six possible uttaranga combinations. Since the purvanga is held constant per each chakra, only varying factor is the uttaranga. Each of the six uttaranga are applied to the constant purvanga to yield the six melakarta.
One refers to a specific uttaranga suffix by a prastaram. There are six prastaram names for the uttaranga.
Pa prastaram has the uttaranga: D1 N1 S (lowest form of each note)
Sri prastaram has the uttaranga: D1 N2 S
Go prastaram has the uttaranga: D1 N3 S
Bhu prastaram has the uttaranga: D2 N2 S
Ma prastaram has the uttaranga: D2 N3 S
Sa prastaram has the uttaranga: D3 N3 S (highest form of each note)
Like the categorization of the cakrams, the prastaram starts from the lowest form of each note to the highest form. When a cakra applies the prastaram, it goes in this order.
EXAMPLE: Derive the first six melas.
The first cakra is Indu Cakra. Its purvanga form is S R1 G1 M1. Write the purvanga form six times in a column.
Then, in the order presented, add the prastarams to the end. Dont forget to use Pa as the sandwich between the purvanga and the uttaranga.
S R1 G1 M1 P D1 N1 S (Pa prastaram)
S R1 G1 M1 P D1 N2 S (Sri prastaram)
S R1 G1 M1 P D1 N3 S (Go prastaram)
S R1 G1 M1 P D2 N2 S (Bhu prastaram)
S R1 G1 M1 P D2 N3 S (Ma prastaram)
S R1 G1 M1 P D3 N3 S (Sri prastaram)
Comparing the mathematical theory of the seventy melakarta scales to the ten scales (thāts) of North Indian music will make Carnatic music very wealthy in melody. Seventy-two melas are only parent ragams which can only result in a variety of thousands of ragams. Understanding how the mela works will help one appreciate the scientific nature of Carnatic music.
UPDATED: April 2, 2009