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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.

**1A: ****S R1**** G1 1B: D1 N1 S**

**2A: ****S R1**** G2 2B: D1 N2 S**

**3A: ****S R1**** G3 3B: D1 N3 S**

**4A: ****S R2**** G2 4B: D2 N2 S**

**5A: ****S R2**** G3 5B: D2 N3 S**

**6A: ****S R3**** G3 6B: D3 N3 S**

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