The Melakarta Scheme

The Melakarta Scheme

Contemporary Carnatic music is based on a system of 72 melakarta ragas. These 'creator' ragas are also called janaka ragas and thai (mother) ragas. The current system can be traced to the works of Venkatamakhi who appears to be the first to use 72 melakartas. Earlier works generally contain fewer melakartas and most have flaws in organization. At that time, (16th century) many of Venkatamakhi's melakartas were unknown and were not assigned names. Later, all 72 were given names and this system is sometimes referred to as the Kanakaambari - Phenadhyuthi system after the names of the first two melakartas in it. Muthuswamy Dikshithar's compositions are generally based on the raga names and lakshanams (definitions) in this system while Thyagaraja used a later scheme devised by Govindacharya in the late 18th century. Venkatamakhi did not believe that melakartas must be of simple sampoorna arohanam - avarohanam but favored the idea of calling a raga as a melakarta if all the seven swaras occurred in either the arohanam or the avarohanam. Thus a raga which went Sa-Ri-Ma-Pa-Ni-Sa, Sa-Da-Pa-Ga-Ri-Sa could be a melakarta under this scheme. Govindacharya's insistence on sampoorna arohanam - avarohanam leads to a system which is more elegant from a mathematical viewpoint. In this scheme, the melakartas arise out of systematic permutation of the seven swaras into the twelve swara sthanas. Seen this way, the melakarta scheme is a product of mathematical abstraction and the naming of swaras (and the introduction of vivadi swaras) is of no consequence as far as the organization of the melakartas is concerned. No wonder, Venkatamakhi is reputed to have said that even Lord Maheswara could not create more melakartas!
As we noted before, all melakartas employ a complete (sampoornam) arohanam - avarohanam structure. The purvangam of a melakarta refers to the lower half of the Arohanam - Avarohanam, namely Sa-Ri-Ga-Ma and uttarangam refers to the upper half or Pa-Da-Ni-Sa. First let us examine the possible variations in the uttarangam. Pa is fixed. Da can occupy three sthanas and so can the Ni. But, the Ni has to be always above the Da and that leaves us with the following six possible uttarangams.
(1) Pa-Suddha Dhaivatham-Suddha Nishadam-Sa
(2) Pa-Suddha Dhaivatham-Kaisika Nishadam-Sa
(3) Pa-Suddha Dhaivatham-Kakali Nishadam-Sa
(4) Pa-Chatusruthi Dhaivatham-Kaisika Nishadam-Sa
(Suddha Nishadam occupies the same swara sthana as Chatusruthi Dhaivatham and hence the two cannot occur together)
(5) Pa-Chatusruthi Dhaivatham-Kakali Nishadam-Sa
(6) Pa-Shatsruthi Dhaivatham-Kakali Nishadam-Sa
These six uttarangam combinations are denoted by the names Pa, Sri, Go, Bhu, Ma and Sha respectively. The following series of figures illustrate the keyboard locations of the swaras in these six uttarangam combinations as also the corresponding numbered swara sthanams (the number 13 refers to the Sa of the next octave) for one kattai sruthi.
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Da ## ## __ __ __ __ __ __ Pa Ni Sa ________________________________Swara Locations for the 'Pa' uttarangam (8-9-10-13)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Da Ni ## __ __ __ __ __ __ Pa Sa ________________________________Swara Locations for the 'Sri' uttarangam (8-9-11-13)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Da ## ## __ __ __ __ __ __ Pa Ni Sa ________________________________Swara Locations for the 'Go' uttarangam (8-9-12-13)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ni ## __ __ __ __ __ __ Pa Da Sa ________________________________Swara Locations for the 'Bhu' uttarangam (8-10-11-13)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## __ __ __ __ __ __ Pa Da Ni Sa ________________________________Swara Locations for the 'Ma' uttarangam (8-10-12-13)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Da ## __ __ __ __ __ __ Pa Ni Sa ________________________________Swara Locations for the 'Sha' uttarangam (8-11-12-13) As in the case of the Da and Ni uttarangam combinations, the Ri and Ga provide six possible combinations. Each of these can occur with either of the two Madhyamams to yield a total of twelve possible purvangams. The twelve purvangam combinations are each called as chakras. The twelve chakras and the corresponding purvangams are as follows.
(1) Indu Sa, Suddha Rishabam, Suddha Gandharam, Suddha Madhyamam (2) Netra Sa, Suddha Rishabam, Sadharana Gandharam, Suddha Ma (3) Agni Sa, Suddha Rishabam, Anthara Gandharam, Suddha Ma (4) Veda Sa, Chatusruthi Rishabam, Sadharana Gandharam, Suddha Ma (5) Bana Sa, Chatusruthi Rishabam, Anthara Gandharam, Suddha Ma (6) Ruthu Sa, Shatsruthi Rishabam, Anthara Gandharam, Suddha Ma (7) Rishi Sa, Suddha Rishabam, Suddha Gandharam, Prati Madhyamam (8) Vasu Sa, Suddha Rishabam, Sadharana Gandharam, Prati Ma (9) Brahma Sa, Suddha Rishabam, Anthara Gandharam, Prati Ma (10) Disi Sa, Chatusruthi Rishabam, Sadharana Gandharam, Prati Ma (11) Rudra Sa, Chatusruthi Rishabam, Anthara Gandharam, Prati Ma (12) Aditya Sa, Shatsruthi Rishabam, Anthara Gandharam, Prati Ma The chakra names are associated with the chakra numbers they represent. For example, there are four Vedas, and Veda chakra is the fourth chakra. The following illustrations depict the swara locations on the keyboard for the twelve chakras, along with the numbered swaras.
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ri ## ## ## ## ## __ __ __ __ __ __ Sa Ga Ma ________________________________Swaras of Indu Chakra (1-2-3-6)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ri Ga ## ## ## ## __ __ __ __ __ __ Sa Ma ________________________________Swaras of Netra Chakra (1-2-4-6)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ri ## ## ## ## ## __ __ __ __ __ __ Sa Ga Ma ________________________________Swaras of Agni Chakra (1-2-5-6)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ga ## ## ## ## __ __ __ __ __ __ Sa Ri Ma ________________________________Swaras of Veda Chakra (1-3-4-6)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## __ __ __ __ __ __ Sa Ri Ga Ma ________________________________Swaras of Bana Chakra (1-3-5-6)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ri ## ## ## ## __ __ __ __ __ __ Sa Ga Ma ________________________________Swaras of Ruthu Chakra (1-4-5-6)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ri ## Ma ## ## ## __ __ __ __ __ __ Sa Ga ________________________________Swaras of Rishi Chakra (1-2-3-7)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ri Ga Ma ## ## ## __ __ __ __ __ __ Sa ________________________________Swaras of Vasu Chakra (1-2-4-7)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ri ## Ma ## ## ## __ __ __ __ __ __ Sa Ga ________________________________Swaras of Brahma Chakra (1-2-5-7)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ga Ma ## ## ## __ __ __ __ __ __ Sa Ri ________________________________Swaras of Disi Chakra (1-3-4-7)
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ma ## ## ## __ __ __ __ __ __ Sa Ri Ga ________________________________Swaras of Rudra Chakra (1-3-5-7)
Each of the twelve purvangams can be combined with the six uttarangams to obtain a total of 72 melakartas. The melakartas are then identified by combining the chakra name with the Pa - Sri designation. Thus, a melakarta described as Rudra-Ma (or no. 65, Mechakalyaani) corresponds to an arohanam and avarohanam containing Shadjam - Chatusruthi Rishabam - Anthara Gandharam - Prati Madhyamam - Panchamam - Chatusruthi Dhaivatham - Kakali Nishadam - Shadjam. The following table lists all the 72 melakartas and the swaras used in each of them using the chakra and Pa - Sri notation as described. The first 36 melakartas use Suddha Madhyamam and melakartas 37 through 72 use Prati Madhyamam. These two groups are sometimes identified as Suddha Madhyama melakartas or Purva melakartas and Prati Madhyama melakartas or Uttara melakartas respectively. The table is organized in such a fashion that a Suddha Madhyama melakarta and its Prati Madhyama pair (the melakarta which shares all swaras except the Madhyama) occur on the same line. Thus to find out what is the Prati Madhyama (or Uttara melakarta) pair of Maayaamaalavagowla, one just reads across the table to find Kaamavardhani (which is also known as Pantuvaraali). If it were not for the gamakkas, such pairs would sound very similar and be different only when the Madhyama occurs.
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ri Ma ## ## ## __ __ __ __ __ __ Sa Ga ________________________________Swaras of Aditya Chakra (1-4-5-7)
Melakarta Ragas
Many of the melakartas have alternate names like in the example just cited and some of these are listed in the Appendix. In addition, some of the common ones (like Thodi) are listed with prefixes (Hanumathodi). This is in accordance with the so called 'Katapayaathi' formula. Using this formula, numerical values are assigned to consonants as listed in the following table (the devanagari script is the basis upon which this assignment is done). To find out what is the location of a melakarta in the table, the first two consonants are deciphered using the numerical assignment table and the resulting number is inverted left to right. For example, consider Hanumathodi - the first two consonants being Ha and Na. Ha is assigned 8 and Na is zero. The resulting number if 80 and after inversion, this yields the number 8, which is the melakarta number corresponding to Hanumathodi. One must be careful in decoding prefixes - for example, Thodi, Sankaraabharanam and Kalyaani are melakartas which take on prefixes to identify their melakarta numbers but Naata, Bhairavi and Kaambhoji are not melakartas but actually janya ragas of Chalanaata, Natabhairavi and Harikaambhoji respectively. The naming of melakartas in accordance with the Katapayaathi formula is generally attributed to Govindacharya. Govindacharya was well versed in astrology and the Katapayaathi convention has been widely used in astrology for centuries.
Once the melakarta number is known, one can use the chakra scheme to identify the swaras in it. As an example, consider Shanmugapriya. The consonants are Sha and Ma. Sha=6 and Ma=5 to yield the melakarta number 56. Dividing 56 by 6 yields a quotient of 9 and a remainder of 2. This means that Shanmugapriya belongs to the 10th (or Disi) chakra and is the second (or Sri) raga in that chakra. Thus Shanmugapriya is identified as Disi-Sri. Then, the swaras in Shanmugapriya are (collecting the purvangam and uttarangam from the tables) Sa - Chatusruthi Rishabam - Sadharana Gandharam - Prati Madhyamam - Pa - Suddha Dhaivatham - Kaisika Nishadam - Sa. Note that in figuring out the chakra, we need to add one to the quotient to obtain the chakra number. We can use the melakarta table to directly find that Shanmugapriya is Disi-Sri and end up with the same swaras. The following keyboard diagram illustrates the location of the swaras in Shanmugapriya for one kattai sruthi.
========================================== ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ga Ma Da Ni ## __ __ __ __ __ __ Sa Ri Pa Sa ________________________________Swaras in Raga Shanmugapriya
Table. Letter Values in Katapayaathi Formula
Values Letters
Ka series Ta Pa Ya
1 Ka Ta (as in Tom) Pa Ya2 Kha Tha Pha Ra3 Ga Da (as in dumb) Ba La4 Gha Dha Bha Va5 Nga (as in Bengal) Na (as in Anna) Ma Sa (as in Siva)6 Cha (as in chip) Ta (as in with) Sha(as in Shut)7 Chha Tha Sa (as in Sea)8 Ja Da Ha9 Jha Dha0 Ngya Na (as in Pen)It is worthwhile to observe here that the Pa, Sri, Go, Bhu, Ma, Sha designation is also based on the Katapayaathi formula (with Sri treated as ra). The formal organization of the melakartas provides some insights into the similarities between certain ragas. Ragas in the same chakra share their purvangam and thus, sound similar in that portion. This explains, for example, the similarity between Kharaharapriya and Kiravaani. Ragas whose melakarta numbers differ by a multiple of six (meaning they have the same Pa-..-Sha designation) have the same uttarangam and this too causes similarity, as in the case of Lataangi and Kaamavardhani. One can find many pairs of melakarta ragas that differ by a single swaram, as in the case of Lataangi and Kaamavardhani (which differ only in Ri). Locating such pairs is often very instructive. A good musician makes it a point not to dwell on chains of swaras that are shared by various ragas, but often introduces contrasting swaras that are designed to let the listener identify the similarities and the differences simultaneously. This aspect can be used as a test of how good a musician really is. In a recent concert, a popular musician was performing a composition in the raga Chaarukesi. Chaarukesi can be seen to have the same purvangam as Sankaraabharanam and the same uttarangam as Shanmugapriya or Thodi. However, singing the purvangam portion of Sankaraabharanam and then the uttarangam of Shanmugapriya or Thodi has very little to do with the true swaroopam of Chaarukesi. This is like arguing that glueing a lion's head to a human torso results in the creation of a new being, when all it really does is create neither a lion nor a human being. The resulting creature is a poor excuse for a human or a lion and can be seen only as such. The use of gamakkas is also intricately connected to the concept of raga swaroopam and even though swaras may be the same, the gamakkas are often different, leading to ragas that are quite distinct in character.
The melakarta ragas in which vivadi swaras appear are called as vivadi melakartas. Thus all melakartas of Indu, Ruthu, Rishi and Aditya chakras as well as all melakartas with Pa or Sha designation are vivadi melakartas. The Pa and Sha designated ragas have a vivadi swara in their uttarangam while the Indu, Ruthu, Rishi and Aditya chakra ragas have a vivadi swara in their purvangams. Thus, there are 40 vivadi melakartas, out of which 8 have two vivadi swaras and the rest one vivadi swara each. If a melakarta system is constructed without the vivadi melakartas, a number of fairly common ragas will have to be treated as being outside the system (eg. Gaanamurthy, Jhaalavaraali). Further, janya ragas like Naata will have no associated melakarta, exposing the limitations of the classification system.