https://en.wikipedia.org/wiki/Carnatic_music

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The Melakarta Scheme

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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.

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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.

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The present day , scheme is the one propounded by Govindacharya and followed by Thyagaraja Swami