Melakarta
The postulated number of melakarta derives from arithmetical calculation and not from Carnatic practice, which employs far fewer scale forms. Seven-pitch melakarta are considered subsets of a twelve-pitch scale roughly analogous to the Western chromatic scale. The first and fifth melakarta tones, corresponding to the first and seventh chromatic tones, are invariable in inflection, and the fourth melakarta tone, corresponding to the fifth or sixth chromatic tone, is allowed one of two inflections only, a natural (shuddah) position and a raised (tivra) position. Thus the number of possible forms is equal to twice the square of the number of ways a two-membered subset can be extracted from a four-membered set:
Read more about this topic: Heptatonic Scale