The melakarta ragas of the Carnatic music is named so that the first two syllables of the name will give its number. This system is sometimes called the Ka-ta-pa-ya-di sankhya. The Swaras 'Sa' and 'Pa' are fixed, and here is how to get the other swaras from the melakarta number.
Melakartas 1 through 36 have Ma1 and those from 37 through 72 have Ma2.
The other notes are derived by noting the (integral part of the) quotient and remainder when one less than the melakarta number is divided by 6. If the melakarta number is greater than 36, subtract 36 from the melakarta number before performing this step.
'Ri' and 'Ga' positions: the raga will have:
Ri1 and Ga1 if the quotient is 0
Ri1 and Ga2 if the quotient is 1
Ri1 and Ga3 if the quotient is 2
Ri2 and Ga2 if the quotient is 3
Ri2 and Ga3 if the quotient is 4
Ri3 and Ga3 if the quotient is 5
'Da' and 'Ni' positions: the raga will have:
Da1 and Ni1 if remainder is 0
Da1 and Ni2 if remainder is 1
Da1 and Ni3 if remainder is 2
Da2 and Ni2 if remainder is 3
Da2 and Ni3 if remainder is 4
Da3 and Ni3 if remainder is 5
See swaras in Carnatic music for details on above notation.
Raga Dheerasankarabharanam
Edit
The katapayadi scheme associates dha
↔\leftrightarrow 9 and ra
↔\leftrightarrow 2, hence the raga's melakarta number is 29 (92 reversed). 29 less than 36, hence Dheerasankarabharanam has Ma1. Divide 28 (1 less than 29) by 6, the quotient is 4 and the remainder 4. Therefore, this raga has Ri2, Ga3 (quotient is 4) and Da2, Ni3 (remainder is 4). Therefore, this raga's scale is Sa Ri2 Ga3 Ma1 Pa Da2 Ni3 SA.
Raga MechaKalyani
Edit
From the coding scheme Ma
↔\leftrightarrow 5, Cha
↔\leftrightarrow 6. Hence the raga's melakarta number is 65 (56 reversed). 65 is greater than 36. So MechaKalyani has Ma2. Since the raga's number is greater than 36 subtract 36 from it. 65–36=29. 28 (1 less than 29) divided by 6: quotient=4, remainder=4. Ri2 Ga3 occurs. Da2 Ni3 occurs. So MechaKalyani has the notes Sa Ri2 Ga3 Ma2 Pa Da2 Ni3 SA.
Exception for Simhendramadhyamam
Edit
As per the above calculation, we should get Sa
↔\leftrightarrow 7, Ha
↔\leftrightarrow 8 giving the number 87 instead of 57 for Simhendramadhyamam. This should be ideally Sa
↔\leftrightarrow 7, Ma
↔\leftrightarrow 5 giving the number 57. So it is believed that the name should be written as Sihmendramadhyamam (as in the case of Brahmana in Sanskrit).
Representation of dates
