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Math Behind the Carnatic RagaNames

Updated: Oct 10, 2018







The In-memory technique (from 17th Century) to identify Raga notes from Raga Name is discussed as below.


The Indian carnatic music is based on Ragas. Raga is pattern of swaras (notes) combination - Sa Ri Ga Ma Pa Da Ni. - (with micro tonal variations). Melakarta Raga nomenclature is the collection of 72 fundamental musical scales (Ragas). They are also known as Parent (or Janaka) ragas. This system is originally formulated in 17th century by VenkataMakhi, and later refined by Govindacharya.


Ka-ta-pa-ya-di technique is a method of identifying the Raga number from the Mela-Chart based on the first 2 letters of the Raga name , and swaras associated with the raga by its number. The base swaras (Sapta Swaras) are : Sa Ri Ga Ma Pa Da Ni. The ’Sa’ and ‘Pa’ are fixed notes, also known as ‘Achala’ swaras. other notes : Ri Ga Ma Da Ni has variations.

The associated names for each of the notes are as below.

The Melakarta Ragas are also known as Sampoorna ragas, as these ragas contains all the 7 notes in its moorchana (allowed pattern of notes for a raga in its ascending and descending patterns)

Arohanam (Ascending) : Sa Ri Ga Ma Pa Da Ni

Avarohanam (Descending) : Sa Ni Da Pa Ma Ga Ri


1-36 Ragas are the various combinations of S R G D N and M1. (Sudda Madhyama ragas)

37-72 ragas are the various combinations of S R G D N and M2 (Prati Madhyama Ragas)

The 72 Ragas are further grouped into 12 Groups (are called Chakras). Each Chakra group contains 6 ragas. The groups/chakras are named as, Indu, Netra, Agni, Veda, Bana, Rutu, Rishi, Vasu, Brahma, Disi, Rudra, Aditya.


The Raga names and it numbers and hence corresponding swaras (Notes/frequencies) associated can be found as below.


1. Consider the first 2 syllables of the sampoorna Raga

Ex: Dhi-ra Sankarabharanam, The answer is : dh , ra

2. Get the numbers associated from the below table

Dh. - 9 ra - 2



3. Reverse the number

the answer is 29

4. This is < 36, So It is the M1 group of raga ,

5. Subtract 1 from number and divide by 6 and get the remainder

(Since each group has 6 ragas). (29-1)/6. The remainder is 4.

From the list below of the combinations, This raga has Ri2, Ga3, Da2, N3

  1. '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

  2. '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

6. So the final scale of the Raga is

S Ri2 Ga3 M1 P Da2 Ni3



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