Swaras (notes) and Ragas (scales)

Carnatic swaras (16 notes)
Shadja – S
Suddha Rishabha – R1
Chatusruti Rishabha – R2
Shatshruthi Rishaba – R3
Suddha Gandhara – G1
Sadharana Gandhara – G2
Antara Gandhara – G3
Suddha Madhyama – M1
Prati Madhyama – M2
Panchama – P
Suddha Dhaivata – D1
Chatusruti Dhaivata – D2
Shatshruthi Dhaivata – D3
Suddha Nishada – N1
Kaisika Nishada – N2
Kakali Nishada – N3

Aarohana (ascending Scale): Sa, Re, Ga, Ma, Pa, Dha, Ni,Sa.
Avarohana (descending Scale): Sa, Ni, Dha, Pa, Ma, Ga, Re, Sa.

There are 72 parent scales in Carnatic Music.They are called Melakartha Ragas and are systematically classified in a scheme. A Melakartha, also known as Mela or Janaka Raga, is a set of scales from which other ragas may be generated.

Ragas must contain the following characteristics to be considered Melakarta.

• They are sampurna ragas – they contain all seven swaras (notes) of the octave in both ascending and descending scale
• They are krama sampurna ragas – that is the sequence is strictly ascending and descending in the scales, without any jumps or zig-zag notes
• The upper shadjam is included in the raga scale (ragas like Punnagavarali and Chenchurutti are not melakarta as they end with nishadham)
• The ascending and descending scales must have the same notes

We can broadly divide the ragas into Sudhamadhyama ragas and Pratimadhyama ragas based on the madhyamam they use.  

prati madhyamam - the higher ma, M2, used in the second 36 melakartas and their janyas, which corresponds to F# of the Western key of C
shuddha madhyamam - the lower of 2 ma's (M1), used in the first 36 melakartas, which corresponds to F natural in the Western key of C

Now let us determine all possible combinations of Rishabham and Gandharam in a melakartha. There are 6 possible combinations of the 3 Rishabhams and 3 Gandharams.


Let it be noted that the Raga format has to be in ascending order of frequencies. Rishabham has a lower frequency than Gandharam. Multiplying with the earlier division we get 12 unique combinations of S R G M. These are referred to as  Chakras.
Each chakra will accomodate a unique combination of Daivatam and Nishadam. Repeating the same Rishabham – Gandharam experiment with Daivatam and Nishadam, we get 6 unique combinations. Each chakra accomodates 6 unique combinations of S R G M P D N. We have 6 * 12 i.e. 72 Melakartha ragas in all. Refer to the chart given below for a clearer view of this concept.

The 72 Melakarthas charted according to the systematic classification

The above given chart follows the notation sequence given in the table of the 16 swarasthanas. The chakras are named to maintain the sequence of the Rishbham – Gandharam combinations in the following  manner -

• The first chakra is named Indu which means moon owing to the fact that the earth has only one moon.
• The second chakra is called Netra owing to the fact that we have two eyes.
• The third chakra is named agni due the existence of 3 agnis according to our scriptures (namely fire, lightning and sunlight ).
• The fourth chakra is called Veda as the Vedas are four.
• The fifth chakra is called Baana owing to the 5 arrows used by Kamadeva.
• The sixth chakra is called Rutu as there are six seasons in nature.
• The seventh chakra is called Rishi after the Saptarshis.
• The eight chakra is known as Vasu after the eight sons of Ganga.
• The ninth chakra is known as Brahma due to the existence of nine brahmas
• The tenth chakra is called Disi due to the 10 directions.
• The eleventh chakra is called Rudra after the 11 Rudras.
• The twelfth chakra is called Aditya after the 12 Adityas.

The names of the chakras are ordained using the numerical significance of those terms.

Translation: na (न), nya (ञ) and a (अ)-s i.e. vowels represent zero. The (nine) integers are represented by consonant group beginning with ka, ṭa, pa, ya. In a conjunct consonant, the last of the consonants alone will count. A consonant without vowel is to be ignored.
Explanation
The assignment of letters to the numerals are as per the following arrangement.

1	2	3	4	5	6	7	8	9	0
ka क ക	kha ख ഖ	ga ग ഗ	gha घ ഘ	nga ङ ങ	ca च ച	cha छ ഛ	ja ज ജ	jha झ ഝ	nya ञ ഞ
ṭa ट ട	ṭha ठ ഠ	ḍa ड ഡ	ḍha ढ ഢ	ṇa ण ണ	ta त ത	tha थ	da द ദ	dha ध ധ	na न ന
pa प പ	pha फ ഫ	ba ब ബ	bha भ ഭ	ma म മ	-	-	-	-	-
ya य യ	ra र ര	la ल ല	va व വ	śha श ശ	sha ष ഷ	sa स സ	ha ह ഹ	-	-

• Consonants have numerals assigned as per the above table. For example, ba (ब) is always three 3 whereas 5 can be represented by either nga (ङ) or ṇa (ण) or ma (म) or śha (श).
• All stand-alone vowels like a (अ) and ṛ (ऋ) are assigned to zero 0.
• In case of a conjuct, consonants attached to a non-vowel will not be valueless. For example, kya (क्या) is formed by k (क्) + ya (य) + a (अ). The only consonant standing with a vowel is ya (य). So the corresponding numeral for kya (क्या) will be 1.
• There is no way of representing Decimal separator in the system.
• Indians used the Hindu-Arabic numeral system for numbering, traditionally written in increasing place values from left to right. This is as per the rule aṅkānām vāmato gati (अङ्कानाम् वामतो गति) which means numbers go from left to right.

Carnatic music

Melakarta chart as per Kaṭapayādi

system

• 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.

1. Melakartas 1 through 36 have Ma1 and those from 37 through 72 have Ma2.
2. 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.
3. '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
4. '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.

Examples

• Raga Dheerasankarabharanam

The katapayadi scheme associates dha9 and ra2, hence the raga's melakarta number is 29 (92 reversed). Now 29 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

From the coding scheme Ma 5, Cha 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

You can see that, as per the above calculation we should get Sa 7, Ha 8 giving the number 87 instead of 57 for Simhendramadhyamam. This should be ideally Sa 7, Ma 5 giving the number 57. So it is believed that the name should be written as Sihmendramadhymam (As in the case of Brahmana in Sanskrit).

Recommended websites for further reading & listening:
• http://www.hinduwisdom.info/Hindu_Music.htm
• http://www.karnatik.com
• http://www.carnatica.net
• http://www.carnatica.net/composer-main.htm
• http://www.ecse.rpi.edu/Homepages/shivkuma/music/
• http://www.carnaticcorner.com/about.html
• http://www.sangeethapriya.org/
• http://www.itcsra.org