Melakarta
Mēḷakarta is a collection of fundamental musical scales (ragas) in Carnatic music (South Indian classical music). Mēḷakarta ragas are parent ragas (hence known as janaka ragas) from which other ragas may be generated. A melakarta raga is sometimes referred as mela, karta or sampurna as well, though the latter term is inaccurate, as a sampurna raga need not be a melakarta (take the raga Bhairavi, for example).
Carnatic music 

Tanjavurstyle Tambura 
Concepts 
Compositions 
Instruments 

In Hindustani music the thaat is equivalent of Melakarta. There are 10 thaats in Hindustani music, though the commonly accepted melakarta scheme has 72 ragas.
Rules for Mēḷakarta
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[1][2]
 They are krama sampurna ragas – that is the sequence is strictly ascending and descending in the scales, without any jumps or zigzag notes[2]
 The upper shadjam is included in the raga scale[2] (ragas like Punnagavarali and Chenchurutti are not mēḷakarta as they end with nishadam)
 The ascending and descending scales must have the same notes[2]
History
The mēḷa system of ragas was first propounded by Raamamaatya in his work Svaramelakalanidhi c. 1550. He is considered the father of mela system of ragas. Later, Venkatamakhin, a gifted musicologist in the 17th century, expounded a new mela system known today as mēḷakarta in his work Chaturdandi Prakaasikaa.[3] He made some bold and controversial claims and defined somewhat arbitrarily 6 svaras from the known 12 semitones, at that time, to arrive at 72 mēḷakarta ragas. The controversial parts relate to double counting of R2 (and similar svaras) and his exclusive selection of madyamas for which there is no specific reasoning (also known as asampurna melas as opposed to sampurna ragas). However, today the 72 mēḷakarta ragas use a standardized pattern, unlike Venkatamakhi's pattern, and have gained a significant following. Govindhacharya is credited with the standardization of rules and known for giving different names for standard ragas that have a different structure but the same swaras as those proposed by Venkatamakhi.[3] The scales in this page are those proposed by Govindaacharya.
Determining the Mēḷakarta
A hundred years after Venkatamakhin's time the Katapayadi sankhya rule came to be applied to the nomenclature of the mēḷakarta ragas. The sankhya associates Sanskrit consonants with digits. The digits corresponding to the first two syllables of the name of a raga, when reversed, give the index of the raga. Thus the scale of a mēḷakarta raga can be easily derived from its name.
For example, Harikambhoji raga starts with syllables Ha and ri, which have numbers 8 and 2 associated with them. Reversing them we get 28. Hence Harikambhoji is the 28th Mēḷakarta rāga. See Katapayadi sankhya for more details and examples.
Mēḷakarta scale
Each mēḷakarta raga has a different scale. This scheme envisages the lower Sa (Keezh Shadja), upper Sa (Mael Shadja) and Pa (Panchama) as fixed swaras, with the Ma (Madhyama) having two variants and the remaining swaras Ri (Rishabha), Ga (Gandhaara), Dha (Dhaivata) and Ni (Nishaada) as having three variants each. This leads to 72 sevennote combinations (scales) referred to as the Mēḷakarta ragas as follows.
There are twelve semitones of the octave S, R1, R2=G1, R3=G2, G3, M1, M2, P, D1, D2=N1, D3=N2, N3 (see swaras in Carnatic music for explanation of these notations). A melakarta raga must necessarily have S and P, one of the M's, one each of the R's and G's, and one each of the D's and N's. Also, R must necessarily precede G and D must precede N (krama sampūrṇa rāga). This gives 2 × 6 × 6 = 72 ragas. Finding mēḷakarta ragas is a mathematical process. By following a simple set of rules we can find the corresponding raga and the scale associated with it.
A raga which has a subset of svarās from a Mēḷakarta raga is said to be a janya (means born or derived from) of that Mēḷakarta raga. Every raga is the janya of a mēḷakarta raga. Janya ragas whose notes are found in more than one mēḷakarta raga are assigned (or associated) parent Melakarta based on subjective notions of similarity. This is obvious for ragas that have less than seven notes. For such ragas it can be associated with a Mēḷakarta which has any of the different swaras in that position. For example, Hindolam has Rishabha and Panchama missing. Hence, it could be considered a janya of Todi (also known as Hanumatodi) which has shuddha rishabha or with Natabhairavi which has a chathushruti rishabha. It is popularly associated with Natabhairavi.
Chakras
The 72 Mēḷakarta ragas are split into 12 groups called chakrās, each containing 6 ragas. The ragas within the chakra differ only in the dhaivatam and nishadam notes (D and N), as illustrated below. The name of each of the 12 chakras suggest their ordinal number as well.[1][4]
 Indu stands for the moon, of which we have only one – hence it is the first chakra.
 Nētra means eyes, of which we have two – hence it is the second.
 Agni is the third chakra it indicates three kinds of Agni.(Dakshina, Ahavaniyam and gArhapatyam)So agni indicates 3rd Chakra.
 Vēda denoting four Vedas is the name of the fourth chakra.
 Bāṇa comes fifth as it stands for the five Arrows of Manmatha.
 Rutu is the sixth chakra standing for the 6 seasons of Hindu calendar, which are Vasanta, Greeshma, Varsha, Sharat, Hemanta and Shishira.
 Rishi, meaning sage, is the seventh chakra representing the seven sages.
 Vasu stands for the eight vasus of Hinduism.
 Brahma comes next of which there are 9.
 Disi Chakra indicates Ten directions(East, West, North, South, North East, North West, South East, South West, Above and Below). Hence it is 10th Chakra.
 Eleventh chakra is Rudra of which there are eleven.
 Twelfth comes Aditya of which there are twelve.
These 12 chakras were also established by Venkatamakhi.
Table of Melakarta ragas
The 72 Mēḷakarta ragas can be divided into two parts. viz.,. suddha Madhyama and prati Madhyama ragas. When a given suddha madhyama raga's M1 is replaced by M2, we get the corresponding prati madhyama raga. See Katapayadi sankhya for more information on how to derive the various swaras of a raga from its melakarta number.
See swaras in Carnatic music for explanation of the notations like R1, G2, N2, etc.
'Mēḷakartā Rāgas'  

'Shuddha Madhyama'  'Prati Madhyama'  
No.  Raga  Scale  No.  Raga  Scale 
1.Indu Chakra  7. Rishi Chakra  
1  Kanakangi  S R₁ G₁ M₁ P D₁ N₁ Ṡ  37  Salagam  S R₁ G₁ M₂ P D₁ N₁ Ṡ 
2  Ratnangi  S R₁ G₁ M₁ P D₁ N₂ Ṡ  38  Jalarnavam  S R₁ G₁ M₂ P D₁ N₂ Ṡ 
3  Ganamurti  S R₁ G₁ M₁ P D₁ N₃ Ṡ  39  Jhalavarali  S R₁ G₁ M₂ P D₁ N₃ Ṡ 
4  Vanaspati  S R₁ G₁ M₁ P D₂ N₂ Ṡ  40  Navaneetam  S R₁ G₁ M₂ P D₂ N₂ Ṡ 
5  Manavati  S R₁ G₁ M₁ P D₂ N₃ Ṡ  41  Pavani  S R₁ G₁ M₂ P D₂ N₃ Ṡ 
6  Tanarupi  S R₁ G₁ M₁ P D₃ N₃ Ṡ  42  Raghupriya  S R₁ G₁ M₂ P D₃ N₃ Ṡ 
2. Netra Chakra  8. Vasu Chakra  
7  Senavati  S R₁ G₂ M₁ P D₁ N₁ Ṡ  43  Gavambhodi  S R₁ G₂ M₂ P D₁ N₁ Ṡ 
8  Hanumatodi  S R₁ G₂ M₁ P D₁ N₂ Ṡ  44  Bhavapriya  S R₁ G₂ M₂ P D₁ N₂ Ṡ 
9  Dhenuka  S R₁ G₂ M₁ P D₁ N₃ Ṡ  45  Shubhapantuvarali  S R₁ G₂ M₂ P D₁ N₃ Ṡ 
10  Natakapriya  S R₁ G₂ M₁ P D₂ N₂ Ṡ  46  Shadvidamargini  S R₁ G₂ M₂ P D₂ N₂ Ṡ 
11  Kokilapriya  S R₁ G₂ M₁ P D₂ N₃ Ṡ  47  Suvarnangi  S R₁ G₂ M₂ P D₂ N₃ Ṡ 
12  Rupavati  S R₁ G₂ M₁ P D₃ N₃ Ṡ  48  Divyamani  S R₁ G₂ M₂ P D₃ N₃ Ṡ 
3. Agni Chakra  9. Brahma Chakra  
13  Gayakapriya  S R₁ G₃ M₁ P D₁ N₁ Ṡ  49  Dhavalambari  S R₁ G₃ M₂ P D₁ N₁ Ṡ 
14  Vakulabharanam  S R₁ G₃ M₁ P D₁ N₂ Ṡ  50  Namanarayani  S R₁ G₃ M₂ P D₁ N₂ Ṡ 
15  Mayamalavagowla  S R₁ G₃ M₁ P D₁ N₃ Ṡ  51  Kamavardani  S R₁ G₃ M₂ P D₁ N₃ Ṡ 
16  Chakravakam  S R₁ G₃ M₁ P D₂ N₂ Ṡ  52  Ramapriya  S R₁ G₃ M₂ P D₂ N₂ Ṡ 
17  Suryakantam  S R₁ G₃ M₁ P D₂ N₃ Ṡ  53  Gamanashrama  S R₁ G₃ M₂ P D₂ N₃ Ṡ 
18  Hatakambari  S R₁ G₃ M₁ P D₃ N₃ Ṡ  54  Vishwambari  S R₁ G₃ M₂ P D₃ N₃ Ṡ 
4. Veda Chakra  10. Disi Chakra  
19  Jhankaradhwani  S R₂ G₂ M₁ P D₁ N₁ Ṡ  55  Shamalangi  S R₂ G₂ M₂ P D₁ N₁ Ṡ 
20  Natabhairavi  S R₂ G₂ M₁ P D₁ N₂ Ṡ  56  Shanmukhapriya  S R₂ G₂ M₂ P D₁ N₂ Ṡ 
21  Keeravani  S R₂ G₂ M₁ P D₁ N₃ Ṡ  57  Simhendramadhyamam  S R₂ G₂ M₂ P D₁ N₃ Ṡ 
22  Kharaharapriya  S R₂ G₂ M₁ P D₂ N₂ Ṡ  58  Hemavati  S R₂ G₂ M₂ P D₂ N₂ Ṡ 
23  Gourimanohari  S R₂ G₂ M₁ P D₂ N₃ Ṡ  59  Dharmavati  S R₂ G₂ M₂ P D₂ N₃ Ṡ 
24  Varunapriya  S R₂ G₂ M₁ P D₃ N₃ Ṡ  60  Neetimati  S R₂ G₂ M₂ P D₃ N₃ Ṡ 
5. Bana Chakra  11. Rudra Chakra  
25  Mararanjani  S R₂ G₃ M₁ P D₁ N₁ Ṡ  61  Kantamani  S R₂ G₃ M₂ P D₁ N₁ Ṡ 
26  Charukesi  S R₂ G₃ M₁ P D₁ N₂ Ṡ  62  Rishabhapriya  S R₂ G₃ M₂ P D₁ N₂ Ṡ 
27  Sarasangi  S R₂ G₃ M₁ P D₁ N₃ Ṡ  63  Latangi  S R₂ G₃ M₂ P D₁ N₃ Ṡ 
28  Harikambhoji  S R₂ G₃ M₁ P D₂ N₂ Ṡ  64  Vachaspati  S R₂ G₃ M₂ P D₂ N₂ Ṡ 
29  Dheerasankarabaranam  S R₂ G₃ M₁ P D₂ N₃ Ṡ  65  Mechakalyani  S R₂ G₃ M₂ P D₂ N₃ Ṡ 
30  Naganandini  S R₂ G₃ M₁ P D₃ N₃ Ṡ  66  Chitrambari  S R₂ G₃ M₂ P D₃ N₃ Ṡ 
6. Rutu Chakra  12. Aditya Chakra  
31  Yagapriya  S R₃ G₃ M₁ P D₁ N₁ Ṡ  67  Sucharitra  S R₃ G₃ M₂ P D₁ N₁ Ṡ 
32  Ragavardhini  S R₃ G₃ M₁ P D₁ N₂ Ṡ  68  Jyoti swarupini  S R₃ G₃ M₂ P D₁ N₂ Ṡ 
33  Gangeyabhushani  S R₃ G₃ M₁ P D₁ N₃ Ṡ  69  Dhatuvardani  S R₃ G₃ M₂ P D₁ N₃ Ṡ 
34  Vagadheeswari  S R₃ G₃ M₁ P D₂ N₂ Ṡ  70  Nasikabhushani  S R₃ G₃ M₂ P D₂ N₂ Ṡ 
35  Shulini  S R₃ G₃ M₁ P D₂ N₃ Ṡ  71  Kosalam  S R₃ G₃ M₂ P D₂ N₃ Ṡ 
36  Chalanata  S R₃ G₃ M₁ P D₃ N₃ Ṡ  72  Rasikapriya  S R₃ G₃ M₂ P D₃ N₃ Ṡ 
Alternate Mēḷakarta scheme
Muthuswami Dikshitar school followed a different set of scales as the 72 Mēḷakarta ragas.[5] These were taught by Venkatamakhin.[3] Many of the scales were asampurna (not sampurna ragas) because Dikshitar chose to follow the earlier established structure to mitigate illeffects of usage of direct vivadi swaras in the scales.[3]
See also
Wikimedia Commons has media related to Carnatic ragams (svg). 
Wikimedia Commons has media related to Melakarta ragams (svg). 
 Janya raga
 List of Janya Ragas
 Illustration of the notes in Melakarta ragas in a Keyboard layout at Wikimedia commons
 Katapayadi system
 List of film songs based on ragas
References
 Ragas in Carnatic music by Dr. S. Bhagyalekshmy, Pub. 1990, CBH Publications
 A practical course in Carnatic music by Prof. P. Sambamurthy, 15th edition published 1998, The Indian Music publishing house
 Shree Muthuswami Dikshitar Keertanaigal, by A Sundaram Iyer, Madras Book Publications, Mylapore, Chennai
 South Indian Music Book III, by Prof. P Sambamoorthy, Published 1973, The Indian Music Publishing House
 Shree Muthuswami Dikshitar Keerthanaigal, Appendix III and IV, by A Sundaram Iyer of Kallidaikurichi, Music Books Publishers, Mylapore, Chennai