Carnatic Music is Carnataka Sangeetham
Melakarta is the collection of Ragas in Carnatic music. Melakarta ragas are fundamental ragas from which other ragas may be generated. For this reason the melakarta ragas are also known as janaka(parent) ragas. Melakarta ragas are also known as sampoorna ragas as they contain all seven swaras (notes) of the octave in both the ascending and the descending mode. There are 72 melakarta ragas.
Indian Music
Indian classical music
Carnatic music
Composers
List of Carnatic composers
Singers
List of Carnatic singers
Hidustani music
Modern music
Filmi music
Folk music (Indian)
Concepts
Śruti
Raga
Melakarta
Katapayadi sankhya
Swara
Tala
Mudra
Contents
History
The mela 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 Venkatamakhi expounded in the 17th century in his work Caturdandi Prakaasikaa a new mela system known today as melakarta. He had made some bold and controversial claims and defined somewhat artificially 16 swaras from the known 12 semitones at that time to arrive 72 melakarta ragas. The controversial parts relate to his double counting of R2 etc. and his exclusive selection of madyamas for which there is no basis. However, today the 72 melakarta ragas have gained significant following, though to this day this system is being criticized. Venkatamakhi was known to be extremely critical of Raamamaatya.
Determining the Melakartha
A hundred years later than Venkatamakhi's time the Katapayadi sankhya rule came to be applied to the nomenclature of the melakarta ragas. The sankhya associates Sanskrit consonants with digits. The digits corresponding to the first two letters (syllables) of the name of a raga, when reversed, give the index of the raga. Thus the scale of a melakarta raga can be easily derived from its name.
Melakartha scale
Each melakarta raga has a different scale. The scales are constructed as follows: out of the twelve semitones of the octave S, R1, R2=G1, R3=G2, G3, M1, M2, P, D1, D2=N1, D3=N2, N3, a melakarta raga must necessarily have S and P, one of the M's, two of the R's and G's, and two of the D's and N's. Also, R must necessarily precede G and D must precede N. This gives 2 � 6 � 6 = 72 melakarta ragas. Finding melakartha ragas is a mathematical problem and following a simple set of rules, we can find the corresponding raga and the scale associated with it.
This scheme envisages the lower Sa (Keezh Shadjamam), upper Sa (Mael Shadjamam) and Pa (Panchamam) as fixed swaras, with the Ma (Madhyamam) having two variants and the remaining swaras Ri (Rishabam), Ga (Gandhaaram), Dha (Dhaivatham) and Ni (Nishaadham) as having three variants each. This leads to 72 seven-note combinations referred to as the Melakartha ragas.
A raga which has the same scale as a Melakartha raga (or a subset thereof) is said to be a janya of it (janya means born or derived from). Every raga is the janya of a melakarta raga. Ragas whose notes are found in more than one melakarta raga are assigned janyas based on subjective notions of similarity.
Table of Melakarta ragas
It can be said that the entire set of 72 melakarta ragas can be divided into two parts. viz.,. suddha Madhyamam and prati Madhyamam ragas. When a given suddha madhyamam raga's M1 is replaced by M2, we get the corresponding Prati Madhyamam raga. See Katapayadi sankhya for more information on how to derive the various swaras of a raga from its Melakarta number.
Mēḷakartā Rāgas
Suddha Madhyamam
Prati Madhyamam
1.Indu Chakra
6. Ritu Chakra
7. Rishi Chakra
12. Aditya Chakra
No. Raga Scale
1 Kanakangi S R1 G1 M1 P D1 N1
2 Ratnangi S R1 G1 M1 P D1 N2
3 Ganamoorti S R1 G1 M1 P D1 N3
4 Vanaspati S R1 G1 M1 P D2 N2
5 Manavati S R1 G1 M1 P D2 N3
37 Salagam S R1 G1 M2 P D1 N1
38 Jalarnavam S R1 G1 M2 P D1 N2
39 Jhalavarali S R1 G1 M2 P D1 N3
40 Navaneetam S R1 G1 M2 P D2 N2
41 Pavani S R1 G1 M2 P D2 N3
6
Tanarupi
S R1 G1 M1 P D3 N3
42
Raghupriya
S R1 G1 M2 P D3 N3
2. Netra Chakra
8. Vasu Chakra
7
Senavati
S R1 G2 M1 P D1 N1
43
Gavambodhi
S R1 G2 M2 P D1 N1
8
Hanumatodi
S R1 G2 M1 P D1 N2
44
Bhavapriya
S R1 G2 M2 P D1 N2
9
Dhenuka
S R1 G2 M1 P D1 N3
45
Subhapantuvarali
S R1 G2 M2 P D1 N3
10
Natakapriya
S R1 G2 M1 P D2 N2
46
Shadvidhamargini
S R1 G2 M2 P D2 N2
11
Kokilapriya
S R1 G2 M1
D2 N3
47
Suvarnangi
S R1 G2 M2 P D2 N3
12
Roopavati
S R1 G2 M1 P D3 N3
48
Divyamani
S R1 G2 M2 P D3 N3
3. Agni Chakra
9. Brahma Chakra
13
Gayakapriya
S R1 G3 M1 P D1 N1
49
Dhavalambari
S R1 G3 M2 P D1 N1
14
Vakulabharanam
S R1 G3 M1 P D1 N2
50
Namanarayani
S R1 G3 M2 P D1 N2
15
Mayamalavagoula
S R1 G3 M1 P D1 N3
51
Kamavardhini
S R1 G3 M2 P D1 N3
16
Chakravakam
S R1 G3 M1 P D2 N2
52
Ramapriya
S R1 G3 M2 P D2 N2
17
Sooryakantam
S R1 G3 M1 P D2 N3
53
Gamanasrama
S R1 G3 M2 P D2 N3
18
Hatakambari
S R1 G3 M1 P D3 N3
54
Viswambhari
S R1 G3 M2 P D3 N3
4. Veda Chakra
10. Disi Chakra
19
Jhankaradhwani
S R2 G2 M1 P D1 N1
55
Syamalangi
S R2 G2 M2 P D1 N1
20
Natabhairavi
S R2 G2 M1 P D1 N2
56
Shanmukhapriya
S R2 G2 M2 P D1 N2
21
Keeravani
S R2 G2 M1 P D1 N3
57
Simhendramadhyamam
S R2 G2 M2 P D1 N3
22
Kharaharapriya
S R2 G2 M1 P D2 N2
58
Hemavati
S R2 G2 M2 P D2 N2
23
Gourimanohari
S R2 G2 M1 P D2 N3
59
Dharmavati
S R2 G2 M2 P D2 N3
24
Varunapriya
S R2 G2 M1 P D3 N3
60
Neetimati
S R2 G2 M2 P D3 N3
5. Bana Chakra
11. Rudra Chakra
25
Mararanjani
S R2 G3 M1 P D1 N1
61
Kantamani
S R2 G3 M2 P D1 N1
26
Charukesi
S R2 G3 M1 P D1 N2
62
Rishabhapriya
S R2 G3 M2 P D1 N2
27
Sarasangi
S R2 G3 M1 P D1 N3
63
Latangi
S R2 G3 M2 P D1 N3
28
Harikambhoji
S R2 G3 M1 P D2 N2
64
Vachaspati
S R2 G3 M2 P D2 N2
29
Dheerasankarabharanam
S R2 G3 M1 P D2 N3
65
Mechakalyani
S R2 G3 M2 P D2 N3
30
Naganandini
S R2 G3 M1 P D3 N3
66 Chitrambhari S R2 G3 M2 P D3 N3
31 Yagapriya S R3 G3 M1 P D1 N1
67 Sucharitra S R3 G3 M2 P D1 N1
32 Ragavardhini S R3 G3 M1 P D1 N2
68 Jyotiswarupini S R3 G3 M2 P D1 N2
33 Gangeyabhusani S R3 G3 M1 P D1 N3
69 Dhatuvardhini S R3 G3 M2 P D1 N3
34 Vagadheeswari S R3 G3 M1 P D2 N2
70 Nasikabhusani S R3 G3 M2 P D2 N2
35 Sulini S R3 G3 M1 P D2 N3
71 Kosalam S R3 G3 M2 P D2 N3
36 Chalanata S R3 G3 M1 P D3 N3
72 Rasikapriya S R3 G3 M2 P D3 N3
=====
Indian Classical Music
Music is an integral part of Indian culture. It is the one art which is evident in all the strata of society. Indian music is one of the living systems of music in the world.
Indian music is a typical example of Modal music (music based on modes). The individuality of a mode is extablished by notes of defined frequencies in its structure. It is not the inter-relationship of each note to the basic tonic note. This tonic note may be actually heard through a rone or even in its absence, a trained ear is able to recognise the raga, bearing in mind the presumed tonic note. Memory thus plays an important part in Indian music.
India has developed forms of culture, lifeways and music that are distictive of its own.Yet because of its size and its variety of terrain, there are also great regional differences. The largest such division is between the Hindi related language groups of the North and Dravidian-speaking people of the south; the northern Hindustani style and the southern Karnataka (Carnatic) tradition.
History of Carnatic Music
Carnatic Music has its roots in the distance past. The earliest extend theoritical work is the Natya Sastra by Bharatha, a treatise on theater, dance and music dating between the second century B.C to the fifth century A.D. Through centuries many more important scholarly books on music have been written, perhaps the most noteworthy of which was the medieval Sangeetha Ratnakara by Sarangadeva.
Purandaradasa (1484-1564), sometimes called the Father of Carnatic Music, composed not only many songs but the standard lessons and exercices that are still memorized by every music student today. A golden age occurred between about 1750 and 1850 when the forms and performaces style that have continued to the present day were set. Thousands of new krithis (compositions) were composed, new ragas were invented, and the conceptual form of older ragas expanded.The Sangitha trimurthis (big three) , Sama Sastry (1762-1827), Tyagaraja (1767-1847) and Muthuswamy Dikshitar (1777-1847) dominated this period.
The Sangitha Trimurthys: Sama Sastry, Tyagaraja and Muthusamy Dikshitar
A south Indian proverb compares the compositions of thrimurthys. Dikshitar is said to have written music that is like a coconut: the hard shell of his brilliantly intellectual musical structures and complex, scholarly and sometimes esoteric texts must be broken to taste the sweat nut and milk inside. By contrast, Sama Sastri's music is said to be like a banana: the fruit is not so difficult to get in, but one must still peel off the bitter skin - Sastri's complicated talas rhythms and talas of five and seven beats before enjoying its flavour. But Tyagaraja's music is said to be like fresh, ripe grapes; both poetry and melody are immediately accessible to enjoy it one needs to merely bite into it. Even the skin is soft and sweat.
Swara
Indian music has seven notes or swaras as with all systems of music. Swara is defined as "that which is able to please of its own accord". These seven swaras are called Shadjamam, Rishabham, Gandharam, Madhyamam, Panchamam, Dhivatham and Nishadham. These are often represented as Sa, Re, Ga, Ma, Pa, Da and Ne, by their first syllable.
Swara and Swara Stanam
Of these seven swaras, Sa and Pa donot admit variations and are called achala (fixed) or avikratha (changeless) swaras. The other five (Re, Ga, Ma, Da and Ne) admint of two varieties each. The terms Komal and Tivra are used to distinguish these two, with komala swaram lower in note than the tivra swaram. Thus we have
Sudha (Komal) and Chathusruthi (Tivra) Rishabam,Sadharana (komal) and Antara (tivra) gandharam, Sudha (Komal) and Prati (Tivra) Madhyamam, Sudha (Komal) and Chatussruthi (Tivra) dhivatham and Kaisiki (komal) and Kakali (Tivra) Nishadham.
With this, there are 12 distictive swaras corresponding to notes in Carnatic Music.
In addition, four of the swaras, Ri, Ga, Da and Ne extend to another variety overlaping with the next swarastanam. This give rise to four more swaras totalling 16. Note however that the note (swara stana) is shared between two swaras.
Swaram
Notation
Western
Stanam
Sadjamam
Sa
C
1
Suddha Rishabam (Komal)
Re1
C #
2
Chathusruthi Rishabam (Tivra)
Re2
D
3
Shatsruthi Rishabam
Re3
D #/ E b
4
Suddha Gandharam
Ga1
D
3
Sadharana Gandharam
Ga2
D # /E b
4
Anthara Gandharam
Ga3
E
5
Suddha Madhyamam
Ma1
F
6
Prati Madhyamam
Ma2
F #/G b
7
Panchamam
Pa
G
8
Suddha Dhaivatham
Da1
G #/A b
9
Chathusruthi Dhaivatham
Da2
A
10
Shatsruthi Dhaivatham
Da3
A #/ B b
11
Suddha Nishadam
Ne1
A
10
Kaisiki Nishadam
Ne2
A #/B b
11
Kakali Nishadam
Ne3
B
12
The sudha swaras, also known as Prakrithi swaras, have the prefix Sudha. This is usually the lowest pitched note for that swara. The vikratha swaras have prefixes like chatussruthi, shatshuruthi, sadharana, antara, etc. In Hindustani music, sudha swara usually refer to Sankarabharana scale (Bilval).
Raga
Raga is the Pivotal concept of Carnatic music. This concept is India's proud contribution to world music. The ideal of absolute music is reached in the concept of Raga. Raga is much more than a scale. It is defied as that which colors the mind in ancient text. (Raga (Sanskrith): coloriing, dyeing, tingering). A raga is in some ways a kind of mystical expression with a musical personality of its own. The whole structure of Indian music is built around the concept of raga. Indian melodies of the classical type are based on ragas. As for folk melodies a good number of them will be found to be in some recognisable raga. Some folk meledies are in mixed ragas. The same goes with popular film music tunes.
Raga can be loosely defined as melody type or expressive mode. It consists of series of upto seven notes, which bear a definite relationship to adhara shadja and which occur in a particular sequence. They derive their personality through notes of defined pitch entering into their formation. It is the arrangement of particular swaras, in conformity to recognised aesthetic laws that establish the rupa (form) of raga.
Raga alapana is the presentation of pharases admissible in the raga in such a manner as to bring out its distictive characteristics. The arohana and avarohana constitute the briefest description of a raga. It gives the concsise form of the outline or framework of the raga.
Raga classification
Melam and Janyam Ragas are classifed into Janaka ragas and Janya ragas. Janaka ragas, also known as Melakartha or Sampurna raga has all seven notes (saptha swara) in their arohana and avarohana. There are 72 such janaka ragas arranged in a definete, serial order. A Janya raga is said to be derived from a janaka raga. It takes the same swaras as in its melakartha raga, but may take fewer swaras.
Example: Kanakangi (1st Melakartha) and its Janyams
Ragam
Melam
No
Aarohanam
Avarohanam
Kanakangi
Kanakaangi
1
Sa Re1 Ga1 Ma1 Pa Da1 Ne1 Sa
Sa Ne1 Da1 Pa Ma1 Ga1 Re1 Sa
Kadagapriya
Kanakaangi
1
sa ga re ga ma pa da pa ne sa
sa da pa da ma ga re sa
Kanakambari
Kanakaangi
1
sa ga re ga ma pa da ne da sa
sa ne da pa ma ga re sa
Mukthambari
Kanakaangi
1
sa re ga ma pa ne sa
sa ne da ma ga re sa
Peragasindhamani
Kanakaangi
1
sa re pa ma pa da ne sa
sa da pa ma ga re sa
Vaageswari
Kanakaangi
1
sa re ga ma pa da sa
sa da pa ma ga re sa
Sudha Madhyama and Prathhi Madhyama Raga: There are seventy two such melakartha ragas each with its own set ot janya ragas. As mentioned before ragas can take variations only in Re (Re1, Re2, Re3), Ga (Ga1, Ga2, Ga3), Ma (Ma1, Ma2), Dha (Dha1, Dha2, Dha3) and Ne (Ne1, Ne2, Ne3). The first 36 of 72 melams use Sudha Madhyamam (Ma1) and are called Sudha Madhyama ragas. The later 36 use Prathi Madhyaman (Ma2) and are called Parathi Madhyama ragas. So within each category they can differ only in Re, Ga, Dha and Ne. These are systematically divided into six chakras, with six melams per chakra.
Click here
for mela chakra details
Sudha Madhyama Ragas
Indu
Netra
Agni
Vedha
Baana
Ruthu
Kanakaangi
Seanavathi
Gaayaga Priya
Jangharadhwani
Maara Rajnani
Yaagha Priya
Ratnaangi
Hanumat Thodi
Vagulaa Baranam
Nata Bhiravi
Chaarukesi
Raaga Vardhani
Ganamurthi
Dheanuka
Maaya Malava Gaula
Keeravani
Sarasaangi
Kaangheya Bhushani
Vanaspathi
Naataka Priya
Chakra Vaagham
Karagara Priya
Hari Kaamboji
Vaagha Dheeswari
Maalavathi
Kokila Priya
Suurya Kantham
Gauri Manogari
Dheera Shankara Bharanam
Seelini
Dhaana Roopini
Roopavathi
Haatakambhari
Varuna Priya
Naaga Nandhini
Chala Naata
Prathi Madhyama Ragas
Rishi
Vasu
Brahma
Dishi
Rudra
Aditya
Jaalakam
Kavaambhodi
Thavalaambari
Syamalaanghi
Kandhaamani
Su Charithra
Jaalarnavam
Bhava Priya
Naama Naarayani
Shanmughapriya
Rishabha Priya
Swodhis Ruupini
Jaala Varaali
Subha Bhandhu Varali
Kaama Vardhani
Simmhendhra Madhyamam
Lathaangi
Thadhu Vardhani
Navaneetham
Shatvidha Maarghani
Raama Priya
Heamavathi
Vaachaspathi
Naasigha Bhushani
Bhaavani
Swarnaanghi
Gamana Priya
Dharmavathi
Measha Kalyani
Koochalam
Raghupriya
Dhivyamani
Viswambhari
Neethimathi
Chitraambhari
Raghasya Priya
Click here
for Katapayadhi Sankkya details.
Katapayadhi Sankya: The name and number of Melakartha raga is systematically defined by Katapayadhi Sankya method. The letters Ka, Ta, Pa, Ya, etc are assiged numeric numbers. From the first two characters of each melam, and mapping it to the number corresponding to the character, the mela raga's number is identified. For example, the raga "Dheera Shankarabaranam" has Dhe and Ra as its first characters, tha map to 9 and 2. By juxtaposing the 2nd character's number with the 1st one we get 29, which is the mela kartha number of the raga. Ragas like Chakravagham are represented with Cha and Ka (6 and 1, thereby 16) instead of 'k'.
Vajra Raga: Janya ragas is called Vajra raga if upto three swaras are deleted in the arohaana, avarohana or both., Vajra ragas are furher classified into shadava (only six swaras present in aarohanam / avarohanam of raga; or one vajra) and audava (only five swaras present; two being vajra). As mentioned before, a raga with all seven notes is called sampurna raga. Note that a raga with only four notes in aarohana or avarohana is not considered since atleast five swaras are required to give an individuality to the raga. Also janayas can have different number of swaras in arohanam and avarohanam giving rise to eight types of varja ragas.
Eight kinds of Varja ragas with example
Ragam
Melam
No
Aarohanam
Avarohanam
Varja Type
Kamboji
Hari Kamboji
28
sa re ga ma pa da sa
sa ne da pa ma ga re sa
Shadava (6)- Sampurja (7)
Bilahari
Dheera Shankarabharanam
29
Sa re ga pa da sa
Sa ne da pa ma ga re sa
Audava (5) - Sampurna (7)
Bhairavam
Suryakantham
17
Sa re ga ma pa da ne sa
Sa da pa ma ga re sa
Sampurna (7) - shadava (6)
Saramathi
Natabhiravi
20
Sa re ga ma pa da ne sa
Sa ne da ma ga sa
Sampurna (7) - Audava (5)
Sriranjani
Karagapriya
22
Sa re ga ma da ne sa
Sa ne da ma ga re sa
Shadava (6) - Shadava (6)
Natakurunji
Hari Kamboji
28
Sa re ga ma da ne sa
Sa ne da ma ga sa
Shadava (6) - Audava (5)
Malahari
Mayamalavagaula
15
Sa re ma pa da sa
Sa da pa ma ga re sa
Audava (5) - Shadava (6)
Mohanam
Hari Kamboji
29
Sa re ga pa da sa
Sa da pa ga re sa
Audava (5)- Audava (5)
Upanga and Bashanga Raga: Another type of raga classification classifies them as Upanga raga if janya takes only the swaras of the melakartha (as they usually do), Bashanga raga if they take a foreign swara in either arohanam, avarohanam or both (from somether melakartha) and vakra raga if arohana or avarohana or both take zig-zag course or twist. Vakra ragas are further classifed into Sampurna vakra if arohana and avarohana are sampurna (with all seven notes present) or Vakra varja if they have less than seven notes. Vakra ragas also are classified into Ekaswara vakra, Dviswara vakra, Triswara vakra or Chatusswara vakra based on number of vakra swaras in the raga (one, two, three and four respectively). Four is the maximum number of vakra swara that a raga can accomadate. In Bashanga raga, the foreign note is known as annya swara. The number of Bhashanga ragas used in Carnatic music is 26.
Examples of Bhasanga and Vakra Janya ragas
Ragam
Melam
No
Aarohanam
Avarohanam
Type
Kathana kuthuhalam
Deera Sankarabharanam
29
Sa re ma da ne ga pa sa
Sa ne da pa ma ga re sa
Sampurna vakra
Karnataka Byag
Hari Kamboji
28
Sa re ga ma pa da ne sa
Sa ne da ne pa da ma ga re ga sa
Sahana
Hari Kamboji
28
Sa ra ga ma pa ma da ne sa
Sa ne da pa ma ga ma re ga re sa
Nalinakanthi
Sarasangi
27
Sa ga re ma pa ne sa
Sa ne pa ma ga re sa
Vakra varja
Devamanohari
Karagarapriya
22
Sa re ma pa da ne sa
Sa ne da ne pa ma re sa
Bangala
29
Sa re ga ma pa ma re pa sa
Sa ne pa ma re ga re sa
Nilambari
Deera Sankarabharanam
29
Sa re ga ma pa da pa ne sa
Sa ne pa ma ga re ga sa
Ekasvara
Suposhini
Sa re sa ma pa ne da sa
Sa da ne pa ma re ma sa
Dviswara
Bhairavi
Natabhiravi
20
Sa ga re ga ma pa da ne sa
Sa ne da pa ma ga re sa
Chathusruthi dhivatham (annya swaram) in aarohanam, Sudha dhivatham in avarohanam
Bhasanga
=====
The katapayadi sankhya is a way of determining the number of a melakarta ragam from the first two syllables of the name of the raga.
A detailed discussion of the Katapayadi coding scheme and its possible relation to the modern hashing technique was published in the IEEE Annals in a 1997 article, subsequently reprinted elsewhere. This article, which can be found at:
http://citeseer.ist.psu.edu/532626.html
also describes several anecdotal applications of the technique in history, among which is a mnemonic to remember the digits of pi to 17 places.
Contents
1 How to use it
1.1 Katapayadi sankhya
1.2 कटपयादि संख्या
1.2.1 An Algorithm to derive the Swarasthanas
How to use it
Following is the Katapayadi sankhya in the Roman alphabet and in Devanagari.
Katapayadi sankhya
1 �� 2 �� 3 �� 4 �� 5 �� 6 �� 7 �� 8 �� 9 �� 0 ��
Kadi nava ka kha ga gha nga ca cha ja jha nya
< >Tadi nava
ṭa ṭha ḍa ḍha ṇa ta tha da dha na
Padi pancha pa pha ba bha ma
Yadi ashta ya ra la va śha sha sa ha
कटपयादि संख्या
१ २ ३ ४ ५ ६ ७ ८ ९ ०
कादि नव क ख ग घ ङ च छ ज झ ञ
टादि नव ट ठ ड ढ ण त थ द ध न
पादि पंच प फ ब भ म
यादि अष्ट य र ल व श ष स ह
To use the sankhya, take the first two syllables of the name of the ragam, and locate the corresponding columns on the table. Then take the two numbers and reverse them to get the mela number.
Actually, Katapayadi sankhya is a(n) (over-)simplification of Āryabhaṭa's Sanskrit numerals, due probably to Haridatta who lived at Kerala, c. 620-700.
An Algorithm to derive the Swarasthanas
Once the mela number is obtained, it is possible to derive the individual Swaras of the ragam. Here is how the SwaraSthanas are derived:
There is only one Sa in an Octave. so, 'Sa' is fixed.
'Ri' and 'Ga' notes:
divide the melakarta number by 36 and note the remainder. The raga will have...
Ri1 and Ga1 if remainder is less than 7 and greater than 0
Ri1 and Ga2 if remainder is less than 13 and greater than 6
Ri1 and Ga3 if remainder is less than 19 and greater than 12
Ri2 and Ga2 if remainder is less than 25 and greater than 18
Ri2 and Ga3 if remainder is less than 31 and greater than 24
Ri3 and Ga3 if remainder is either zero or greater than 30
Melakartas 1 to 36 use Ma1 (shudhdha madhyamam) while 37 to 72 use Ma2 (prathi madhyamam)
'Pa' is fixed as well.
'Da' and 'Ni' notes:
divide the melakarta number by 6 and note the remainder. The raga will have...
Da1 and Ni1 if remainder is 1
Da1 and Ni2 if remainder is 2
Da1 and Ni3 if remainder is 3
Da2 and Ni2 if remainder is 4
Da2 and Ni3 if remainder is 5
Da3 and Ni3 if remainder is 0
Example:
Lets take the melakarta#29, namely Dheerasankarabharanam. Its Melakarta number is 29. Lets apply the above Algorithm to obtain the swarasthanas of this ragam:
Since we know that 'sa' and 'pa' are fixed, we just need to determine Ri, Ga, Ma, Da and Ni.
Ri and Ga:
When dividing 29 by 36, the Remainder is 29. This is less than 31 and greater than 24. Hence using the above set of rules, we determine that Dheerasankarabharanam has Ri2 and Ga3.
Ma:
Since 29 is less than 37 this raga has Ma1.
Da and Ni:
On dividing 29 by 6 we get 5. This means that this raga has Da2 and Ni3.
To conclude, this raga's scale is: Sa Ri2 Ga3 Ma1 Pa Da2 Ni3 SA.
Thus, we have just derived the entire scale of this raga from its Melakarta number (see Melakarta Table).
Melakarta is the collection of Ragas in Carnatic music. Melakarta ragas are fundamental ragas from which other ragas may be generated. For this reason the melakarta ragas are also known as janaka(parent) ragas. Melakarta ragas are also known as sampoorna ragas as they contain all seven swaras (notes) of the octave in both the ascending and the descending mode. There are 72 melakarta ragas.
Indian Music
Indian classical music
Carnatic music
Composers
List of Carnatic composers
Singers
List of Carnatic singers
Hidustani music
Modern music
Filmi music
Folk music (Indian)
Concepts
Śruti
Raga
Melakarta
Katapayadi sankhya
Swara
Tala
Mudra
Contents
History
The mela 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 Venkatamakhi expounded in the 17th century in his work Caturdandi Prakaasikaa a new mela system known today as melakarta. He had made some bold and controversial claims and defined somewhat artificially 16 swaras from the known 12 semitones at that time to arrive 72 melakarta ragas. The controversial parts relate to his double counting of R2 etc. and his exclusive selection of madyamas for which there is no basis. However, today the 72 melakarta ragas have gained significant following, though to this day this system is being criticized. Venkatamakhi was known to be extremely critical of Raamamaatya.
Determining the Melakartha
A hundred years later than Venkatamakhi's time the Katapayadi sankhya rule came to be applied to the nomenclature of the melakarta ragas. The sankhya associates Sanskrit consonants with digits. The digits corresponding to the first two letters (syllables) of the name of a raga, when reversed, give the index of the raga. Thus the scale of a melakarta raga can be easily derived from its name.
Melakartha scale
Each melakarta raga has a different scale. The scales are constructed as follows: out of the twelve semitones of the octave S, R1, R2=G1, R3=G2, G3, M1, M2, P, D1, D2=N1, D3=N2, N3, a melakarta raga must necessarily have S and P, one of the M's, two of the R's and G's, and two of the D's and N's. Also, R must necessarily precede G and D must precede N. This gives 2 � 6 � 6 = 72 melakarta ragas. Finding melakartha ragas is a mathematical problem and following a simple set of rules, we can find the corresponding raga and the scale associated with it.
This scheme envisages the lower Sa (Keezh Shadjamam), upper Sa (Mael Shadjamam) and Pa (Panchamam) as fixed swaras, with the Ma (Madhyamam) having two variants and the remaining swaras Ri (Rishabam), Ga (Gandhaaram), Dha (Dhaivatham) and Ni (Nishaadham) as having three variants each. This leads to 72 seven-note combinations referred to as the Melakartha ragas.
A raga which has the same scale as a Melakartha raga (or a subset thereof) is said to be a janya of it (janya means born or derived from). Every raga is the janya of a melakarta raga. Ragas whose notes are found in more than one melakarta raga are assigned janyas based on subjective notions of similarity.
Table of Melakarta ragas
It can be said that the entire set of 72 melakarta ragas can be divided into two parts. viz.,. suddha Madhyamam and prati Madhyamam ragas. When a given suddha madhyamam raga's M1 is replaced by M2, we get the corresponding Prati Madhyamam raga. See Katapayadi sankhya for more information on how to derive the various swaras of a raga from its Melakarta number.
Mēḷakartā Rāgas
Suddha Madhyamam
Prati Madhyamam
1.Indu Chakra
6. Ritu Chakra
7. Rishi Chakra
12. Aditya Chakra
No. Raga Scale
1 Kanakangi S R1 G1 M1 P D1 N1
2 Ratnangi S R1 G1 M1 P D1 N2
3 Ganamoorti S R1 G1 M1 P D1 N3
4 Vanaspati S R1 G1 M1 P D2 N2
5 Manavati S R1 G1 M1 P D2 N3
37 Salagam S R1 G1 M2 P D1 N1
38 Jalarnavam S R1 G1 M2 P D1 N2
39 Jhalavarali S R1 G1 M2 P D1 N3
40 Navaneetam S R1 G1 M2 P D2 N2
41 Pavani S R1 G1 M2 P D2 N3
6
Tanarupi
S R1 G1 M1 P D3 N3
42
Raghupriya
S R1 G1 M2 P D3 N3
2. Netra Chakra
8. Vasu Chakra
7
Senavati
S R1 G2 M1 P D1 N1
43
Gavambodhi
S R1 G2 M2 P D1 N1
8
Hanumatodi
S R1 G2 M1 P D1 N2
44
Bhavapriya
S R1 G2 M2 P D1 N2
9
Dhenuka
S R1 G2 M1 P D1 N3
45
Subhapantuvarali
S R1 G2 M2 P D1 N3
10
Natakapriya
S R1 G2 M1 P D2 N2
46
Shadvidhamargini
S R1 G2 M2 P D2 N2
11
Kokilapriya
S R1 G2 M1
D2 N3
47
Suvarnangi
S R1 G2 M2 P D2 N3
12
Roopavati
S R1 G2 M1 P D3 N3
48
Divyamani
S R1 G2 M2 P D3 N3
3. Agni Chakra
9. Brahma Chakra
13
Gayakapriya
S R1 G3 M1 P D1 N1
49
Dhavalambari
S R1 G3 M2 P D1 N1
14
Vakulabharanam
S R1 G3 M1 P D1 N2
50
Namanarayani
S R1 G3 M2 P D1 N2
15
Mayamalavagoula
S R1 G3 M1 P D1 N3
51
Kamavardhini
S R1 G3 M2 P D1 N3
16
Chakravakam
S R1 G3 M1 P D2 N2
52
Ramapriya
S R1 G3 M2 P D2 N2
17
Sooryakantam
S R1 G3 M1 P D2 N3
53
Gamanasrama
S R1 G3 M2 P D2 N3
18
Hatakambari
S R1 G3 M1 P D3 N3
54
Viswambhari
S R1 G3 M2 P D3 N3
4. Veda Chakra
10. Disi Chakra
19
Jhankaradhwani
S R2 G2 M1 P D1 N1
55
Syamalangi
S R2 G2 M2 P D1 N1
20
Natabhairavi
S R2 G2 M1 P D1 N2
56
Shanmukhapriya
S R2 G2 M2 P D1 N2
21
Keeravani
S R2 G2 M1 P D1 N3
57
Simhendramadhyamam
S R2 G2 M2 P D1 N3
22
Kharaharapriya
S R2 G2 M1 P D2 N2
58
Hemavati
S R2 G2 M2 P D2 N2
23
Gourimanohari
S R2 G2 M1 P D2 N3
59
Dharmavati
S R2 G2 M2 P D2 N3
24
Varunapriya
S R2 G2 M1 P D3 N3
60
Neetimati
S R2 G2 M2 P D3 N3
5. Bana Chakra
11. Rudra Chakra
25
Mararanjani
S R2 G3 M1 P D1 N1
61
Kantamani
S R2 G3 M2 P D1 N1
26
Charukesi
S R2 G3 M1 P D1 N2
62
Rishabhapriya
S R2 G3 M2 P D1 N2
27
Sarasangi
S R2 G3 M1 P D1 N3
63
Latangi
S R2 G3 M2 P D1 N3
28
Harikambhoji
S R2 G3 M1 P D2 N2
64
Vachaspati
S R2 G3 M2 P D2 N2
29
Dheerasankarabharanam
S R2 G3 M1 P D2 N3
65
Mechakalyani
S R2 G3 M2 P D2 N3
30
Naganandini
S R2 G3 M1 P D3 N3
66 Chitrambhari S R2 G3 M2 P D3 N3
31 Yagapriya S R3 G3 M1 P D1 N1
67 Sucharitra S R3 G3 M2 P D1 N1
32 Ragavardhini S R3 G3 M1 P D1 N2
68 Jyotiswarupini S R3 G3 M2 P D1 N2
33 Gangeyabhusani S R3 G3 M1 P D1 N3
69 Dhatuvardhini S R3 G3 M2 P D1 N3
34 Vagadheeswari S R3 G3 M1 P D2 N2
70 Nasikabhusani S R3 G3 M2 P D2 N2
35 Sulini S R3 G3 M1 P D2 N3
71 Kosalam S R3 G3 M2 P D2 N3
36 Chalanata S R3 G3 M1 P D3 N3
72 Rasikapriya S R3 G3 M2 P D3 N3
=====
Indian Classical Music
Music is an integral part of Indian culture. It is the one art which is evident in all the strata of society. Indian music is one of the living systems of music in the world.
Indian music is a typical example of Modal music (music based on modes). The individuality of a mode is extablished by notes of defined frequencies in its structure. It is not the inter-relationship of each note to the basic tonic note. This tonic note may be actually heard through a rone or even in its absence, a trained ear is able to recognise the raga, bearing in mind the presumed tonic note. Memory thus plays an important part in Indian music.
India has developed forms of culture, lifeways and music that are distictive of its own.Yet because of its size and its variety of terrain, there are also great regional differences. The largest such division is between the Hindi related language groups of the North and Dravidian-speaking people of the south; the northern Hindustani style and the southern Karnataka (Carnatic) tradition.
History of Carnatic Music
Carnatic Music has its roots in the distance past. The earliest extend theoritical work is the Natya Sastra by Bharatha, a treatise on theater, dance and music dating between the second century B.C to the fifth century A.D. Through centuries many more important scholarly books on music have been written, perhaps the most noteworthy of which was the medieval Sangeetha Ratnakara by Sarangadeva.
Purandaradasa (1484-1564), sometimes called the Father of Carnatic Music, composed not only many songs but the standard lessons and exercices that are still memorized by every music student today. A golden age occurred between about 1750 and 1850 when the forms and performaces style that have continued to the present day were set. Thousands of new krithis (compositions) were composed, new ragas were invented, and the conceptual form of older ragas expanded.The Sangitha trimurthis (big three) , Sama Sastry (1762-1827), Tyagaraja (1767-1847) and Muthuswamy Dikshitar (1777-1847) dominated this period.
The Sangitha Trimurthys: Sama Sastry, Tyagaraja and Muthusamy Dikshitar
A south Indian proverb compares the compositions of thrimurthys. Dikshitar is said to have written music that is like a coconut: the hard shell of his brilliantly intellectual musical structures and complex, scholarly and sometimes esoteric texts must be broken to taste the sweat nut and milk inside. By contrast, Sama Sastri's music is said to be like a banana: the fruit is not so difficult to get in, but one must still peel off the bitter skin - Sastri's complicated talas rhythms and talas of five and seven beats before enjoying its flavour. But Tyagaraja's music is said to be like fresh, ripe grapes; both poetry and melody are immediately accessible to enjoy it one needs to merely bite into it. Even the skin is soft and sweat.
Swara
Indian music has seven notes or swaras as with all systems of music. Swara is defined as "that which is able to please of its own accord". These seven swaras are called Shadjamam, Rishabham, Gandharam, Madhyamam, Panchamam, Dhivatham and Nishadham. These are often represented as Sa, Re, Ga, Ma, Pa, Da and Ne, by their first syllable.
Swara and Swara Stanam
Of these seven swaras, Sa and Pa donot admit variations and are called achala (fixed) or avikratha (changeless) swaras. The other five (Re, Ga, Ma, Da and Ne) admint of two varieties each. The terms Komal and Tivra are used to distinguish these two, with komala swaram lower in note than the tivra swaram. Thus we have
Sudha (Komal) and Chathusruthi (Tivra) Rishabam,Sadharana (komal) and Antara (tivra) gandharam, Sudha (Komal) and Prati (Tivra) Madhyamam, Sudha (Komal) and Chatussruthi (Tivra) dhivatham and Kaisiki (komal) and Kakali (Tivra) Nishadham.
With this, there are 12 distictive swaras corresponding to notes in Carnatic Music.
In addition, four of the swaras, Ri, Ga, Da and Ne extend to another variety overlaping with the next swarastanam. This give rise to four more swaras totalling 16. Note however that the note (swara stana) is shared between two swaras.
Swaram
Notation
Western
Stanam
Sadjamam
Sa
C
1
Suddha Rishabam (Komal)
Re1
C #
2
Chathusruthi Rishabam (Tivra)
Re2
D
3
Shatsruthi Rishabam
Re3
D #/ E b
4
Suddha Gandharam
Ga1
D
3
Sadharana Gandharam
Ga2
D # /E b
4
Anthara Gandharam
Ga3
E
5
Suddha Madhyamam
Ma1
F
6
Prati Madhyamam
Ma2
F #/G b
7
Panchamam
Pa
G
8
Suddha Dhaivatham
Da1
G #/A b
9
Chathusruthi Dhaivatham
Da2
A
10
Shatsruthi Dhaivatham
Da3
A #/ B b
11
Suddha Nishadam
Ne1
A
10
Kaisiki Nishadam
Ne2
A #/B b
11
Kakali Nishadam
Ne3
B
12
The sudha swaras, also known as Prakrithi swaras, have the prefix Sudha. This is usually the lowest pitched note for that swara. The vikratha swaras have prefixes like chatussruthi, shatshuruthi, sadharana, antara, etc. In Hindustani music, sudha swara usually refer to Sankarabharana scale (Bilval).
Raga
Raga is the Pivotal concept of Carnatic music. This concept is India's proud contribution to world music. The ideal of absolute music is reached in the concept of Raga. Raga is much more than a scale. It is defied as that which colors the mind in ancient text. (Raga (Sanskrith): coloriing, dyeing, tingering). A raga is in some ways a kind of mystical expression with a musical personality of its own. The whole structure of Indian music is built around the concept of raga. Indian melodies of the classical type are based on ragas. As for folk melodies a good number of them will be found to be in some recognisable raga. Some folk meledies are in mixed ragas. The same goes with popular film music tunes.
Raga can be loosely defined as melody type or expressive mode. It consists of series of upto seven notes, which bear a definite relationship to adhara shadja and which occur in a particular sequence. They derive their personality through notes of defined pitch entering into their formation. It is the arrangement of particular swaras, in conformity to recognised aesthetic laws that establish the rupa (form) of raga.
Raga alapana is the presentation of pharases admissible in the raga in such a manner as to bring out its distictive characteristics. The arohana and avarohana constitute the briefest description of a raga. It gives the concsise form of the outline or framework of the raga.
Raga classification
Melam and Janyam Ragas are classifed into Janaka ragas and Janya ragas. Janaka ragas, also known as Melakartha or Sampurna raga has all seven notes (saptha swara) in their arohana and avarohana. There are 72 such janaka ragas arranged in a definete, serial order. A Janya raga is said to be derived from a janaka raga. It takes the same swaras as in its melakartha raga, but may take fewer swaras.
Example: Kanakangi (1st Melakartha) and its Janyams
Ragam
Melam
No
Aarohanam
Avarohanam
Kanakangi
Kanakaangi
1
Sa Re1 Ga1 Ma1 Pa Da1 Ne1 Sa
Sa Ne1 Da1 Pa Ma1 Ga1 Re1 Sa
Kadagapriya
Kanakaangi
1
sa ga re ga ma pa da pa ne sa
sa da pa da ma ga re sa
Kanakambari
Kanakaangi
1
sa ga re ga ma pa da ne da sa
sa ne da pa ma ga re sa
Mukthambari
Kanakaangi
1
sa re ga ma pa ne sa
sa ne da ma ga re sa
Peragasindhamani
Kanakaangi
1
sa re pa ma pa da ne sa
sa da pa ma ga re sa
Vaageswari
Kanakaangi
1
sa re ga ma pa da sa
sa da pa ma ga re sa
Sudha Madhyama and Prathhi Madhyama Raga: There are seventy two such melakartha ragas each with its own set ot janya ragas. As mentioned before ragas can take variations only in Re (Re1, Re2, Re3), Ga (Ga1, Ga2, Ga3), Ma (Ma1, Ma2), Dha (Dha1, Dha2, Dha3) and Ne (Ne1, Ne2, Ne3). The first 36 of 72 melams use Sudha Madhyamam (Ma1) and are called Sudha Madhyama ragas. The later 36 use Prathi Madhyaman (Ma2) and are called Parathi Madhyama ragas. So within each category they can differ only in Re, Ga, Dha and Ne. These are systematically divided into six chakras, with six melams per chakra.
Click here
for mela chakra details
Sudha Madhyama Ragas
Indu
Netra
Agni
Vedha
Baana
Ruthu
Kanakaangi
Seanavathi
Gaayaga Priya
Jangharadhwani
Maara Rajnani
Yaagha Priya
Ratnaangi
Hanumat Thodi
Vagulaa Baranam
Nata Bhiravi
Chaarukesi
Raaga Vardhani
Ganamurthi
Dheanuka
Maaya Malava Gaula
Keeravani
Sarasaangi
Kaangheya Bhushani
Vanaspathi
Naataka Priya
Chakra Vaagham
Karagara Priya
Hari Kaamboji
Vaagha Dheeswari
Maalavathi
Kokila Priya
Suurya Kantham
Gauri Manogari
Dheera Shankara Bharanam
Seelini
Dhaana Roopini
Roopavathi
Haatakambhari
Varuna Priya
Naaga Nandhini
Chala Naata
Prathi Madhyama Ragas
Rishi
Vasu
Brahma
Dishi
Rudra
Aditya
Jaalakam
Kavaambhodi
Thavalaambari
Syamalaanghi
Kandhaamani
Su Charithra
Jaalarnavam
Bhava Priya
Naama Naarayani
Shanmughapriya
Rishabha Priya
Swodhis Ruupini
Jaala Varaali
Subha Bhandhu Varali
Kaama Vardhani
Simmhendhra Madhyamam
Lathaangi
Thadhu Vardhani
Navaneetham
Shatvidha Maarghani
Raama Priya
Heamavathi
Vaachaspathi
Naasigha Bhushani
Bhaavani
Swarnaanghi
Gamana Priya
Dharmavathi
Measha Kalyani
Koochalam
Raghupriya
Dhivyamani
Viswambhari
Neethimathi
Chitraambhari
Raghasya Priya
Click here
for Katapayadhi Sankkya details.
Katapayadhi Sankya: The name and number of Melakartha raga is systematically defined by Katapayadhi Sankya method. The letters Ka, Ta, Pa, Ya, etc are assiged numeric numbers. From the first two characters of each melam, and mapping it to the number corresponding to the character, the mela raga's number is identified. For example, the raga "Dheera Shankarabaranam" has Dhe and Ra as its first characters, tha map to 9 and 2. By juxtaposing the 2nd character's number with the 1st one we get 29, which is the mela kartha number of the raga. Ragas like Chakravagham are represented with Cha and Ka (6 and 1, thereby 16) instead of 'k'.
Vajra Raga: Janya ragas is called Vajra raga if upto three swaras are deleted in the arohaana, avarohana or both., Vajra ragas are furher classified into shadava (only six swaras present in aarohanam / avarohanam of raga; or one vajra) and audava (only five swaras present; two being vajra). As mentioned before, a raga with all seven notes is called sampurna raga. Note that a raga with only four notes in aarohana or avarohana is not considered since atleast five swaras are required to give an individuality to the raga. Also janayas can have different number of swaras in arohanam and avarohanam giving rise to eight types of varja ragas.
Eight kinds of Varja ragas with example
Ragam
Melam
No
Aarohanam
Avarohanam
Varja Type
Kamboji
Hari Kamboji
28
sa re ga ma pa da sa
sa ne da pa ma ga re sa
Shadava (6)- Sampurja (7)
Bilahari
Dheera Shankarabharanam
29
Sa re ga pa da sa
Sa ne da pa ma ga re sa
Audava (5) - Sampurna (7)
Bhairavam
Suryakantham
17
Sa re ga ma pa da ne sa
Sa da pa ma ga re sa
Sampurna (7) - shadava (6)
Saramathi
Natabhiravi
20
Sa re ga ma pa da ne sa
Sa ne da ma ga sa
Sampurna (7) - Audava (5)
Sriranjani
Karagapriya
22
Sa re ga ma da ne sa
Sa ne da ma ga re sa
Shadava (6) - Shadava (6)
Natakurunji
Hari Kamboji
28
Sa re ga ma da ne sa
Sa ne da ma ga sa
Shadava (6) - Audava (5)
Malahari
Mayamalavagaula
15
Sa re ma pa da sa
Sa da pa ma ga re sa
Audava (5) - Shadava (6)
Mohanam
Hari Kamboji
29
Sa re ga pa da sa
Sa da pa ga re sa
Audava (5)- Audava (5)
Upanga and Bashanga Raga: Another type of raga classification classifies them as Upanga raga if janya takes only the swaras of the melakartha (as they usually do), Bashanga raga if they take a foreign swara in either arohanam, avarohanam or both (from somether melakartha) and vakra raga if arohana or avarohana or both take zig-zag course or twist. Vakra ragas are further classifed into Sampurna vakra if arohana and avarohana are sampurna (with all seven notes present) or Vakra varja if they have less than seven notes. Vakra ragas also are classified into Ekaswara vakra, Dviswara vakra, Triswara vakra or Chatusswara vakra based on number of vakra swaras in the raga (one, two, three and four respectively). Four is the maximum number of vakra swara that a raga can accomadate. In Bashanga raga, the foreign note is known as annya swara. The number of Bhashanga ragas used in Carnatic music is 26.
Examples of Bhasanga and Vakra Janya ragas
Ragam
Melam
No
Aarohanam
Avarohanam
Type
Kathana kuthuhalam
Deera Sankarabharanam
29
Sa re ma da ne ga pa sa
Sa ne da pa ma ga re sa
Sampurna vakra
Karnataka Byag
Hari Kamboji
28
Sa re ga ma pa da ne sa
Sa ne da ne pa da ma ga re ga sa
Sahana
Hari Kamboji
28
Sa ra ga ma pa ma da ne sa
Sa ne da pa ma ga ma re ga re sa
Nalinakanthi
Sarasangi
27
Sa ga re ma pa ne sa
Sa ne pa ma ga re sa
Vakra varja
Devamanohari
Karagarapriya
22
Sa re ma pa da ne sa
Sa ne da ne pa ma re sa
Bangala
29
Sa re ga ma pa ma re pa sa
Sa ne pa ma re ga re sa
Nilambari
Deera Sankarabharanam
29
Sa re ga ma pa da pa ne sa
Sa ne pa ma ga re ga sa
Ekasvara
Suposhini
Sa re sa ma pa ne da sa
Sa da ne pa ma re ma sa
Dviswara
Bhairavi
Natabhiravi
20
Sa ga re ga ma pa da ne sa
Sa ne da pa ma ga re sa
Chathusruthi dhivatham (annya swaram) in aarohanam, Sudha dhivatham in avarohanam
Bhasanga
=====
The katapayadi sankhya is a way of determining the number of a melakarta ragam from the first two syllables of the name of the raga.
A detailed discussion of the Katapayadi coding scheme and its possible relation to the modern hashing technique was published in the IEEE Annals in a 1997 article, subsequently reprinted elsewhere. This article, which can be found at:
http://citeseer.ist.psu.edu/532626.html
also describes several anecdotal applications of the technique in history, among which is a mnemonic to remember the digits of pi to 17 places.
Contents
1 How to use it
1.1 Katapayadi sankhya
1.2 कटपयादि संख्या
1.2.1 An Algorithm to derive the Swarasthanas
How to use it
Following is the Katapayadi sankhya in the Roman alphabet and in Devanagari.
Katapayadi sankhya
1 �� 2 �� 3 �� 4 �� 5 �� 6 �� 7 �� 8 �� 9 �� 0 ��
Kadi nava ka kha ga gha nga ca cha ja jha nya
< >Tadi nava
ṭa ṭha ḍa ḍha ṇa ta tha da dha na
Padi pancha pa pha ba bha ma
Yadi ashta ya ra la va śha sha sa ha
कटपयादि संख्या
१ २ ३ ४ ५ ६ ७ ८ ९ ०
कादि नव क ख ग घ ङ च छ ज झ ञ
टादि नव ट ठ ड ढ ण त थ द ध न
पादि पंच प फ ब भ म
यादि अष्ट य र ल व श ष स ह
To use the sankhya, take the first two syllables of the name of the ragam, and locate the corresponding columns on the table. Then take the two numbers and reverse them to get the mela number.
Actually, Katapayadi sankhya is a(n) (over-)simplification of Āryabhaṭa's Sanskrit numerals, due probably to Haridatta who lived at Kerala, c. 620-700.
An Algorithm to derive the Swarasthanas
Once the mela number is obtained, it is possible to derive the individual Swaras of the ragam. Here is how the SwaraSthanas are derived:
There is only one Sa in an Octave. so, 'Sa' is fixed.
'Ri' and 'Ga' notes:
divide the melakarta number by 36 and note the remainder. The raga will have...
Ri1 and Ga1 if remainder is less than 7 and greater than 0
Ri1 and Ga2 if remainder is less than 13 and greater than 6
Ri1 and Ga3 if remainder is less than 19 and greater than 12
Ri2 and Ga2 if remainder is less than 25 and greater than 18
Ri2 and Ga3 if remainder is less than 31 and greater than 24
Ri3 and Ga3 if remainder is either zero or greater than 30
Melakartas 1 to 36 use Ma1 (shudhdha madhyamam) while 37 to 72 use Ma2 (prathi madhyamam)
'Pa' is fixed as well.
'Da' and 'Ni' notes:
divide the melakarta number by 6 and note the remainder. The raga will have...
Da1 and Ni1 if remainder is 1
Da1 and Ni2 if remainder is 2
Da1 and Ni3 if remainder is 3
Da2 and Ni2 if remainder is 4
Da2 and Ni3 if remainder is 5
Da3 and Ni3 if remainder is 0
Example:
Lets take the melakarta#29, namely Dheerasankarabharanam. Its Melakarta number is 29. Lets apply the above Algorithm to obtain the swarasthanas of this ragam:
Since we know that 'sa' and 'pa' are fixed, we just need to determine Ri, Ga, Ma, Da and Ni.
Ri and Ga:
When dividing 29 by 36, the Remainder is 29. This is less than 31 and greater than 24. Hence using the above set of rules, we determine that Dheerasankarabharanam has Ri2 and Ga3.
Ma:
Since 29 is less than 37 this raga has Ma1.
Da and Ni:
On dividing 29 by 6 we get 5. This means that this raga has Da2 and Ni3.
To conclude, this raga's scale is: Sa Ri2 Ga3 Ma1 Pa Da2 Ni3 SA.
Thus, we have just derived the entire scale of this raga from its Melakarta number (see Melakarta Table).