Archive for November, 2015

Melakartha Chart (Scales of Carnatic Music)

November 26, 2015

Melakartha Chart – (Scales of Carnatic Music)

L V Nagarajan

Prologue:

Some time back I was listening to a young upcoming Carnatic vocalist in Shanmukhananda Hall in Mumbai. After a few items, he started the alap of an unfamiliar raga. Some of the knowledgeable members of the audience were guessing what raga it could be. Somebody said it is like another rare raga but with prati-madyama. Another one said it is a janya of melakartha75(?!) or so. After a short alap he allowed the violinist to play the raga. Violinist started a little hesitantly. Vocalist leaned towards him and spoke a few words. Violinist nodded and continued more confidently. Then the vocalist proudly announced the rare raga as Gopriya, janya of Rishabapriya scale. Some in the audience were happy but I was not happy. If he had told us the Melakartha number I could have also understood the scale easily; but Rishabapriya? Luckily I happen to know something about Katapayadi Sankhya, a code into which these Melakartha names are encoded. Now let us see:

Ka (adi) nava – Ka, Kka, Ga Gga, Gna, Cha, Ccha Ja, Jja.

Ta (adi) nava – Ta, Tta, Da, dda, Nna, Tha, Ttha, Dha, Ddha.

Pa (adi) pancha – Pa, Ppa, Ba, Bba, Ma

Ya (adi) ashta – Ya, Ra, La, Va, Sya, Sha, Sa, Ha

Ri-Sha-bapriya is the Mela. Ri is second letter in Yaadiashta and Sha is 6th in the same series. Hence It is Mela number 62. (i.e) =10×6 +2, 11th cycle of the Melakartha scheme, 5th Cycle of Prathi-madhyama group and the second raga in the cycle. (i.e.) S R2 G3 M2 P D1 N2 S is the scale. QED.

How nice it could have been if the vocalist told us this number 62 as he did to the violinist.

 

Dialogue

1. He! I understand all systems of music have seven notes. But, tell me, what is this scale, Mela or Melakartha?

The concept of present day scales in Carnatic Music has been imported from the western music. In the West an octave of eight notes are defined starting from a note of a specific frequency to its resonant note of double the frequency. This octave (set of eight notes) was initially divided into 7 frequency intervals between the notes, denoted as C-D-E-F-G-A-B-C. The musical scale of these major notes is known as Major scale. The frequency ratios selected for these intervals is same as Sankarbharanam (scale) of Carnatic music. However, a set of semi tones (or half intervals) were introduced, 2 between C-D-E and 3 between F-G-A-B.  In a piano or harmonium the white keys represent the major notes and the black keys(^) represent semi-tones – (C^D^EF^G^A^BC). The semi tone between C and D is called D-Flat or C-Sharp according the musical context. Same way the other semitones are also treated. For our convenience, we will call them as

C, D1, D2, E1, E2, F1, F2, G, A1, A2, B1, B2, C.

Frequency ratios of these semi-tones follow the rule of consonance and assonance. Many scales were developed using the 7 selected notes from these 12 semitones. Some of our main ragas (scales) like Karaharapriya and Mayamalavagowla matched these semitones.  Somewhere in the 17th century this concept of scale was adopted by theoreticians of carnatic music. They were also influenced by the keyed instruments of western music like piano and harmonium. Hence attempts were made to fit our ancient musical system into the keys of the above instruments. At this point scales were introduced in carnatic music, to group all the notes used in a raga. These attempts lead to the development of our own basic scales, Mela Karthas. Melas or new melodies were born out of these scales and hence the name Melakartha or melody-maker. (However, subsequently, sacrificing some amount of consonance and assonance between notes, Western music adopted 12 equal intervals for these 12 semitones. This system was called ‘equi-tempered’ as opposed to the earlier system called ‘just-tempered’ or ‘just intonations’ which takes care of consonance ratios. Western musical instruments are tuned accordingly.)

2. But how do these 12 semitones make 72 Melakarthas, I often hear about?

At this point it may be better to discuss about what constitutes a present day scale. A full scale constitutes seven notes or saptha swaras (sa, ri, ga, ma, pa, da, ni) in an octave. For convenience let us call these notes in short as S R G M P D N. These are selected from 12 basic nodes, which we may call as Sruthis’s, though they are called semitones in western music. The rules for selecting a basic-scale (a set of seven swaras from these 12 sruthis) can be summarized as below:

Swaras S       R       G      M P       D      N S
Semitones C D1 D2 E1 E2 F1 F2 G A1 A2 B1 B2 C
Sruthis 1 2 3 4 5 6 7 8 9 10 11 12 1
(12) Swara-sthanas S R1 R2 G1 G2 M1 M2 P D1 D2 N1 N2 S
(4) Vivadi-Swaras Gr Rg Nd Dn  
(16) Swara-sthanas S R1 R2 R3 M1 M2 P D1 D2 D3 S
G1 G2 G3 N1 N2 N3  

It may be noted above that notes nos. 3 and 4 are used as both Ri and Ga. Similarly notes 10 and 11 are used as both Da and Ni (though such usages are known as Vivadi Prayoga). In carnatic music system, these 16 swara-sthanas are called respectively: Shadjam, Suddha-Chatusruthi-Shatsruthi Rishabams, Suddha-Sadarana-Antara Gandharams, Suddha-Prati Madhyamams, Panchamam, Suddha-Chatusruthi-Shatsruthi Dhaivatams and Suddha-Kaisika-Kakali Nishadams. Here itself we can make out the attempt of reducing the number of sruthis from the original twenty-two to twelve. (Even in Western Music double-sharp and double-flat notes are used in a scale)

Any basic scale has two parts: Poorvanga, the notes upto and including M, (SRGM) and Uttaranga, the notes including P and above (PDNS). For each M (sudda-M1 and prati-M2), there are six types poorvangas based on six different combinations of notes R and G; namely R1-G1, R1-G2, R1-G3, R2-G2, R2-G3 and R3-G3. Similarly there are six types of uttarangas based on six different combinations of notes D and N. Hence we have 72 Melakartas – [(6+6) x 6].

3. Really ingenious! But what is this Katapayadi mumbo-jumbo being mentioned?

The above 72 melakarthas require some identification as most of them are not naturally available scales. They divided these in to twelve groups, each group having a specific R-G-M1 and R-G-M2 combinations with increasing order of R and G. Within each of this group, six scales with increasing order of D and N were included. Thus 36 scales or melakarthas using M1 were numbered 1 to 36. The others with M2 were numbered 37 to 72. Please refer to the chart at the end of this write-up. Each of this 12 groups known as chakras were named as Indu, Netra, ……, Rudra and Aditya. (Indu – one Moon, Netra – 2 eyes, ….., 11 Rudras and 12 Adityas). In the chart below each row represents two chakras. Since many of these scales were not in existence, these, as melakarthas, required some names also. The earlier day musicologists used a code to name these scales in such a way that one can find the number of a melakartha from the name itself. The code is known as Katapayadi Sankhya and is used in many applications of ancient Hindu science and mythology.

The numbers 1 to 9 are coded by using following letters: (Ka Ta Pa Ya)

Ka (adi) nava – 1 to 9 –  Ka, Kka, Ga Gga, Gna, Cha, Ccha Ja, Jja.

Ta (adi) nava – 1 to 9 – Ta, Tta, Da, dda, Nna, Tha, Ttha, Dha, Ddha.

Pa (adi) pancha – 1 to 5 – Pa, Ppa, Ba, Bba, Ma

Ya (adi) ashta – 1 to 8 – Ya, Ra, La, Va, Sya, Sha, Sa, Ha

Other letters are rendered as zero. In the scale Kamavardini, Ka decodes into number 1, and Ma decodes into number 5. Hence the number of the scale decodes into 5 tens plus one, 51. The same way other scales were also given such names. However, some scales are already established as popular and well known ragas from ancient times. Hence these names were modified, such as, DdheeraSankarabharanam (29), HanumaTodi (8), MechaKalyani (65), to fall into the Katapayadi scheme.

4. Looks neat! Why then people prefer melakartha numbers instead of names?

DdheeraSankarabharanam and Sulini are two different scales, the first one being a well known raga. Can you spot how these scales compare? Yes, only when one compares the numbers 29 and 35. we can now say immediately: Sulini uses R3 instead of R2 in Sankarabharanam. And Kosalam (71) is immediately identified as M2 of Sulini, (or R3, M2 of Sankarabharanam). With names these relationships are not immediately evident. Hence, the preference for numbers. Of course there are many who have completely memorized the Melakartha table

5. Is there a way to name these scales in a way to reflect these inter relationships?

To my knowledge, nobody has tried so far. However, I propose, in the following paragraphs, a way of encoding such relationships in the name itself.

Earlier the scale was split into two parts Poorvanga (SRGM) and Uttaranga (PDNS). Let us now split the scale into three parts: SRG, M, PDN. If we consider the variations in these parts, we get SRG(6) x M(2) x PDN(6) = 72 Scales. Let us now name these parts along with their variations:

S R1 G1 – athi M1- Daya P D1 N1- Vathi
S R1 G2 – Sakala P D1 N2 – Nidhi
S R1 G3 – Sarva P D1 N3 – Kari
S R2 G2 – Parama M2 – Kripa P D2 N2 – Varshini
S R2 G3 – Poorna P D2 N3 – Varithi
S R3 G3 – Poojya

P D3 N3 – Sagari

With these code names, Sankarabharanam (29) will be called as Poorna Daya Varithi. And Kalyani (65) will be known as Poorna Kripa Varithi. It is clear from the name that Kalyani scale is same as Sankarabharanam, but with M2. Poojya Daya Varithti is Sankarabharanam with R3, i.e. Shulini (35). Here I take the liberty of using the Melakarta Chart as developed by Dr. Mukund (http://www.carnaticcorner.com/articles/mukund_chart.htm). This chart is prepared on the same principle as mentioned above. I have superimposed the above code names on this chart, as shown below. We may use this chart to get used to the proposed new names. The melakarthas using Athi, Poojya, Vathi and Sagari codes are the 40 Nos. of Vivadi melas – the outer most squares of the chart.

Mukund-Chart

6. Umm…! I really need time to study and understand this.

Please take your time and do write your comments.

Epilogue:

  1. The material discussed in this blog has been extracted from my more detailed write-up on Melakartha scheme done in 2006. However I did not have a blog-spot then, to publicize it. I sent it to a few musicians and musicologists but there was not any response. I was enthused to write this note again, when I recently came across Mukund’s Chart. (http://www.carnaticcorner.com/articles/mukund_chart.htm).
  2. The rasikas of Chennai Music Festival (2015) may use this chart while attending the concerts.
  3. The above suggested codes/names can definitely be improved by musicologists like Dr. Mukund. It is only an idea to be adopted, or improved (or rejected, if found not suitable).
  4. While there are numerous advantages of this Melakartha scheme, there are a few disadvantages also. Though Melakartha formulation helps us to classify, formulate and document our music, it has limitations in formulating such nutpa-sruthis as Madhyama of Varali or Rishaba of Saveri. Possibly this was the reason why Harmonium (or Piano) was not preferred as a part of carnatic music ensemble. More so due to the equi-tempered tuning of Harmonium, where the 12 notes of the octave are tuned with equal frequency intervals. Here-in, even Sa-Pa consonance is sacrificed. We should not allow the Melakartha scheme to restrict our music to just 12 flat notes and 72 basic scales. We may discuss more about this later.  The author of this note is only a normal listener and follower of Indian music and whatever knowledge (or lack of it) displayed here are purely incidental. Let our Music and its traditions live forever.
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