Melakartha ragas
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Introduction
Carnatic Music, in its present form rests on the structure set out in the Melakartha Scheme. Formulated first by Venkatamakhi, who is placed in the 17th Century A.D., the Scheme envisaged some Asampurna ragas, that is, those ragas without the full complement of the seven swaras or notes of the octave. It was later modified by Govindacharya to include only ragas with the complete set of seven swaras (Sampurna). This is what is followed at present. It is, of course, to be noted that the octave of seven notes, is basic to vitually all music systems of the world. To add colour and bring life to this, manodharma or "bhava" as it is called is very essential and is of paramount importance.The Scale
This Scheme envisages the Small Sa(Keezh Shadjamam), Big 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. The omission of one or more notes in the Arohana or Ascending and / or Avarohana or Descending swara sequences from any Melakartha leads to a very large number of Janya Ragas. Janya means born of, or derived from and these ragas are listed as those which are derived from the 72 Melakartha Ragas.RULES TO FIGURE OUT THE MELAKARTA
The Melakartha raga scale is based purely on mathematics with each swara being chosen statistically. Thus, the raga scale can be expressed in mathematical terms and we can write a small algorithm to find out the Melakartha and its corresponding scale. Given a melakartha raga number X where X >= 1 and X <= 72 we will try to derive its Arohanam-Avarohanam.Step1
As it is Sampoorna-Sampoorna (Sampoorna means complete), it has Sa Pa Sa by default as explained above. So we have something like this Sa _ _ _ Pa _ _ SaStep2
If X <= 36, Ma is shuddha madhyamam otherwise it is Prathi madhyamam. Using this rule we can derive the Ma.Thus we have Sa _ _ Ma Pa _ _ Sa
Step3
Then calculate X (modulo) 6. The Dha and Ni depend on this value.X mod 6 = 1 => Dha is shuddha dhaivatham and Ni is shudha nishadham. (Eg. Kanakanghi)
X mod 6 = 2 => Dha is shuddha dhaivatham and Ni is kaisika nishadham. (Eg. Thodi)
X mod 6 = 3 => Dha is shuddha dhaivatham and Ni is kaakali nishadham. (Eg.Ganamoorthy)
X mod 6 = 4 => Dha is sadhushrudhi dhaivatham and Ni is kaisika nishadham.(Eg. Karaharapriya)
X mod 6 = 5 => Dha is sadhushrudhi dhaivatham and Ni is kaakali nishadham.(Eg. Kalyani)
X mod 6 = 0 => Dha is shatshrudhi dhaivatham and Ni is kaakali nishadham.(Eg. ChalaNattai)
Using this rule we can derive the Dha and Ni. Now we have Sa _ _ Ma Pa Dha Ni Sa
Step4
Then calculate ((CEIL(X / 6)) mod 6) [CEIL is the operator which converts the operand to the nearest higher integer which is greater than or equal to the operand] [mod is modulo operator]The Ri and Ga depend on this value.
((CEIL(X / 6)) mod 6) = 1 => Ri is shuddha Rishabam and Ga is shuddha Gandharam. (Eg: Kanakanghi)
((CEIL(X / 6)) mod 6) = 2 => Ri is shuddha Rishabam and Ga is sadharana Gandharam. (Eg: Thodi)
((CEIL(X / 6)) mod 6) = 3 => Ri is shuddha Rishabam and Ga is andhara Gandharam. (Eg: Panduvarali)
((CEIL(X / 6)) mod 6) = 4 => Ri is sadhushrudhi Rishabam and Ga is sadharana Gandharam. (Eg: Shanmugapriya)
((CEIL(X / 6)) mod 6) = 5 => Ri is sadhushrudhi Rishabam and Ga is andhara Gandharam. (Eg: HariKambodhi)
((CEIL(X / 6)) mod 6) = 0 => Ri is shatshrudhi Rishabam and Ga is andhara Gandharam. (Eg: ChalaNattai)
Using this rule we can derive the Ri and Ga. So now we have the entire scale.
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