My uncle Sri L R Ramaswamy (Ramu Mama to me) & Smt Nagalakshmi Santhanagopalan (disciple of Dr S Ramanathan & Prof T R Subramanian) played a major role in getting me interested in the technical aspects of music. Had it not been for these two, concepts such as Sruthi Bedam, sooladisaptathalas, scheme of 72 mela ragas, etc would be as foreign to me as Greek National Anthem to a 5-year-old school boy in India.
In one of our evening theory music classes my fellow classmates were surprised when I was able to perform without hesitation (& error) the arohana avarohana of any of the 72 melakarta ragas when our Nagalakshmi teacher would mention only the number of that raga, at random!
Needless to say, I was not aware of the name of most of the ragas, as we were still in the process of learning by heart the names of these 72 ragas. What surprised my class mates more was my attendance in this theory class was a mere 5% as I was preparing & appearing for my Chartered Accountancy Entrance examination parallelly & could not set aside time to attend theory classes. It was at this stage that Nagalakshmi teacher made a statement which still reverberates in my ears. MATHS & MUSIC ARE INTER RELATED; IT IS EASY FOR ANY ONE WHO KNOWS UNDERSTANDS & LOVES ONE; TO LEARN THE OTHER VERY EASILY. After 4 decades since, as my understanding of music matures gradually I am still trying to understand the full implication of what she said.
Maths & Music - Talam / Layam: In Indian music one compares sruthi to mother & layam to father. Initially one can observe the nexus between Maths & music when the beginner starts with sarali varisai. The paatu vadhiyar or teacher would insist on the talam & sarali being rendered simultaneously. Emphasis normally would be on talam initially. The lesson has to end exactly at the beat where the talam ends. As one progresses from sarali varisai & janta varisai & mel sthayi to Geetham, the relationship between maths & music under goes a slight change. The emphasis shifts to melody from laya. Probably because of the variation in raga; having practised & being exposed in the initial stages only to Mayamalavagoulai, the student gradually gets familiar with Malahari, Mohanam, Bilahari, Sudha Saveri, Kalyani, Kamas, etc. At this stage irrespective of the talam the student is comfortable juggling ragams & talams as he / she is already familiar with the sapta talas, having practised the lessons in different speeds one is bound to have a sense of achievement having mastered a fair bit of maths & music! After Geetham the student cruises gently to varnams – starting with basic Adi tala varnams. The maths gets a bit complicated when one starts with Viriboni – the Bhairavi Ata tala varnam. As we all know the eduppu for ata tala varnams is not in samam. So one has to be extra careful when rendering the ata tala varnams in 2 or 3 speeds.
Once the student successfully masters several varnams the vadhyar / teacher starts with the customary Vinayagar krithi. At this stage the student is encouraged to attend live concerts & to hear recordings of established musicians to increase kelvi gnanam. In a typical live concert when the artists render the kalpana swara part in a song, there is a very high chance of a “formation - swara korvai” in the end. Certainly, this involves some maths as one has to ensure that korvai ends in the proper swara & proper tala sthanam where the eduppu of the sahityam / song begins! For the student this is yet another bit of maths in music. The pinnacle of combining maths (laya / talam) & music is the RTP; rendered in a complicated talam in 3 speeds. Occasionally thisram, kantam, mishram would be thrown in for good measure alongwith Anulomam, pratilomam.
Maths & Music – Other aspects: One would remember my opening para where I have mentioned that some people can sing / perform a melakarta ragam if they know the number of the ragam (in the scheme of 72 melakarta ragas), even without knowing the name. A little bit of basic maths can help one to perform this perfectly!
The 7 swaras Sa, Ri, Ga, Ma, Pa, Dha Ni have to be placed in a mela raga in the proper ascending order.
Of the 7 swaras Sa & Pa have only 1 type each, Ma has 2 types, Ri, Ga, Dha, Ni having 3 types each, but Ri 2 = Ga 1 & Dha 2 = Ni 1. Also Ri 3 greater than or equal to Ga 1 & Ga 2, similarly Dha 3 greater than or equal to Ni 1 & Ni 2. The total number of ragas is therefore: 3(Ri) * 2(Ga) * 2(Ma) * 1(Pa) * 3(Da) * 2(Ni) = 72.
The numbering scheme splits the 72 ragas into 36 Sudha Madhyama Ragas & 36 Prathi Madhyama Ragas. The 36 ragas are further grouped into 6 ragas in 6 groups (called chakrams). 6 (ragas) * 6 (chakrams) * 2 (Madyamams) = 72.
Let me end this with 2 quotations linking music & mathematics.
Martin Gardner - A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?
Gottfried Leibniz - Music is the pleasure the human mind experiences from counting without being aware that it is counting.
More about the nexus between (Indian - carnatic) music and maths in my next.
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