Some mathematical gimmicks in Carnatic music

Legend Dr.Balamurali Krishna once beautifully described how Carnatic music got its name. In Sanskrit, “Karna" means ear and "Ataka" means something which is amusing/pleasing.Therefore Karnataka Sangeedham aka Carnatic music is the music which is pleasant or amusing to our ears!

‘Sruti matha, laya pitha’ is the crux of Carnatic music .It means the drone and rhythm are mother and father to music. Subduing sruthi and laya is required to master the art.Carnatic music expresses these two by the way of Raga and Tala respectively.

Raga:

A Raga is a sequence of swara/sound. There are 7 swaras in Carnatic music known as Saptaswara ("Sapta" means seven in Sanskrit) which stand for:

1. Sa -Satjamam
2. Ri - Rishabam
3. Ga - Gandharam
4. Ma - Madhyamam
5. Pa - Panchamam
6. Dha - Dhaivadham
7. Ni- Nishadham

While Sa and Pa are constants, the swaras Ri,Ga,Ma,Dha,Ni have further variants.
*Ri & Ga have 3 variants which are indexed as R1,R2,R3 and G1, G2, G3. Similarly Dha & Ni have 3 variants - D1, D2,D3 and N1,N2,N3. (Each variant has tongue twisting sanskrit names which I have ignored here for the sake of convenience)

*1-3 being biggest to smallest sound
*Ri,Ga,Ma,Pa,Dha,Ni are in ascending order of sound

Group I :R1,R2,R3, G1,G2,G3
Group 2: M1,M2
Group 3:D1,D2,D3,N1,N2,N3

*(Ri-R,Ga-G,Ma-M,Dha-D,Ni-N)

Each raga has the following qualities:

1.It has all 7 swaras
2.Within a group, the succeeding swara cannot have a smaller sound than its predecessor. E.g. N1 cannot follow D2 or D3. Likewise G2 cannot follow R3.
3.The swaras have to follow the regular sequence – Sa Ri Ga Ma Pa Dha Ni Sa and Sa Ni Dha Pa Ma Ga Ri Sa
4.Each raga can have either M1 or M2

And so,

Group I can possibly have 6 combinations:

(i)D1, N1
(ii)D1,N2
(iii)D1,N3
(iv)D2,N2
(v)D2,N3
(vi)D3,N3

Similarly, Ra & Ga will have 6 combinations.

Putting all these together,

1 (of Sa) x 1 (of Pa) x 6 (1 of the 6 combo of Ri & Ga) x 6 (1 of the 6 combo of Dha & Ni) x 2 (1of M1& M2) = 1x1x6x6x2=72 melakartha ragas