The number is not a matter of convention. It follows from four conditions and a multiplication.
The count of melakarta ragas was not arrived at by choice or by tradition. It is the result of applying a small set of strict conditions to the twelve positions of the octave and enumerating every scale that satisfies them. That enumeration yields 72. Under those conditions, no other total is possible.
The conditions are set out below, each with the factor it contributes to the total.
Two constraints apply: Gandharam must lie above Rishabham, and the two cannot occupy the same position. Three of the nine combinations violate one of these and are consequently not scales at all.
= the two names denote the same position · ↓ Gandharam would fall below Rishabham
Dhaivatam and Nishadam present an identical structure: three positions against three, the same two constraints, and the same six admissible pairs.
Rishabham–Gandharam pairs × Madhyamam × Dhaivatam–Nishadam pairs
That constitutes the entire derivation. The total is 72 because six multiplied by two multiplied by six is 72, and for no other reason.
Three selections, each one narrowing the set of remaining possibilities.
Madhyamam is the middle factor in the product, and it therefore divides the list precisely in half: ragas 1–36 take M1, and 37–72 repeat the identical sequence with M2.
Every melakarta consequently has a counterpart exactly 36 places away, identical in every swara but Madhyamam. Sankarabharanam is 29 and Kalyani is 65; 65 − 36 = 29, and the two differ in nothing but which Madhyamam is used.
Were the only requirement that a scale begin on Shadjam and use seven of the twelve positions, there would be 462 such scales. Requiring Panchamam as well reduces the number to 252. Adding the remaining condition — that each of Rishabham, Gandharam, Madhyamam, Dhaivatam and Nishadam appear exactly once, within its own range and in order — excludes a further 180.
Seventy-two remain. The conditions are therefore not ornamental: they are what makes the set finite, ordered, and possible to learn in full.
The 72 are parent scales. A janya raga is derived from a melakarta by altering how that parent's swaras are used — omitting one in ascent or descent, introducing vakra movement, or placing emphasis differently. Mohanam, for example, is derived from Harikambhoji with two swaras omitted. The greater part of the performed repertoire consists of such derived ragas, and unlike the melakartas their number is not fixed.
