I realize I am opening myself up for pot shots from Sanskrit scholars for some errors in my method. My knowledge of Sanskrit is quite limited. But then this is my method, bugs included.
I took this portion of the manthra:
tát savitúr váreṇyaṃ
bhárgo devásya dhīmahi
dhíyo yó naḥ pracodáyāt Om
and wrote out the number of syllables in the words ( here is where there can be some mistakes )
That came to: 1 3 3 2 3 3 2 1 1 4 1
I took a little bit of liberty and rewrote the sequence as : 1 3 3 2 3 3 2 2 2 2 1
Next task is to map it to the Arohana/Avarohana.
Start counting the numbers in the above sequence. When it reaches 12, that is the Arohanam/Avarohanam boundary.
So we get:
Arohanam: 1 3 3 2 3
Avarohanam: 3 2 2 2 2 1
These numbers are interpreted as the number of semitones between swaras. ( e.g. number of semitones between S and R1 is 1 and R1 and G3 is 3 ). That is the reason for counting up to 12 ( since there are 12 semitones in an Octave ).
For example: In Arohanam, Start with S, the first number is 1, so the next swara is R1. The next number is 3 which maps to G3. And so on. And we get the following scale.
gAyathri
Arohanam: S R1 G3 P D2 S
Avarohanam: S D2 P M1 G2 R1 S