We will need to understand few other mathematically relevant points before we are able to understand the detail mathematics of 22 Shrutis. Pythagoras had worked out his own scale of notes called as 'Pythagorean Octave'.
As he was a Mathematician, his method of finding the positions of notes was simply a cycle of Panchams which are called 'Pure fifths' in the West.
When Shadja has a frequency of 100 Hz, Pancham can be found only and accurately on 150 Hz. Progressively, he found further notes at 50 % addition of previous notes till he completed his octave.
As, such a Pancham is also accurately judged by the brain, this is not only a mathematically elegant system, but also one of the easiest to tune by ear. (Refer to following table)