I don’t think that there is one unification theory or if there is one, I’m not familiar with it. I think you would be very interested in Set Theory applied to music. It’s a very popular subject among music theorists. Reading about Nicolas Slonimsky may be a good starting point. Some people have developped tools to think about scales, modes, harmony and everything you can think about using mathematical tools.
There must be many different ways to code scale rotation in Sonic Pi. It is tricky to do ring manipulation in Sonic Pi but it’s definitely possible as highlighted by @samaaron himself here : Rings.