I don't know enough about e.g. Indian ragas to say, but you can certainly derive plenty of other scales from exploring relations of the form (a/b)^c == (d/e)^f + error, for integers a-f, while trying to balance small a,b,c,d,e,f against a small error. Any such derivation can be clustered to a piano keyboard of sorts, obviously with a different shape. I remember doing this once (though I forget which for) and making a keyboard that looked much like ours i.e. mostly alternating black/white notes, but the number in each "group" of "consecutive" blacks was different, e.g. 3+4 rather than the 3+2 we all know.
