[lelf]

The problem is that we use approximate with irrational numbers. Naturally they are all integer ratios.

In the perfect world you have e.g.:

+ C major scale: C D E F G A B C, where frequencies of all notes depend on frequency of note C (like, “fifth” from C is G and it's exactly 3/2 of C)

+ and D major: D E* F♯* G* A* B* C♯* … D (and depend likewise). But now G is not necessary equal to G*, but they are close. So here comes the idea of equal temperament where octaves are strictly 2:1 as they suppose to be, but all notes between are equally scattered (on log scale) in between.

So TL;DR: nowadays it's all approximation. You can do it perfectly, but only for one root.