I haven't found an introduction to music theory that makes sense to me. I vaguely understand that complications arise because we want nice harmonics, ie frequencies whose ratio is a "nice" rational number, such as 2/3 or 3/5 or so. But our chosen notes should be invariant under doubling of frequencies ("shifting by an octave"), because that's basically the same note. The problem then is that roots of 2 are irrational…
If you're trying to learn music theory by thinking about the mathematical relationship between frequencies, you are severely overcomplicating things for yourself. I have a tendency to do the same thing. What question are you trying to answer with what you just wrote?
I guess you're right. I was trying to understand why it's so complicated, and how one could express it in a simpler manner (that refers to the underlying reality, namely frequencies).