Universal in the sense that a number of rocks or a number of sheep can be doubled just as a frequency can?

Yes thats what I meant, the doubling of frequency. It might seem trivial but the fact that doubling frequency sounds "right" to humans is actually quite interesting. Why does it sound "right"?

Interference is most of the answer. With frequencies f and 2f you get the smoothest interference patterns, even if the tones have a lot of harmonics. This applies reducingly to increasingly fractional ratios.