Truthfully, I don't know what you mean by "it's". What is?
You're making me dig into the cobwebs of my memory here (which I've frankly been doing all along), and I don't remember the formal name of the branch(es) of math and formal disciplines we're talking about, and honestly it's too early in a long day for me to dig my books out and look them up. I do remember that on the computer that it deals a lot with non-linear dynamics, neural networking and computer constructs called cellular automata (sp?).
The point is, this is another one of the many cases where people have a ton of pet theories (I've had a few of my own over the years too) where the theories are really just the individual's way of filling in voids in their personal knowledge that are not voids in the actual achieved knowledge of man, it's just that the number of people that learn about it is smaller because it's not taught until well into college, and even then only in certain majors.
And yeah, you're going to find some easy mathematical relationships all over mom nature where things fall on multiples of some base values (which is really all "harmonics" are.) But that's usually because that just how math works, for lack of a better way of putting it offhand. From quantum energy states to the vibration of guitar strings to the orbital mechanics of the planets, harmonious patterns can be found. That's mathematics. But just as equally, so can non-harmonious patterns and values, and to ignore those and single out the harmonious ones ans something more important, because the human brain tends to find those as more attractive is to ignore the true nature of most of the world around us.
Here's an analogy; we tend to be attracted to the perfect mathematical shapes and solids of the Greek philosophers; squares, circles, triangles, cubes, spheres, etc., and tend to see them and admire them when they occur in nature, and they do occur. But the vast majority of the universe does NOT conform to those basic geometric shape but rather tends to have a more chaotic form to it, and to ignore that far more complex nature is to ignore the majority of reality.
Similarly there are simple harmonies in nature, and we find those harmonies very attractive, because that's how our brains are wired and trained. But there's so much more out there above and beyond those simple harmonies that swamp out those harmonies when one considers the whole of the truth, that one can pretty quickly see that those harmonies are only special cases within how nature operates and not the basis on which it operates. It's like whole numbers or integers (1,2,3,4, etc.). They are very attractive and easy and do occur in nature, but on the whole, nature tends not to operate in integers, but rather in more irrational values.
So when a few of Jupiter's moons and some of the planets orbiting the sun do fall into a mathematical pattern of some type that just so happen to mathematically resemble in some way other aspects of nature like the harmonies of sound or of waves on the ocean, that's going to happen, sure, because that's joust how the mathematics work and how our brains tend to want to organize things. But there are more cases where the math does NOT work that way than where it does, and we cannot make broad statements or conclusions about laws of how things work by ignoring the majority and focusing only on the attractive exceptions.
G.
The behavior is already fairly well-documented in many books, journals and papers. I suggest that you might want to start out with the book "Artificial Life" by Steven Levy. It dates back to 1992 so it's not a new book (though I have not read any later editions which probably have updates), but that just goes to show you how matured the knowledge is by now.
