Found this nice layout of the harmonics on a guitar fretboard, and noticed it is identical to the wave-forms I've been using to try to work on the Goldbach Conjecture and other problems with prime numbers/divisibility.
I find it amazing that the physical phenomenon that we hear as music is essentially just waves of tones/frequencies that directly relate to the divisibility of integers. I've always liked the quote: "Music is the pleasure the human mind experiences from counting without being aware that it is counting." (Gottfried Leibniz). With this layout of the harmonics, you can easily see the symmetry that arises when multiple waves are overlapped.
Why does that matter? Well, I guess it depends on your perspective of our universe... is it infinitely divisible (yielding smaller and smaller particles as you get smaller and smaller, never reaching a "smallest" particle) or is the universe finite (if so there would have to be some "smallest" particle, from which all other matter is created)?
If finite, then each larger and large particle could possibly be defined in terms of these "smallest" particles. However, there could be some order to the crazy quantum mess that we currently understand to be random. Look under the red domes in the picture above... when all of the waves are overlapped, and their wave-lengths are not coinciding, it looks pretty chaotic, but once you zoom out, you can see that the apparent chaos is actually just a small portion of a fully symmetric structure.
If the universe is truly infinite, and infinitely divisible, then questions of continuity and differentiability come into play. Most of our physics is contingent upon equations involving limits and infinite sums, which would require this infinite divisibility. But we can't ever really know at the smallest or largest scales how "accurate" our math/science is.
I believe the same symmetries that exist in music are also present in mathematics (discrete and continuous), and that it is those symmetries which we have detected as reproducible patterns in our physical world (yielding functions and formulas based on our observations). We may not have the exact formulas or functions to yield perfectly accurate results, but at the same rate, our approximations of objects like spheres and circles would never come close to the "real" shape, which can't exist in our universe as we understand it - but even though the shape can't physically exist, we can figure out an exact formula for that shape to base our approximations on.
It is the same with the laws of physics. Our formulas and functions are just trying to explain the perfect shape that we see should be there, but that we may never acheive due to our finite limitations.
I wonder if Music Theory has ever been directly applied to quantum mechanics and particle physics? Sounds like a blog for another day... will do some research and see!
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