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Based on my understanding of music, math, physics, and even philosophy, I do not understand why the beauty of harmonic simplicity and strength between whole numbers is not discussed much at all when talking about intelligent design, the nature of nature, and what "it's" all about. It's not created by an outside entity or derived from some theories and special constants; it is simply a fundamental of mathematics, physics and nature by definition.

When "things" are more harmonic and work better together they have superior strength, power, and a logical reason to become building blocks in nature that rise to the top of form and function longevity.

Math and physics derive many more complex concepts beyond this through observation and pattern matching but it seems like harmonic quality is the foundation of it all.

At a minimum this seems to be true in our perceived world of 4d space-time reality and understanding of nature.

EDIT

Thanks for the great responses. I obviously need better terminology.

By “harmonic simplicity and strength” i meant high consonance between two frequencies (musical or otherwise) where the combined wave form has fewer peaks and valleys. In music the most consonant intervals are the octave 2:1, the perfect fifth 3:2, the perfect fourth 4:3 etc. As we continue on, more dissonance occurs which is used by musicians of course to create tension and repose in their songs. Much like a great book or movie, it modulates feelings, but I digress.

I certainly did not mean to imply that everything is a ratio of integers.

Proportion is just a low level fundamental. As we expand our constructs, functions and recursion bring much to the table as in circles, phi, pi, fractals, etc. When speaking of circles, though, we break into the realm of cycles, curves, calculus and infinite precision. A circle’s circumference and area are only as accurate as your precision of pi. Without infinity (underrated imho) a circle is just a many-sided polygon. It’s the old game of points vs waves, digital vs analog, pixels vs vectors, prickles and goo as Alan Watts would say.

I still feel there is something very fundamental in the known universe having to do consonant or equal frequencies (i.e., attraction: birds of a feather flock together). Feeling empathy, playing in a band, being in tune, perhaps even quantum entanglement to some degree (imagination is more important than knowledge; right, Albert?)

In a tug of war or moving a 5-ton rock, the power of a team is inherently based on synchronizing the components to work together in harmony, whether it is 1:1, 2:1, 3:2 … just try to keep the dissonance down.

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    What is "harmonic simplicity and strength"? If things that "work better together they have superior strength" are simply called "harmonic" then this is a tautology, and if such things are supposed to have small integer ratios to each other then this is simply false. Circles are "harmonic", but the ratio of the circumference to the diameter is π. This sort of "everything is a ratio of integers" mentality is ascribed to ancient Pythagoreans before they discovered the irrationals. It is not talked about much since then because it turned out to be too naive.
    – Conifold
    May 2 at 3:35
  • Harmonic series is a basic foundational nature of modern physics wave mechanics theory which determines the modalities of frequency domain and gives standing wave phenomenon which lies at the heart of forming quantized energy level of QM. But as Galileo observed long ago proportion alone is not enough, civil structure under proportional enlarge alone would collapse, that’s why our high rise building has a limit... May 2 at 3:43
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The harmonic ratios in music are a consequence of the fact that when you set up conditions to support a standing wave of frequency f (such as a string under tension or a closed or half-closed tube of air), it will also support two standing waves of frequency 2f, three standing waves of frequency 3f, etc.

For example if you pluck a string, the middle of the string vibrates back and forth with a certain frequency, say f. But at the same time that vibration is happening, there are two more vibrations going on around that middle point, so when the point at the middle of one half is up, the point at the middle of the other half is down, and vice versa. It's an S curve swapping back and forth. At the same time, there are three waves going on, each taking up one third of the string. When the middle of the first third is up, the middle of the second third is down, and the middle of the third third is up.

So the harmonic ratios are just a simple physical consequence of the way that vibrations work in a constrained system; it doesn't have any metaphysical or mystical significance, although the ancient Greeks thought it did. They probably got that idea from the Mesopotamians and/or Egyptians, along with geometry, arithmetic, astrology, and numerology.

The human mind is always searching for regularities and patterns, ways to regularize and unify what we know, to make everything fit into a single box. That's why the ancients came up with numerology, astrology, and the music of the spheres (which is the main application of their approach to harmonics). Another example is the Platonic solids. Plato thought that all matter was made of atoms in the shapes of the Platonic solids, and Kepler, who is famous for the three laws of planetary motion, spent a lot of time trying to fit the orbits of the planets into the Platonic solids. Aristotle decided that all matter was made of fire, air, water, and earth, and developed a sophisticated cosmology on that basis. He assigned the properties warm/cold and moist/dry to each material as an indicator of what proportions of what element they were part of.

However, physics has moved on from those early efforts. After Newton, people began to think that the universe was best explained in terms of rates of change and principles of conservation. Then quantum mechanics came along, and people started thinking that the universe is best explained with wave functions and probabilities.

So the reason people don't get excited about harmonic ratios any more is because harmonic ratios have come to be seen as just an accidental special case of something more fundamental.

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