[HN Gopher] How the physics of resonance shapes reality
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How the physics of resonance shapes reality
Author : dr_dshiv
Score : 45 points
Date : 2022-02-04 16:42 UTC (6 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| motohagiography wrote:
| This rabbit hole is part of why I got into eurorack/modular. It
| was to apply my musical ear to intuitions to help learn about
| waves and harmonics. There is a lot of woo around that crossover,
| but when I can hear the difference in a transform and then see it
| reflected on an oscilloscope or in a spectrogram, its easier to
| get a feel for what the constants and coefficients are supposed
| to do. (especially with the Maths module) A generation of kids
| playing with their parents' rigs and getting that feel may yield
| a new renaissance in physics in a couple of short decades. I'm
| just a hacker and a writer, and beneath what might be called an
| artist, but I have the sense that an emerging trend of popular
| quantitative culture is building momentum.
| nyc111 wrote:
| "Such a bump is the unmistakable signature of "resonance," one of
| the most ubiquitous phenomena in nature."
|
| If so then, physicists call "resonance" a "particle". Or what
| physicists call particles are resonances. But why? If you observe
| resonance call it resonance. I don't get it.
| p_noumenon wrote:
| It's still called a particle because that's a useful
| abstraction, and also keep in mind that correctly identifying
| it as resonance happened much later than people first started
| to use said abstraction.
|
| In reality, we know by now that there's no such thing as a
| particle:
|
| https://arxiv.org/abs/0807.3930
| peterburkimsher wrote:
| Does resonance work at other scales too?
|
| Say, perhaps, an audience waving their hands to the beat of the
| music? The muscle movements would then require pressure from the
| heart, which begins to beat synchronously as well.
|
| Also, what about very small respiratory particles; could they be
| resonated and "dance themselves to pieces" by using light or
| sound at the right wavelength?
| papavancato wrote:
| Very interesting!
| m-atoms wrote:
| If particles can be understood as resonances in a field then it's
| hard for me to understand "stable" particles. What keeps them
| around? My mental model for resonance and waves requires some
| kind of constant input energy to maintain the oscillations in the
| field which produce the particles. What am I missing?
| kurthr wrote:
| Part of the difficulty in that analogy is that we normally
| think of things as damped by some surrounding media. For
| particles (modeled as field resonances storing quantized
| spatially concentrated energy) the only damping is coupling to
| other resonances (e.g. other particles). The particles were
| created by those interactions and they be annihilated (or
| decay) into other particles depending on how those resonances
| couple. Often due to quantization, this requires multiple
| particles including photons to "transmute" and that combination
| tends to reduce the likelihood of the interaction. That's my
| intuition from 30 years ago, anyway.
| m-atoms wrote:
| This was the most helpful for me, thanks!
| evanb wrote:
| Resonances are like vibrations on a trampoline; stable
| particles are more like lumps in a carpet.
|
| Usually what keeps particles stable is that they carry some
| quantum number(s) that is/are conserved, and no lighter
| combination of particles can be made with that combination.
| kurthr wrote:
| The observables are conserved, but I guess I always thought
| of the internal complex quantum states spinning away on their
| own.
| klyrs wrote:
| Superconductors can theoretically produce perpetual motion:
| once you set up a supercurrent, it will keep going forever. The
| caveat being that the electrons that are to move perpetually
| cannot do work of any kind*. That is, the field generated by
| the supercurrent cannot be interacted with.
|
| Likewise, an ideal LC circuit made of superconducting material
| can theoretically ring forever, provided "nobody hears the
| sound". So, given my understanding of the physics, nature does
| not forbid stable perpetual resonances (though engineering
| constraints may forbid even microscopic perpetual resonators).
|
| * When people talk about "perpetual motion machines" they tend
| to want to extract energy from them. That's folly.
| dr_dshiv wrote:
| "Resonance underlies aspects of the world as diverse as music,
| nuclear fusion in dying stars, and even the very existence of
| subatomic particles."
|
| I learned recently that the harmonics of consonant musical notes
| have aligned frequencies. Meaning: the most consonant notes
| produce the most resonance between the strings. For example, two
| strings at a consonant interval of a fifth (3:2) have harmonic
| resonance every 3rd and every 2nd harmonic band. This is much
| easier to show with a visual of the spectrograms:
| https://docs.google.com/presentation/d/1cdRfvPtek44rH8k2GpMV...
|
| As oscillations of neurons in the brain will also show this
| harmonic structure (due to the frequency following responses
| [1]), consonant notes may also produce the most neural resonance!
| But, we don't have the ability to measure and test this
| hypothesis yet.
|
| [1] Bidelman, G. M., & Momtaz, S. (2021). Subcortical rather than
| cortical sources of the frequency-following response (FFR) relate
| to speech-in-noise perception in normal-hearing listeners.
| Neuroscience Letters, 746, 135664.
| systemsignal wrote:
| Why would we not have ability? Is it not in the same area where
| implants typically are? Could try in primates potentially too
| _moof wrote:
| This gets a little more complicated when you discover that not
| all fifths are the same interval, as any string player will
| attest. Violinists playing double stops have to use ever-so-
| slightly different finger positions than they do when playing
| single notes. And instruments with fixed tuning like pianos use
| something called "equal temperament," which isn't quite the 3:2
| perfect fifth.
| powersnail wrote:
| Perfect fifths are a bitch to play on the violin indeed. You
| need to cover two strings with one finger, which needs to be
| placed at just the right angle. And it's very obvious when
| you are slightly out of tune, unlike single notes.
|
| But pianos don't exactly use equal temperament, either.
| There's a curve applied to equal temperament, which makes
| everything sounds more in tune.
|
| At the end of the day, musicians follow their ears. Whatever
| sounds the best is the most important.
| p_noumenon wrote:
| And thank god for equal temperament, because the last thing
| you want is perfect intervals that don't leave any space for
| proper resonance.
|
| <<In general, the interference equation can be used to
| measure resonant amplitudes for any musical interval under
| any temperament or octave division. This equation tells us
| that minimum resonance occurs at the fourth root of an octave
| (or square root of twelve) while maximum resonance occurs at
| the cube root of half an octave. Taken together, these
| results offer clear evidence that harmonic interference
| balances naturally around 12 as the most rational and
| harmonic number possible.>>
|
| <<We find here the most amazing thing. The arithmetic mean
| converges toward PI, or mathematical constant p [?] 3.14159,
| located in the middle of the curve. We further find this
| point in the distribution curve to be equal to Unity (or 1)
| when the domain value X = 12. This is significant because
| twelve is the square root of 144, the value shared by both
| harmonic and Fibonacci series in a 12-step octave. Squaring
| each of the table values and dividing by twelve confirms that
| 12.02383 [?] 12 is the point of balance between foreground
| and background.
|
| The significance of twelve as a point of balance in the
| octave interference pattern is proven further by plugging it
| into the equation, confirming the curve height equal to Unity
| at the octave. But even more significant than this is the
| fact that plugging the square root of twelve into the
| equation results in the amplitude y = 5.0666. Care to guess
| what this number represents?
|
| It is none other than the y-axis amplitude for the golden
| ratio in an octave. Yes, the square root of twelve in the
| Gaussian interference pattern occurs precisely at Ph, right
| in the "cracks between the keys" of a major 3rd and minor 3rd
| in an octave. Just like the dense lattice region between a
| major 6th and minor 6th, the infinite golden ratio also
| provides an anti-harmonic proportion in the lower half of an
| octave. This occurs naturally at the square root of 12 (or
| fourth root of 144) in a 12-step octave.
|
| No matter how you do the math, both harmonic and Fibonacci
| series reach a harmonic balance with one another at n=12 and
| an anti-harmonic dead zone at n=[?]12. Division of the octave
| by twelve (not eleven, nineteen or any other number) is
| revealed here as a completely natural pattern produced by
| linear harmonics that are curved in pitch space by Fibonacci
| proportions as they converge to Ph. Could Gioseffo Zarlino's
| decision to divide the octave into twelve steps have involved
| some knowledge of this simple relation between harmonics and
| the Fibonacci series?>>
|
| <<As a surprising correspondence between music and math, this
| little trick reveals the Pythagorean comma accurate to 3
| decimal places. More amazing still, if we recalculate using
| the un-rounded arithmetic mean 12.02383 found earlier in
| place of 12, we obtain a slightly better estimate for the
| Pythagorean comma good to 4 decimal places. This bizarre
| associative property in the interference equation using the
| anti-harmonic golden ratio location of n=[?]12 proves the
| golden ratio is a physical property in the natural harmonic
| series and not some kind of error or "evil" in nature as
| portrayed by the Church. Vibration needs room to resonate in
| space and the Pythagorean comma created by the golden ratio
| appears to be just the right amount of room needed.>>
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