@@waz1yat time of viewing you only had 4.5k views and 1k subscribers. But the quality was so good I genuinely misread it to be 45k views and 100k subs. At any rate, your channel will get there soon if the quality stays at this level. Wonderful video
I'm working on a video about synthesis methods and in it I talk about FM synthesis, but I didn't want to go into bessel functions because it would have made it way longer. But this is a perfect resource to point people towards, because what you're doing in the first half is exactly how you calculate the sidebands in FM synthesis. I'm also a physics enthusiast so I love seeing how these kinds of mathematics relate to areas in physics. Awesome work! Also, I'd recommend working on your annunciation, and if you can, put a compressor/expander on your vocal track. It helps keep the volume in a consistent range and makes it easier to listen to on different kinds of speakers, especially if there's noise around.
The connection between drums and qm is probably just be in their differential equation. One way we were taught to visualize electrons (after that no one bothered) was to imagine a spherical membrane which is struck by something. the pattern we get is then projected onto the sphere so the high amplitude parts are more dense on the sphere. This doubles as an insight into the probabilistic nature of the equation as well. Also not really a major issue but a small nitpick i had was you just mentioned the zeroeth order bessel function directly. you could have first explained the different types of bessel functions (crying in second kind) Besides that great video. I didn't know about vibrato and the musical stuff so that way a learning experience for me. Good luck and looking forward to your videos in the future.
If I had to pick what the coolest Wikipedia page would be, it would be "Vibrations of a circular membrane". That the solution for the drumhead are also bessel functions, just like the hydrogen atom, is just such a cool funfact
I play a few instruments and do some orbital analysis for my job. Today I found out that vibrato is mathematically related to elliptical orbits. It does start to make intuitive sense for vibrato. Vibrato is basically nesting one wave inside of the other, hence the whole sin(wt + e*cos(wt)) form coming out. The connection for the musical and astrodynamic case seems that this wave nesting is happening acoustically in one, and spatially in the other. It's still surprising to me that the humble ellipse can lead to such nonlinearity.
Hey I really like your exposition, could you do a video about UHF algebras, the way they’re classified by supernatural numbers and how they relate to physics?
I wouldn’t say there is much of an answer to the question of is there an intuitive answer to why these fields seem to have this seemingly random connection. Though from what I’ve understood, when you try to solve a problem, no matter how complex, you always try to strip it down to its most simple form; when you do such a thing seemingly random occurrence start to feel a little too familiar. I am still new to all this math, but from what I’ve gathered, usually what is deemed basic intuition is enough to solve ( a striped down version) of most problems, let it be simple motion equations of planetary objects, to heat distribution, to phenomena in biology. The solution that are being produced may not always make the best model, approximations can only get you so far before “chaos” takes hold, but it is hella interesting. I really liked the video!
2:57 My approach to the exercise: Say we have a sinusoid with argument a(t) and instantaneous angular frequency w(t). If a(0)=0 (no initial phase shift) we can approximate a(t) as: a(t)~sum[w(t)*delta_t] since the argument can be thought of as a sum of phase contributions from w(t) multiplied over little slices of time when w(t) is approximately constant. In the limit as delta_t goes to zero, this Riemann sum (with any nicely behaved, physical frequency) converges to an integral, giving us: a(t)=int[w(t)dt] which matches the equation given in the video. A cool corollary of this equation (which is shown implicitly in your video) is that frequency modulation and phase modulation are basically the same thing.
Oh btw, the Bessel function expansion of vibrato you showed also appears in a somewhat niche part of laser physics called Pound-Drever-Hall (PDH) laser locking. This is what LIGO uses to stabilize their lasers to detect gravitational waves. If you want to read up on it there's a paper called "An introduction to Pound-Drever-Hall laser frequency stabilization" by Eric Black that gives a good overview.
Very nice video. I only paid attention to Kepler’s Laws before (which can be proved by Newton’s Law), but did not look into the Kepler’s equation. Indeed, Bessel function is very important in engineering!
This is huge, You should musically analyse Rachmaninov's etude tableaux, He looped in time to ensure coherence within the piece itself as it's own defined unit. He also used a lot of this stuff to make his music through matrix transforms and he even included references to reality! He uses tempo shifts sometimes to alter perceived pitch and amplitudes. Kind of a pseudo solution to wave function collapse or us perceiving tonicisation
Oh yes, Negative harmony... Rachmaninoff It'll open doors in physics I think! Etude tableaux op.33 no.3 uses this to change tonicisation of an identical phrase right at the opening
@ His whole series is great. And he has videos of quantum harmonics and how those are built up and such which will explain why the probability distributions follow the same 'harmonics-laws'
What you say towards the end (16:15) about electron probabilities distributions in atoms is wrong in two ways at once: first, the probability distributions you show at 16:25 have nothing to do with electrons responding to where other electrons are; you get these distributions even for atoms with only a single electron (hey, the depiction of this picture even says this is about hydrogen atoms - which only have one electron!). And second, no, the probability distributions in atoms are not the same as the vibrations of the drum - they are described by quite different functions. Bessel functions are _not_ used for quantum mechanical description of atoms. (Rather, what is used are the spherical harmonics for the angular part of the wave function and Legendre functions for the radial part.)
only reason i clicked on this is because i drew the thumb nail as a technical concept yesterday based off imagining ideal geometry for the specific purpose
@@waz1y im pretty sure i have discalculia but i can intuitionally visualize wave ands geometric shape pretty quickly, and do most mental math pretty quick but as soon as i have to plot something or solve for more than one term equations dont stay still
Such fast 'vibratos' are physically not possible lol When you increase the rate of amplitude modulation (AM) from a “slow” vibrato (a few Hz) into the audible range, you’re no longer just modulating the perceived loudness but you’re actually imprinting a periodic envelope onto your carrier signal that has its own distinct spectrum. In other words, a fast amplitude vibrato essentially “smears” the energy of a pure tone (like A440) into a series of spectral sidebands. By pushing the amplitude modulation frequency into the audible range, you effectively “split” a pure tone into a set of sidebands. These sidebands can be arranged (depending on the modulation frequency and depth) such that they correspond to musical intervals like a tritone or even more complex chord-like structures. This is a fundamental property of time-domain multiplication (modulation) and its Fourier transform, and it’s one of the reasons why techniques like ring modulation and frequency modulation synthesis can produce such varied and surprising timbral effects.
If only you would speak more slowly and a more consistent volume, we could understand what you are saying. Why do you soften your voice at the end of each sentence, making your words almost inaudible? I'm sure I'd love this video if I could hear your highly intelligent explanations!
@@waz1y Cursive writing is a type of writing where you write words without lifting you pen from the paper. When written in a hurry, cursive writing just looks like a line with squiggles which looks kind of like a sum of sinusoids (think doctor's handwriting)
@shardulkakade9365 Oh thank you for your reply. Absolutely correct. I had papers that I printed from my C++ program, 20 years ago, but I think I have lost programming workspaces, and packed the prints away. I wish I had the equations I used to get some patterns. But I moved on and got older. I did not understand the Taylor functions or learn about Bessel Functions and I am so pleased you have found some of these patterns. My best one approximated to acawacawacawa if I remember .... I cannot find similar squirgles, whirgles in online image search....yet The graphing apps will probably prove fruitful, with poke-and- find techniques, if enough people get involved.
India has ancient buildings built to specifically amplify narrow frequency bands. Again someone here might come forward to spread some knowledge of detail????
Constantinople had the first university. It passed much knowledge to the west, via arabic scholarsand especially via Toledo in Spain. Pythagoras talked of the music of the spheres. Trigonometry is connected with these many topics.
why so little views? this deserves so much more
Thanks for the support!
Don't worry. It'll pick up soon
@@waz1yat time of viewing you only had 4.5k views and 1k subscribers.
But the quality was so good I genuinely misread it to be 45k views and 100k subs.
At any rate, your channel will get there soon if the quality stays at this level.
Wonderful video
I'm working on a video about synthesis methods and in it I talk about FM synthesis, but I didn't want to go into bessel functions because it would have made it way longer. But this is a perfect resource to point people towards, because what you're doing in the first half is exactly how you calculate the sidebands in FM synthesis. I'm also a physics enthusiast so I love seeing how these kinds of mathematics relate to areas in physics. Awesome work!
Also, I'd recommend working on your annunciation, and if you can, put a compressor/expander on your vocal track. It helps keep the volume in a consistent range and makes it easier to listen to on different kinds of speakers, especially if there's noise around.
Thanks, I’ll definitely work on that
The connection between drums and qm is probably just be in their differential equation. One way we were taught to visualize electrons (after that no one bothered) was to imagine a spherical membrane which is struck by something. the pattern we get is then projected onto the sphere so the high amplitude parts are more dense on the sphere. This doubles as an insight into the probabilistic nature of the equation as well.
Also not really a major issue but a small nitpick i had was you just mentioned the zeroeth order bessel function directly. you could have first explained the different types of bessel functions (crying in second kind)
Besides that great video. I didn't know about vibrato and the musical stuff so that way a learning experience for me. Good luck and looking forward to your videos in the future.
Thanks!
Pls don't stop makeing content, it is great! 🎉
Leaving a comment to help a fellow math guy! Great video
If I had to pick what the coolest Wikipedia page would be, it would be "Vibrations of a circular membrane". That the solution for the drumhead are also bessel functions, just like the hydrogen atom, is just such a cool funfact
I play a few instruments and do some orbital analysis for my job. Today I found out that vibrato is mathematically related to elliptical orbits. It does start to make intuitive sense for vibrato. Vibrato is basically nesting one wave inside of the other, hence the whole sin(wt + e*cos(wt)) form coming out. The connection for the musical and astrodynamic case seems that this wave nesting is happening acoustically in one, and spatially in the other. It's still surprising to me that the humble ellipse can lead to such nonlinearity.
JUst discovered your channel! Incredible videos!
Hey I really like your exposition, could you do a video about UHF algebras, the way they’re classified by supernatural numbers and how they relate to physics?
I wouldn’t say there is much of an answer to the question of is there an intuitive answer to why these fields seem to have this seemingly random connection. Though from what I’ve understood, when you try to solve a problem, no matter how complex, you always try to strip it down to its most simple form; when you do such a thing seemingly random occurrence start to feel a little too familiar. I am still new to all this math, but from what I’ve gathered, usually what is deemed basic intuition is enough to solve ( a striped down version) of most problems, let it be simple motion equations of planetary objects, to heat distribution, to phenomena in biology. The solution that are being produced may not always make the best model, approximations can only get you so far before “chaos” takes hold, but it is hella interesting. I really liked the video!
2:57 My approach to the exercise:
Say we have a sinusoid with argument a(t) and instantaneous angular frequency w(t). If a(0)=0 (no initial phase shift) we can approximate a(t) as:
a(t)~sum[w(t)*delta_t]
since the argument can be thought of as a sum of phase contributions from w(t) multiplied over little slices of time when w(t) is approximately constant. In the limit as delta_t goes to zero, this Riemann sum (with any nicely behaved, physical frequency) converges to an integral, giving us:
a(t)=int[w(t)dt]
which matches the equation given in the video.
A cool corollary of this equation (which is shown implicitly in your video) is that frequency modulation and phase modulation are basically the same thing.
Oh btw, the Bessel function expansion of vibrato you showed also appears in a somewhat niche part of laser physics called Pound-Drever-Hall (PDH) laser locking. This is what LIGO uses to stabilize their lasers to detect gravitational waves. If you want to read up on it there's a paper called "An introduction to Pound-Drever-Hall laser frequency stabilization" by Eric Black that gives a good overview.
great video! nice animations too. niceee
Thanks!
My week just got saved
My week just got saved by your comment.
Nice Work!
Very nice video. I only paid attention to Kepler’s Laws before (which can be proved by Newton’s Law), but did not look into the Kepler’s equation. Indeed, Bessel function is very important in engineering!
Love those animations. So cool.
Can you translate the video into brainrot? My puny mortal brain cannot comprehend all the squiggly lines and big words. Thanks❤
That’s a crazy thing to say 😭😭😭
This is huge,
You should musically analyse Rachmaninov's etude tableaux,
He looped in time to ensure coherence within the piece itself as it's own defined unit. He also used a lot of this stuff to make his music through matrix transforms and he even included references to reality! He uses tempo shifts sometimes to alter perceived pitch and amplitudes.
Kind of a pseudo solution to wave function collapse or us perceiving tonicisation
Oh yes,
Negative harmony... Rachmaninoff
It'll open doors in physics I think!
Etude tableaux op.33 no.3 uses this to change tonicisation of an identical phrase right at the opening
Really nice!!
I think you're really going to want to see Richard Behiel's videos for some of the connections you mention.
Especially his video on spinors.
I just watched it, didn't understand everything, but definitely helped with understanding quaternions. Thanks for the suggestion!
@@waz1y quaternions are spinors. They're all the same thing. Look at geometric algebra
Yep, that's what the video helped me understand
@ His whole series is great. And he has videos of quantum harmonics and how those are built up and such which will explain why the probability distributions follow the same 'harmonics-laws'
3:04 The expression for the instantaneous phase is wrong, \int{440+12 \sin{12 \pi t}} = 440 t - \frac{\cos{12 \pi t}}{\pi}
9:35 I think you can ad a transmissionline loudspeaker enclosure here as well.
Very nice explanations however, constitency in the notations is also important
The audio at the start felt like I was encountering an eldritch horror, or something deeply wrong ngl
mhm, it is pretty scary
I was hearing the embodiment of frequency modulation
but the vibrato doesn't work when I shake the violin
You’re going to have to work on that bud
the intro was destroying my head since i am very used to identify notes by hearing them
I'm interested to know how you created all the animations.
I think probably manim
yep, manim
Nice, did you use manim?
yep 👍
What you say towards the end (16:15) about electron probabilities distributions in atoms is wrong in two ways at once: first, the probability distributions you show at 16:25 have nothing to do with electrons responding to where other electrons are; you get these distributions even for atoms with only a single electron (hey, the depiction of this picture even says this is about hydrogen atoms - which only have one electron!). And second, no, the probability distributions in atoms are not the same as the vibrations of the drum - they are described by quite different functions. Bessel functions are _not_ used for quantum mechanical description of atoms. (Rather, what is used are the spherical harmonics for the angular part of the wave function and Legendre functions for the radial part.)
fire video 🔥🔥🔥🔥
My hero Wazly!
Do not fear, for I am here!
only reason i clicked on this is because i drew the thumb nail as a technical concept yesterday based off imagining ideal geometry for the specific purpose
Woah, that’s a crazy coincidence! The thumbnail btw is the sum of the (1,1), (1,2) and (1,3) modes of vibration for a drum surface
@@waz1y the shape i was thinking was something like eulers constant or harmonic series but the thumbnail is what i drew
@@waz1y im pretty sure i have discalculia but i can intuitionally visualize wave ands geometric shape pretty quickly, and do most mental math pretty quick but as soon as i have to plot something or solve for more than one term equations dont stay still
Such fast 'vibratos' are physically not possible lol
When you increase the rate of amplitude modulation (AM) from a “slow” vibrato (a few Hz) into the audible range, you’re no longer just modulating the perceived loudness but you’re actually imprinting a periodic envelope onto your carrier signal that has its own distinct spectrum. In other words, a fast amplitude vibrato essentially “smears” the energy of a pure tone (like A440) into a series of spectral sidebands.
By pushing the amplitude modulation frequency into the audible range, you effectively “split” a pure tone into a set of sidebands. These sidebands can be arranged (depending on the modulation frequency and depth) such that they correspond to musical intervals like a tritone or even more complex chord-like structures. This is a fundamental property of time-domain multiplication (modulation) and its Fourier transform, and it’s one of the reasons why techniques like ring modulation and frequency modulation synthesis can produce such varied and surprising timbral effects.
Beautiful
Young Sheldon’s test
If only you would speak more slowly and a more consistent volume, we could understand what you are saying. Why do you soften your voice at the end of each sentence, making your words almost inaudible? I'm sure I'd love this video if I could hear your highly intelligent explanations!
3:50 brooooo
.....and cursive calligraphy has equations which are variations of these forms......
What's cursive calligraphy?
@@waz1y Cursive writing is a type of writing where you write words without lifting you pen from the paper. When written in a hurry, cursive writing just looks like a line with squiggles which looks kind of like a sum of sinusoids (think doctor's handwriting)
@shardulkakade9365 oh I see, so I guess it can be described mathematically with some of the Fourier stuff I mentioned in the video?
@@waz1y Yes
@shardulkakade9365
Oh thank you for your reply. Absolutely correct. I had papers that I printed from my C++ program, 20 years ago, but I think I have lost programming workspaces, and packed the prints away. I wish I had the equations I used to get some patterns. But I moved on and got older. I did not understand the Taylor functions or learn about Bessel Functions and I am so pleased you have found some of these patterns. My best one approximated to acawacawacawa if I remember .... I cannot find similar squirgles, whirgles in online image search....yet
The graphing apps will probably prove fruitful, with poke-and- find techniques, if enough people get involved.
This relate to string theory?
Not that i know of… but it’s possible there’s a connection
@@waz1y vibrating strings as well
ibn sina said sounds and math are connected
yeah, music has a lot of interesting and unexpected connections all sorts of fields
India has ancient buildings built to specifically amplify narrow frequency bands. Again someone here might come forward to spread some knowledge of detail????
@@kateknowles8055 ISTANBUL? WTF ARE U TALKING ABOUT?
Constantinople had the first university. It passed much knowledge to the west, via arabic scholarsand especially via Toledo in Spain. Pythagoras talked of the music of the spheres. Trigonometry is connected with these many topics.
So that's what the python program was for.
Yes
WTF no offense, you explained the FT in few sentence which i wish i heard from many books and many of my teachers
Very nice video, but I think you should take more time to explain and also go slower, a bit hard to follow your train of thought.
Some of my friends also told me that, so I’ll definitely work on it in the future 👍
Multiplication connect music, astronomy, quantum mechanics, accounting, painting, engineering, biology… what a stupid clickbait!
Blame AS, Artificial Stupidity !