The full music of Fourier Elise is here: kzfaq.info/get/bejne/sNdjZcV62sqXf4E.html And to hear me Fourier-roll you with more circle music, you can subscribe to my Patreon: www.patreon.com/posts/fourier-astlise-103232956 Oh, and of course a free way to support my channel (and do something positive for your brain!) is to head to brilliant.org/MarcEvanstein. Literally just clicking and exploring helps me out.

2:58 You just had to didn't you...

Fourier Elise

The Steve Mould reference is so good.Completely out of the blue, but a perfect fit.

That random angle one looks like he's having so much fun

"Thanks for all the circles, Beethoven" - Elise

Ok, now do through the fire and flames.

2:59 Fourier rickroll

I wish you showed the entire traced path as a shape.

this is something that inspires me to learn math

5:05 Turn Beethoven into Chopin with this One Simple Trick

Oh this is *almost* what I've been hoping for. I was hoping you'd find a path such that your speed-based approach of placing notes happens to match the rhythm too

this is SO SICK!! i love the wobbly elise

Theres an old video about someone converting all sounds in songs into a midi piano, or at least thats what I think they did, I'm not too familiar with music. But the thing is, in the video, the recognisability of the lyrics are maintained only if you are familiar with the source material, otherwise you can only tell there is 'speech', and thats only because I was looking to hear speech I suppose... I suspect a similar thing could be happening here, the more you've heard Für Elise the more some of your experiments will sound like Für Elise.

Your later pieces are what you get when a mathematician jazz pianist is asked to play a classic

"Fourier Elise" was an excellent, excellent pun.

Please PLEASE make a piano concerto using circles, that would be insane.

Fascinating and very original take on Fourier analysis. It brings mind that the ancient Greeks and later Ptolemy were trying to do something like this with the observed motions of planets in the sky. The planets appear to move at variable speeds and even exhibit retrograde ("backwards") motion. The ancient astronomers built complex models of epicycles (like these) to characterize what amounted to a complicated recurring wave of planetary position. Following the Copernican Revolution, which described planetary motions in terms of gravitation and elliptical orbits, the Ptolemaic epicycles came to be derided as a scientific dead end. But it looks like the ancient astronomers dimly sensed what Fourier formalized, and this video illustrates.

I know a microtonal scale when I hear one

3:55 “Das Lied, das nie endet” …or “The song that never ends” I knew learning German would pay off one day.

At one point it honestly sounded like Liszt wrote Für Elise

Sometimes it sounds like "La Campanella"

This could be a backround music generator in a game!

“A sort of Fourier Elise” Jail. Now. You.

This is actually one of the most well made and just plain cool videos I have seen on youtube. You deserve way more subs!

Utterly fascinating. Your channel is a gem. Thank you for this

This certainly was a circle video of all time

Your videos bring back curiosity and enjoyment in my life. Thank you!

That was mind-blowingly awesome!

You've just made your way into my lessons over polar functions.

"...a kind of Fourier Elise, if you will..." I will not! I refuse! How dare you! (great video)

Bagging a Brilliant sponsorship this early is a big achievement in my opinion! Keep it up man, this channel's gonna go viral, I can feel it.

_If it can play Fur Elise, then it definitely can play Rush E._ Edit: MOM IM FAMOUS

ABSOLUTELY need an ambient album based on the pulsing circles

This is glorious. Having owned a lot of sequencers, working in a lot of different ways, I can fully see this kind of thing being included alongside things like Euclidean sequencing in future machines.

Absolutely incredible! The final part where the drones pulsate in a weird way which is still somehow coherent to the density of piano notes being played, sounds fantastic. That concept would be great for like, a soundtrack or a sound design for something. Idk if you're into electroacoustic music but that feels like something like it. Analyse, modify, resynthesize!

This is the perfect balance of nerdiness and musicality.

I like seeing that between the high and low notes instead of appearing on the peak they’re on the way up and down from them

Fascinating video and channel as a whole.

"He's gonna be a mathematician one day or another" "No, he's gonna be a musician!"

thanks for your videos ! youre a genius!

Would love to see a version with more of the song included, definitely would not envy you having to optimize your circle rending code for potentially hundreds of circles though

This video revived my intrests❤

Absolutely brilliant! Please release the code for us to create our own!

This is an amazing video, so interesting and well done!

Upload three theme and variations as it's own video!! This was mesmerizing

This is amazing. I love this project and want to see you do more. One thing I'd like to see: - If the pitch of each note is tied only to the radial distance from the origin r, surely we can use the angle theta in some musical way too - For example, could we play rhythm (e.g. crotchets) using the angle theta like a metronome to keep time? And what would the result look like when imposing this constraint for Fur Elise? - Taking it further, what would your animation look like if you took the melody (r) and more complex rhythms (theta - e.g. hihat part) together? Could we see any patterns that point towards whether a song is catchy or not? (would love to see this with the introduction to It Runs Through Me by Tom Misch)

As soon as you added the extra notes between the originals, I already could no longer make out the source tune.

The flowing variation made me think of that crazy piano breakdown in Hedwig's Theme. I bet that would be a fun song to do with circles.

This is Underrated.

Next level unlocked 🎉 - remarkable 👏 This should be the type of method used to generate background music in sci fi tv shows. Would feel more realistic.

it took me a second to realize I was rickrolled, but props to you, my guy

Oh my gosh, you could make such ENGAGING installations using the pulses and exporting the piano line to a MIDI controlled piano with the visuals displayed. I'd seriously consider making that happen!!!!

Beautiful!

This. Is. Amazing.

Fascinating.

Spectacular

That fade to white almost killed my retinas :)

Can you do a video about the harmonic relationship between planets in our solar system?

There should be a VST for this, I want to use this in my DAW

>circle >can it... >Yes Fourier Transforms Can Do It

7:11 ok now I need the sound file with just the component circles! It sounds so beautiful and ominous...

Great video! ❤ Can you continue with Bach?

"What music do you like?" "That's not an easy questioni to answere... How familliar are you with FFT and Circles?"

fourier series was one of my favorite electrical engineering topics + i love experimental music theory videos (you even guessed the exact 3blue1brown video i had in mind at the start). anyways, it felt like i fell right inside the target audience for this video LOL

ngl the droning sounds gave me an idea, think as soon as I can imma tinker with it.

I took a course in the math and physics of music in college many years ago at the same time I was studying programing. Learning Fourier analysis was mind bending. If I'd had python and modern computers, this is the path I'd have taken too. Because I too hear music as geometric shapes. Mostly two dimensional, like these, sometimes in 3D, and very rarely and most powerfully in 4D.

Thinking about 1/f noise as a composing tool, it makes sense that a piece with the same "spectrum" as Für Elise would work as well, even if the fine details were altered. I think the patterns of big and small movement in music can make it pleasing no matter what exact points they hit along the way. Ok, let me try to explain 1/f noise. I will inevitably get it wrong, but since this is the internet I'm sure someone will correct me. ;) When analyzing the spectrum of a waveform, you can represent it as a function that gives an amplitude value for each frequency f - so a melody with slow, gradual, scalewise movement will have a higher amplitude in the low frequency range, creating a downward-sloping curve. A fast wiggly melody with big leaps back and forth will have a higher amplitude in the high frequency range, creating a flat or upward-sloping curve. Taking the square of the amplitude, you get a "power spectrum" which is useful for some mathematical/physics reason. There's a popular opinion that most music follows a 1/f curve in its power spectrum. So if one cycle every four bars represents f=1, then one cycle every two sixteenth notes represents f=12. Did I get that right? Maybe... Anyway the idea is that to make nice music, the power at f=1 should be 12 times the power at f=12 - in both cases the power is proportional to 1/f. Which generally leads to music that flows smoothly most of the time but occasionally makes some exciting dramatic leaps. Some composers have tried to generate music with noise (i.e. randomish values) that fits the 1/f frequency curve. Maybe Mark even did that in a previous video, I should check. :D Being full of arpeggios, I imagine Für Elise has a flatter curve than 1/f... I noticed in the visualization that a lot of the circles are the same size. Anyway, we already know it sounds good, so it makes sense that a piece with the same frequency curve but different specific notes would have the same vibe.

this reminds me of the time i saw a tesseract in my living room on DMT

What determines when it plays a note?

I'd love to see a version that controls the tempo of the beats, along with the note values. You have already made that speed version to change tempo, and maybe that could work, if you can solve for a path that speeds up and slows down to accommodate quarter, half, etc. notes.. Another option could be to make use of the currently-unused angle of the point from the origin. You could use radial lines from the origin as thresholds, and each time the dot crosses the next line, it plays the next note, perhaps staying in the close half of the wedge for a sustain, and waiting in the far half of the wedge for a rest.. I think that could make for a much more dynamic set of songs that you could play. As an aside, for my own preference, I think that only crossing in one direction (i.e. circling the origin in one direction) is much more pleasing than bouncing back and forth, or randomly, and allows for that sustain/rest idea.

In fact an old computer fan played endlessly the straight 1st 12 bars in "Für Elise" without the repetition we can see in the score. If you could reproduce that in circles it will be great. It's assumed Beethoven translated into music notes the tinnitus que suffered from.

The pentagon or pentacle is the associate of the harmonic series, Fib. series, and Fl. analysis. That should inspire something.

wow I need this as a DAW tool

Very nice!

You should overlay a musical grid, where we can de the size and shape of a note and how they are connected in space

This creative approach will give rise to a completely new paradigm, driving a paradigm shift in music theory. In the past, traditional composition methods and music analysis techniques only focused on the surface level of music, and the newly generated music often merely repeated the source material, with only superficial connections. However, by applying the concept of Fourier decomposition to this circular mechanical system, we can truly realize the mathematical beauty of music and its remote variations-the output may sound entirely different, yet subtle and obscure connections can still be found. This marks another paradigm shift in composition theory, moving closer to the neuronal thinking and diversity of the human brain, representing a remarkable evolution.

I can definitely imagine an AI creating a series of circles, and remixing it.

I challenge you to write a sequence where the circles form a specific shape of something while also playing a decent sounding tune.

2:04 Octavarium moment

I would love to see a shepherd's tone on this!

So I would like to see simultaneous motions for songs played repetitiously in a Round.

3:03 aaaaah, got us.

The music being built up with the drones would be excellent film music.

6:35 the music from Bib Boo's Haunt in SM64 :D

Essentially you made a jazz version of Fur Elise

I love that "wonky" Fur Elise sounds like Scriabin

Thank you. More of this please. But think of the notes more of as a clock with the angle around the clock as the letter of the note. The right handed and left handed solutions. remember that Clocks are left handed when viewed face on and that DNA and Plants are right handed. Except like Venus possibly but that may be slowly correcting itself. The radius would then be the integer octave. Why construct it this way? Why construct the sky with polar coordinates but music with square coordinates? The transform needs to sing as the planets sing.

5:12 A "collection of pitches" is a wierd but fun way to name a music key

"Can you see where we're going with this?" No, in fact i have no idea what's going on, but it's all very pretty

I am thinking about this. Using methods like this could actually be used as composting assistance, at least that it could give you ideas how to score certain parts.

just barely taking a course for astronomy.. but pretty sure in it, forgot which big brain guy but with circles on circles were used as epicycles and fine tuned to match orbits of planets as closely as possible.(why later it was seen as inconsistent as the constant need to fine tune the epicycles to the orbit) and im pretty sure you can make any shape with ENOUGH epicycles. so as long as you get the math done for. again ENOUGH. like you mentioned it would go to very high number with a larger cycle. seeing that ya used the fourier series for the conversion makes me wanna study that now. thanks.

Map pitch to one dimension and tone length/duration to the second dimension to resolve curve ambiguity

The seven largest circles turned it into Debussy.

This is cool! Ideas: 1. add a Z axis to represent measures. Each revolution around the circle represents one measure. Each measure can then have its own discrete sets of circles. Keep at least part of each previous/next revolution on the screen (perhaps blurred or faded) for context. 2. Add more polar axes for additional voices and staffs. Differentiate with color or texture. If color, use various color maths when the lines intersect. 3. Support additional note subdivisions. In each measure, each note gets a slot. The time signature defines the grid. If a note is shorter than the bottom number of the time signature, subdivide the time slot. This should get you around the sampling problem. Just random thoughts. Anyway, cool stuff! Keep it up! Subscribed! Edit: see kzfaq.info/get/bejne/aLugm6Sr19-6oI0.htmlsi=XMDK55u4-6vcR_0p for the circular rhythm representation I’m talking about.

I felt the speed-based notes distorted it too much from the source, and once you turned that option on, it was on for the rest of the video

This sounds like a Fourier Transform with extra steps…

hello sir Marc I think it would work very well for Johann Sebastian Bach as well for example prelude 1 book 1 or prelude 2 book 1 from well tempered clavier you're amazing sir I have no idea how you all program this or do it

the fact you did that first before fur elise

the random angles one turned it into chopin lmao