Can a Bunch of Circles Play Für Elise?

[@marcevanstein]

The full music of Fourier Elise is here: kzbin.info/www/bejne/sKKWY5V_qslmha8 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.

[@haarisarain5048]

Is there a program that lets me also use circles to make music?

[@RailsofForney]

OMG *“Fourier Elise”* is soo clever 😂

[@pridepotato314]

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

[@Alceste_]

I didn't get it. :c

[@official-obama]

@@Alceste_ if you ignore the lower pitched notes, it sounds like a slow rickroll

[@marcevanstein]

I did, yes. I will never stop being that guy.

[@Alceste_]

Crazy how just a note here and there made it unrecognizable to me. '-'

[@pridepotato314]

@@marcevanstein Well I guess I will never get this from any other... mathamusician

[@asdfghjkl1755]

Fourier Elise

[@Naeddyr]

I am 100% sure "Fourier Elise" came first, and the idea for the video came second.

[@awaredeshmukh3202]

LOVED that!!

[@davyzeradaspalmera]

Führer Elise

[@AflacMan13]

😂😂😂

[@dannous]

Best comment here!

[@Boxland_]

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

[@eliaskirkwood]

So true

[@thomicrisler9855]

I cracked up so hard at it. xD

[@NotGabe001]

As a Steve Mould viewer, I didn't get it

[@eliaskirkwood]

@@NotGabe001 at 3:23, evanstein talks about replicating what he's explaining on the Disneyland teapots ride he then mentions Steve Mould because that's the kind of funny science Steve usually does I sent this video as a video idea on the Steve Mould discord server but i never got a reply 😥. Perhaps he will see it someday !

[@ddogg9255]

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

[@Somerandomjingleberry]

Me when I anthropomorphize abstract symbols (contextualizing what amounts to “noise” into something we can understand is fundamental to the human experience)

[@pianovii3350]

Bad apple time?

[@Unfocused_Gamer]

Bad apple time.

[@tibetje226]

Already done lmao, (not the music, but the video). The music Version would need some context with the video.

[@LunaticLacewing]

@@tibetje226we need the music tho

[@kaarcher]

Why do people like bad apple so much, it's an awful song lmao

[@e-gaysports3895]

Oh absolutely

[@trippstreehouse]

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

[@gamedog9542]

Agreed

[@korok2619]

there are tons though

[@murfburffle]

"Thanks for all the circles, Beethoven" - Elise

[@daan804]

Ok, now do through the fire and flames.

[@Tsaukpaetra]

Should only need a few million circles, surely...

[@multilk6399]

would it count if you split the song into progressions/circles for each separate instrument and then just charting them separately?

[@daan804]

@multilk6399 i guess, i mean, if you don't, then every instrument sounds the same as well, so it would just sound mediocre.

[@CalebTibster]

At the very least, we need the opening hammer-ons

[@storerestore]

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

[@Kram1032]

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

[@TYsdrawkcaB]

this is SO SICK!! i love the wobbly elise

[@Cyril29a]

It really is

[@johnchessant3012]

2:59 Fourier rickroll

[@unebaguette9745]

Shh don't spoil!

[@KasVrGtag]

Darn you spoiled it for me

[@bevengersio]

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

[@The_Scapes]

this is something that inspires me to learn math

[@kiwipomegranate]

"What instrument do you play?" "Math."

[@therandomguy1701]

Aight bet. After 10 years, reply to this comment if you learned math.

[@The_Scapes]

@@therandomguy1701 really thankful for this inspiring comment man, for sure 😏, already on my way 😁, I've already finished the introduction to complex numbers and other stuff

[@The_Scapes]

@@therandomguy1701 just be kind enough to remind me back

[@w花b]

​@@The_Scapesdaily reminder to learn math

[@jneal4154]

"Fourier Elise" was an excellent, excellent pun.

[@7thgeneration903]

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.

[@marcevanstein]

I know this phenomenon well! When I've made music/art out of mangled speech, it's often been really hard to tell how well someone who's never heard the speech will be able to make sense of it.

[@samsamson3315]

@@marcevanstein Oftentimes I can't even understand lyrics in the original song until I look them up lol. A related thing is the way in which expectations play a big part in what we hear (see: Mondegreens, "misheard lyrics" videos).

[@phyphor]

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

[@roytee3127]

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.

[@shadowfox1221]

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

[@sam_bamalam]

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!!!!

[@marcevanstein]

I definitely will. It's a great idea!

[@WarttHog]

Oh man, I bet lookmomnocomputer would love this idea!

[@BManOfficial1125]

5:42 Jazz Elise

[@elenacottica386]

Next one's rush E right?

[@romeolz]

I know a microtonal scale when I hear one

[@official-obama]

wasn't it snapped to the original notes of fur elise?

[@Dune4915]

​@@official-obama You didn't watch the whole video did you ?

[@official-obama]

@@Dune4915 uhh, i did? was he talking about the pulsing circles?

[@marcevanstein]

Ha ha! I can't remember if I mentioned it in a footnote, but in the final music with the pulsing circles, I was using a just scale, "rationalized" from the pitches of Fur Elise, using Clarence Barlow's method. Maybe I should talk about that sometime. I think it makes a big difference honestly

[@roytee3127]

(moved)

[@CrazedKen]

3:03 aaaaah, got us.

[@JoshuaWillis89]

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

[@AlanKey86]

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

[@ManekaAgarwal]

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.

[@awol_b]

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

[@LetsMars]

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

[@intranexine8901]

Yes it goes on and on my friend (:

[@TotallyDapper]

Some people started singing it, not knowing what it was

[@SidShakal]

and they'll continue singing it forever just because

[@milasjavellana]

Hey look. It Ended. Jk THIS IS THE SONG THAT NEVER ENDS

[@scrambledmandible]

ABSOLUTELY need an ambient album based on the pulsing circles

[@majapaja_]

It reminded me of chapter 11 of the half life alyx OST maybe check that out

[@4stringed]

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

[@vanhavirta]

This could be a backround music generator in a game!

[@katabatica]

That was mind-blowingly awesome!

[@dagamusik]

Sometimes it sounds like "La Campanella"

[@titush.3195]

Finally, a continuous extension of Für Elise

[@nologin5375]

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

[@phoenixshade3]

I was immediately reminded of 3blue1brown's Fourier analysis video, and was in the process of commenting about it when you mentioned it.

[@user-ss6fn3kj1u]

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)

[@danpreston564]

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.

[@rotatingcat1957]

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

[@luigidabro]

*Für

[@KaneyoriHK]

@@luigidabro Not everyone knows how to type that or can.

[@calford2001]

​@@luigidabro you still understood what that person meant tho, which means a correction wasn't necessary.

[@DiggyPT]

No it can't because it can't play more than one note at a time

[@luigidabro]

@@KaneyoriHK then it can also be replaced by a "Fuer"

[@kiligir]

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

[@carterrrrrrr]

7:27 this is an incredible method for writing horror movie soundtracks

[@shrewdagency6588]

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.

[@senacht]

Lends whole new meaning to the term “circular logic.”

[@reto8988]

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.

[@roytee3127]

The ancient Greeks and later Ptolemy refined the epicycles. Unfortunately, Newton et al had a much simpler and more universal explanation.

[@ale305z]

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!

[@bloodredflower4437]

At one point it honestly sounded like Liszt wrote Für Elise

[@mikeciul8599]

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.

[@andrewmalanowicz2207]

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

[@dyneeoh]

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

[@cosmiccowboy3442]

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.

[@RickyMud]

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

[@ferchrissakes]

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

[@gilmoses3777]

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

[@yoavattias2072]

First of all, I am so glad I found your channel. Your content is exactly what I was looking for :) And also: Imagine a ball with inner legs that pop out in response to specific notes within a melody. The legs are always oriented downwards, with each one corresponding to its own note. What path would such a ball take?

[@intranexine8901]

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

[@Ryuusei924]

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

[@aylabennett4781]

This is Underrated.

[@prasaddash5139]

This video revived my intrests❤

[@0hellow797]

It’s tough sometimes but vids like these keep me working and moving 👍

[@marcevanstein]

Aw, I appreciate these comments. It means a lot to me actually, because it takes so much effort to make videos like this and knowing it is motivating to other people is motivating to me!

[@0hellow797]

@@marcevanstein it all comes full circle lolol But thank u for spending the time and energy, producings not easy for sure ❤️❤️

[@Nguyengrays]

To play the full song, i think you'd need a really freaking big main circle. Because the main circle in which the other circles move form a loop, so a song or part of a song will stop and loop again at the point it starts

[@TotalDec]

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

[@SysOpQueen]

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

[@dredre6101]

when you took the first seven circles id like to hear what it would sound like if you kept the original rhythm of fur elise instead of the velocity one

[@michaelleue7594]

I imagine he didn't do that because it would just sound like Fur Elise with a bunch of offkey notes. Considering he said he likes using these sorts of transformations to make pieces that sound novel, that would probably seem boring to him.

[@RichardCharter]

I love that "wonky" Fur Elise sounds like Scriabin

[@phlosen7854]

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

[@Pooneil1984]

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.

[@brotherdust]

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 kzbin.info/www/bejne/aIbTmXSwp96Jprssi=XMDK55u4-6vcR_0p for the circular rhythm representation I’m talking about.

[@jamcdonald120]

0:30 I mean, yes? I saw 3b1b's video about drawing with circles. should be the same

[@jlfqam]

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.

[@ChrisChapin_chapes]

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

[@mikeciul8599]

This is the perfect balance of nerdiness and musicality.

[@tylerbakeman]

An alternative approach to this problem is by using “Trajectoids”, surfaces that are designed to roll along a specific path, periodically. In fact, you can create a 3d representation of the song Fur Elise- or any song- ASSUMING, the song doesn’t play multiple notes at once (then you’d need overlapping layers) *Again, Giving you a 3d representation for any song! Plus,, the math for this particular problem should only take a few steps (because what youre talking about is one of the easiest examples that can be generated).

[@tylerbakeman]

Also, having the extra dimension allows us to add another quality to each note- for example duration. If a rest is played, duration could map to 0, resulting in a cut to the origin. Anyway. Cheers

[@plashplash-fg6hd]

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

[@MerderMarderInMyHead]

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

[@Tferdz]

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

[@Addersea]

Interestingly, for me; I love process-based pieces and found the concept of generation interesting, but I was almost completely off-boarded at the point of using the cirlces to recreate existing music, and the idea of a new piece being created by filling in the gaps in the form. A little more interested when the rate of notes played was tied back in to the speed of movement, but where I'm really glad I hung-on was when the circles generated a their own tone based on their position in the cycle. That was really exciting. Reflecting on why, I think for me it was pushing towards the outcome becoming the core consideration that made me feel like the process was losing relevance. (Why have the circles instead of using the analysis to transcribe it into traditional western notation, for instance.) I feel like once the position of the circles directly played into the output more heavily (even if the pitches were manually predetermined), I was suddenly completely re-invested in what path the circles would take, what the process would output, etc. It felt a little less 'arbitrary', if that's the right word, for how the circle approach impacted the music over another approach. And that's given me a tonne to think about! All in all, another really interesting piece of work! Awesome job and thank you so much :D

[@marcevanstein]

Appreciate that you stuck around for it, and thanks for your thoughts! I had a similar feeling playing with the results; it was intellectually interesting to me the whole way through, but it was only at the end with the drones that it started to become musically really fascinating.

[@SimpPro101]

This certainly was a circle video of all time

[@gljames24]

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

[@rychei5393]

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

[@mcasualjacques]

there's the amplitudes of the harmonics but there's also the phases, so one could modulate/mess the phases of the sinewaves that become spinners

[@mcasualjacques]

the circles have a fixed radius because, it's the spectrum of the whole loop i think yes

[@marcevanstein]

Yes, that's absolutely true. And I think it's possible that the phases are even more important than the amplitudes in shaping the resulting melodic contours.

[@AidenOcelot]

This feels like it'd be amazing for procedural generated music

[@jasonspence]

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.

[@Falconer5752]

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

[@matthewkendrick8280]

What determines when it plays a note?

[@Mirinmaru]

When the point of the outer most circle intersects with with the edge of another circle I think.

[@HalfBakedHeroes]

The soul of Fur Elise.... He's a musical Necromancer

[@Bethos1247-Arne]

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.

[@phlosen7854]

That fade to white almost killed my retinas :)

[@bergercg]

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

[@PatGBass]

Fascinating video and channel as a whole.

[@portalsrule1239]

4:36 could you do this but ensure that the end point has 0 velocity at the time the note is played? i think that would make for a much more satisfying animation although i can imagine it would take a lot more computation

[@darkrai526]

that was the best ad for brilliant dude they better pay you extra

[@NeoNeko420]

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

[@dancoroian1]

This needs to be a plugin! Think of how many riffs and variations you could get on a simple theme...so many possibilities, without any AI or anything. Lots of fertile ground for inspiration

[@MrPomajdor]

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

[@HuxleysShaggyDog]

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

[@dextro808]

"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

[@perseushuffman855]

7:20 now that's what i call a late romantic piano concerto opening

[@AndrewWilsonStooshie]

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

[@Aucelons]

This would work beautifully on the Bach's Goldberg Canons (bwv 1087)