Can a Bunch of Circles Play Für Elise?
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- Опубликовано: 20 май 2024
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The full music of Fourier Elise is here: ruclips.net/video/zq32bIud3OM/видео.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.
Is there a program that lets me also use circles to make music?
2:58 You just had to didn't you...
I didn't get it. :c
@@Alceste_ if you ignore the lower pitched notes, it sounds like a slow rickroll
I did, yes. I will never stop being that guy.
Crazy how just a note here and there made it unrecognizable to me. '-'
@@marcevanstein Well I guess I will never get this from any other... mathamusician
Fourier Elise
I am 100% sure "Fourier Elise" came first, and the idea for the video came second.
LOVED that!!
Führer Elise
The Steve Mould reference is so good.Completely out of the blue, but a perfect fit.
So true
I cracked up so hard at it. xD
As a Steve Mould viewer, I didn't get it
@@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 !
That random angle one looks like he's having so much fun
Me when I anthropomorphize abstract symbols (contextualizing what amounts to “noise” into something we can understand is fundamental to the human experience)
2:59 Fourier rickroll
Shh don't spoil!
Ok, now do through the fire and flames.
Should only need a few million circles, surely...
would it count if you split the song into progressions/circles for each separate instrument and then just charting them separately?
@multilk6399 i guess, i mean, if you don't, then every instrument sounds the same as well, so it would just sound mediocre.
At the very least, we need the opening hammer-ons
I wish you showed the entire traced path as a shape.
Agreed
there are tons though
"Thanks for all the circles, Beethoven" - 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.
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.
@@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).
this is something that inspires me to learn math
"What instrument do you play?"
"Math."
Aight bet. After 10 years, reply to this comment if you learned math.
@@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
@@therandomguy1701 just be kind enough to remind me back
@@The_Scapesdaily reminder to learn math
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
It really is
5:05 Turn Beethoven into Chopin with this One Simple Trick
Please PLEASE make a piano concerto using circles, that would be insane.
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.
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
wasn't it snapped to the original notes of fur elise?
@@official-obama You didn't watch the whole video did you ?
@@Dune4915 uhh, i did? was he talking about the pulsing circles?
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
(moved)
3:55
“Das Lied, das nie endet”
…or
“The song that never ends”
I knew learning German would pay off one day.
Yes it goes on and on my friend (:
Some people started singing it, not knowing what it was
and they'll continue singing it forever just because
Utterly fascinating. Your channel is a gem. Thank you for this
Can you do a video about the harmonic relationship between planets in our solar system?
Your videos bring back curiosity and enjoyment in my life. Thank 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!
Sometimes it sounds like "La Campanella"
That was mind-blowingly awesome!
This could be a backround music generator in a game!
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)
Fascinating video and channel as a whole.
You've just made your way into my lessons over polar functions.
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 is an amazing video, so interesting and well done!
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.
"...a kind of Fourier Elise, if you will..." I will not! I refuse! How dare you!
(great video)
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!
thanks for your videos ! youre a genius!
This video revived my intrests❤
It’s tough sometimes but vids like these keep me working and moving 👍
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!
@@marcevanstein it all comes full circle lolol
But thank u for spending the time and energy, producings not easy for sure ❤️❤️
Beautiful!
ABSOLUTELY need an ambient album based on the pulsing circles
It reminded me of chapter 11 of the half life alyx OST maybe check that out
Absolutely brilliant! Please release the code for us to create our own!
Upload three theme and variations as it's own video!! This was mesmerizing
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!!!!
I definitely will. It's a great idea!
Oh man, I bet lookmomnocomputer would love this idea!
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
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.
Great video! ❤ Can you continue with Bach?
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.
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.
This is amazing.
Can I somehow access this on a website on loop or any downloadable code for it?
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
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.
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.
Are you planning on releasing the code you used to generate this? It would be fun to play with.
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
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.
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.
There should be a VST for this, I want to use this in my DAW
What determines when it plays a note?
When the point of the outer most circle intersects with with the edge of another circle I think.
so, since you can make multiple fourier transformations that fit a song, could you make one that plays two or more distinctly different songs based on where you sample it?
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.
The ancient Greeks and later Ptolemy refined the epicycles.
Unfortunately, Newton et al had a much simpler and more universal explanation.
You should overlay a musical grid, where we can de the size and shape of a note and how they are connected in space
Map pitch to one dimension and tone length/duration to the second dimension to resolve curve ambiguity
“A sort of Fourier Elise”
Jail. Now. You.
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 ruclips.net/video/2UphAzryVpY/видео.htmlsi=XMDK55u4-6vcR_0p for the circular rhythm representation I’m talking about.
Very nice!
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
At one point it honestly sounded like Liszt wrote Für Elise
This is Underrated.
6:35 the music from Bib Boo's Haunt in SM64 :D
Fascinating.
The pentagon or pentacle is the associate of the harmonic series, Fib. series, and Fl. analysis. That should inspire something.
I remember a clip from doctor who where he used the rotations of plants spinning around eachother that are spinning around in galaxies and used that to generate sound, what would that sound like in this setup? Using as much mapped space as we know and put it into this?
How do we make these kind of videos, the animals and the equations required etc. Its there a tutorial on this?
7:11 ok now I need the sound file with just the component circles! It sounds so beautiful and ominous...
How do you make these
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.
This. Is. Amazing.
Spectacular
Do you have the source code published
somewhere
for this? thats so cool
The random angles one looks a lot like a music visualizer setting that (I think) the Window media player in Windows XP had built in. I wonder if it used the same concept?
Is it possible to do the "note frequency depends on path speed" version and construct a path that reproduces the original rhythm?
_If it can play Fur Elise, then it definitely can play Rush E._
Edit: MOM IM FAMOUS
*Für
@@luigidabro Not everyone knows how to type that or can.
@@luigidabro you still understood what that person meant tho, which means a correction wasn't necessary.
No it can't because it can't play more than one note at a time
@@KaneyoriHK then it can also be replaced by a "Fuer"
So many things!
can u do this with Canon in D? I think the periodicity of a Canon piece would work really well with this. This is a really cool concept.
What if you had more than one fourier transform playing the same song but using different patterns at the same time? Would the improv of both work together to make a better song?
To my untrained ear, I lost track of the original tune once you switched to the path speed notes. This is interesting because I've listened to a fair few versions of it which play with those key, recognisable notes. Which is probably where I fall off. I can only recognise the notes, or the grouping in that specific, iconic pattern, not the sequenc/motion they're moving through?
this reminds me of the time i saw a tesseract in my living room on DMT
wow I need this as a DAW tool
Finally, a continuous extension of Für Elise
This certainly was a circle video of all time
0:35 the music of the spheres, abi?
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).
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
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.
As soon as you added the extra notes between the originals, I already could no longer make out the source tune.
The soul of Fur Elise.... He's a musical Necromancer
Great!
This would work beautifully on the Bach's Goldberg Canons (bwv 1087)
I wonder if it's possible to use the degrees of freedom in choosing the angles of the path to reduce the number of circles.
I challenge you to write a sequence where the circles form a specific shape of something while also playing a decent sounding tune.
I love that "wonky" Fur Elise sounds like Scriabin