In which this question is definitively answered. Head to brilliant.com/MarcEvanstein to start your free 30-day trial and get 20% off an annual premium subscription.
The full music of Fourier Elise is here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-zq32bIud3OM.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.
Me when I anthropomorphize abstract symbols (contextualizing what amounts to “noise” into something we can understand is fundamental to the human experience)
@@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
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).
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
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.
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
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 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.
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!
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)
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!
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.
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.
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.
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.
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
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
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.
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.
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!!!!
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
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 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?
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?
I don't know. It is pretty interesting, but seems to be that there are also some missed opportunities. I suppose that it is perfectly sensible to have the radius decide the pitch, but I also think that it should not be limit. Zero distance to the center should be 0 Hz, naturally, and the a linear correlation to infinity. Not limiting predefined notes and such. When a given note is played naturally should not be decided but some specific need. You should conform to the system, not the other way around, in order to make a given piece work. Perhaps a note could be played whenever the tip of the tower of vectors intersect another, or something or rather. N o one say it would be easy, and yet we are still incredible limited. how about amplitude? How ab out multiple frequencies/notes? How about sustain control? I really like the concept, in fact I like it at lot, but more than that I like the potential.
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
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.
What happens if you define Fur Elise to just fit the first 180 or first 90 degrees of the circle? You'd then get a Fourier extension of the melody into the undefined quadrants of the circle
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?
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?
