The Unexpected Beauty of Circle Music (
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- Опубліковано 22 тра 2024
- When I started making music from tracing circles, I found I just couldn't stop.
Patreon: / marcevanstein
Teaching: teaching.marcevanstein.com/
This video makes use of the following creative-commons licensed visuals:
- commons.wikimedia.org/wiki/Fi...
With enough circles, you can Fourier transform any melody into your circle space.
I thought about that! I realized partway through that it's kind of like the 3blue1brown animation
but the pitch repetition rule would have to go
@marcevanstein I'd love to see a follow-up video with this idea!
You've got me wondering now... if you had a piece with two voices in counterpoint, you could map X and Y to the voices, and discretise them with a grid - and if you had sufficient Fourier partials then I believe you could still define the entire piece. Perhaps you could even include the rhythm, and have the transitions between notes made into pitch glides...
@@macronencer In an abstract sense, you can represent any music (any rhythm, any number of voices, dynamics, tempo, etc.) in a 1D format, and then you can FT that into circles or whatever as your new representation. To get music back out from the circles, you just reverse the transformations. Any computer file storing music is already in a 1D format (i.e. string of 1s and 0s). That can be a MIDI file or even a sound file like MP3. The circles representation will probably look a complete mess, but that's a question of aesthetics rather than whether you can do it.
Could be fun to try to reverse-engineer a fitting set of circles to some existing piece of music
That is pretty much what the Fast Fourier Transformation is there for. Just for entire frequencies, not notes.
Google it, you'll find that it does what you describe, just for n equidistant notes, to describe an entire sound, instead of the notes of a song.
@@Timb9o I know, though the task here is slightly different. I'm saying fit the *notes* of existing music as shown on sheet music, rather than the exact waveform.
And ideally to do so on as smooth a path as possible (for this roughly meaning you need as few circles as possible, or alternatively, that the circles shrink as fast as possible from one set to the next)
The musical equivalent of the Ptolemaic system.
@@Kram1032 so a fourier transform, of the note values(a=1,b=2, etc) not the wave function.
@@pressstart2640yep
So it’s the first few terms of a Fourier transform of a melody, but rendered with dithering
I'm surprised that Jospeh Fourier wasn't mentioned a single time in this video 😂
might be cool to use a fourier transform to turn any midi file into some circles that play what the midi files play
Yes! And then seeing what happens with small tweaks from the original analysis.
This should be a VST plugin.
Would unquestionably sell
Would pay absurd amounts of money for that
I'm actually inspired enough to write a JSFX (for REAPER) that generates MIDI notes based on this idea. Currently got the whole thing running, but still finetuning some functionalities. It wouldn't be THAT hard to port it to a VST3 I think
When you hinted at another scale earlily in the video, I was almost sure you were going to use Lucytuning. Its an interesting scale, originally concieved by the legendary John Harrison, which uses pi-based intervals.
Why use a scale at all? There's nothing about the setup that implies that a scale should be used at all. It's a computer it can play whichever pitch it wants.
@@minerscale It could work, but you'd end up with tonal nonsense for the most part unless he actually tuned the equations
I think adding a secondary circle to get a lower note that would be harmonically associated would be awesome!
That is a great idea
This feels like it would be really useful for generating video game music
why would you need some sounds as constant disturbance? use sound design for that, and leave music to do precise emotional work 😉
your feelings are irrational
@@Fire_Axus why do you say this to everyone who says "feels"? are you a bot?
@@Fire_Axusirrational, j-just like pi. Ok never mind.
I was just about to go to sleep. 😭
Edit: It was worth it to watch this! I am absolutely in heaven with this.
Glad it was worth it!
stop getting so emotional
I would strongly recommend connecting the circles edge to edge (rather than center to edge) and have them vary either as constant multiples of each other's radius or circumference. That will likely give you better results.
Connecting the circles at their edges also allows for a more natural pacing/rotation as they rotate around each other.
Harmonic bliss in dissonant abyss kicks brainstorm raindrops reverse-sing gravities' grips
This has the power of a Haiku!
I'm always saying this
that is so nice Marc, especially the transitions through the circle of fifths.
Thanks Chris! Yeah, I felt like it kept getting more interesting as I was exploring it.
The just intonation decision made the whole thing feel so warm and idk why but it just made sense for me. I love when microtonal sounds are used even if it's just in the context of shifting intonation because of the way that individual intervals can have all sorts of new feelings in my brain
your feelings are irrational
@@Fire_AxusWhich I'd say is a good thing
wow... these are creative ambient music !
I really liked your approach to randomness and the arbitrary choices you've made. The final example with the key changes in perfect intonation was fire !
A great video, gives me all sorts of inspiration, and thoughts about possible results from small adjustments, and wonderings about what effects big changes might produce.
So interesting and so creative-- love love love
this is so fucking peak. i was thinking note length could be based of the 10 possible values for any digit in pi, but using the arc velocity or whatever you did sounds much more natural
Your video was an enchanting watch! I am currently developing a mathematical visualization. I have been trying to think of a way to add music for many hours but couldn't find anything. This might finally give me the needed inspiration.
Should have posted this at 15:93 24hr time for the full effect of the meme
For reference that time is 4:33pm on march 14
what
he should have posted it on 3141 AD may 9 at 2:06 and 53 seconds and 58 milliseconds
This is so cool!!! Love it
your feelings are irrational
This is probably the best math music video I ever found. Thank you, I am a composer btw.
I can't believe this has so few views! Extremely interesting concept, then you iterated on it enough that by the end the starting point seemed almost basic by comparison. Keep making great videos like this!
Aww, thanks so much for this comment! It's a funny thing; I do find that the algorithm rewards effort and detailed attention, but unevenly. Sometime you work super hard on a video, and it doesn't pick it up. However, the main thing is it's nice to have one's work appreciated, so a nice comment like this is worth a lot :-)
“few”
Really interesting idea! I hope you upload a longer video of music from this one day so everyone can listen.
This is so incredible. Having a page to play around with this at would be a dream. Having that page output sheet music would be even better.....
This was awesome. Following now
Very nice!
Beautiful!
All part The limitless aspect beyond material "absolute" be-ginning to be seen. Beautiful! Thanks for your offerings!
this video blew my mind, I LOVE this concept it sounds incredible
Bro just discovered the equation of jazz
Thanks for using tuning!
That's beautiful!
0:55 is really beautiful
Beautiful video, beautiful music.
Hard to believe it is all the product of "wheels within wheels".
This was probably the best video I’ve ever seen
Loved the video and the concept. The one modification I was expecting and that you didn’t get to was to let the circles also determine the rhythm. I was thinking you could only sound a note when the distance from center precisely hits the corresponding value for a note in the key
This was great! At the start though I found myself a little confused about how you were determining the notes and tempo, so I would have mentioned the distance correlation and tempo slider earlier
Just a small gripe, keep it up!
The "teacup ride " at Disneyland, and the original carousel of Knotts Berry Farm, all of it tucked away within Orange County California . So wickedly ace ❤. ♤♤♤
very nice new music genre!
Beautiful....
This is a great way of making music
Love this, Marc!!! ...One thing that's really interesting to me about the studies in this video is that you can describe them as "models of physical movement, coupled to pitch production by arc-length." Arc length is closely related to physical quantities like action. It contributes to this vague, general hypothesis I wonder about a lot: That the "unreasonable effectiveness of mathematics" in melody writing hints at some deeper connection between (A) the psychoacoustics of melody appreciation and (B) the auditory recognition of physical processes. Like in some sense, what you're doing over the course of the video is making the model more physically realistic. It starts to sound more like riding the teacups simultaneous with the melody becoming more engaging. I have endless curiosity about that connection.
Concerning planetary motion and improving physical models, check out the Wikipedia page "Deferent and Epicycle."
Ah, interesting point! Yes, I often think about physicality when writing music/teaching composition. Ideas like inertia, or equal and opposite reactions are really helpful analogies. Music is intimately connected with dance/movement, which is connected with physics, right?
It took me a minute to get into tuning of the last one but honestly it feels more organic. A rainy kind of organic? A directional process without an endpoint
Merci.
"avoiding frequencies..". And there's the rub; excellent video.
Its things like this that sometimes spark ingenuity that become a new compression format for files. Imagine if some how with math you could recompress music based on some circle formula for the notes of the music. Very neat program. I enjoyed the inspiration and mini journey into pi day music
I find the shimmery quality at 3:52 the most pleasing. For the slower passages to be pleasing (to my ear) there would have to be more shading in the actual notes (volume, harmonies/orchestration, more richness generally).
Great work! I may have said this before, but we have a lot in common. This is definitely one of my favourite worlds to explore. The circle of fifths was a neat idea, and I think you could generalise it more as well. For example, there are ways to arrange groups of chords so that only one note changes between two adjacent ones (I've done this with a constrained set of tetrads, and the result was a piece of music that will be on my forthcoming album). The idea of only one note changing at a time makes for pleasantly subtle transitions, and reminds me of Gray codes in computer science.
Do you have a link/resource I could check out about that? Sounds interesting!
@@marcevanstein Thanks for the interest. Unfortunately it's still a little early in the release process as I don't have the album mastered yet so nothing's online as I want to be sure of timescales first - but if you find the YT channel called InsidesAndOutsides, that's where the teaser video I made will appear (hopefully soon, as I'm looking for a mastering service now...)
I'm planning lots of BTS stuff for a blog as well, where I'll go into more detail about these things. My album had quite a bit of mathematical inspiration, and also has MIDI generation and audio processing via custom code tools that I write myself in Java, to do things a DAW can't do...
All the best, Mike Torr
A quick update if anyone wants it: I have a mastering engineer booked now, and I'm probably looking at a May release.
I've always found it interesting to see what patterns come from a modified Fourier transformation using other geometric shapes, whether they spin or not
this is insane i need more
This is fascinating, especially as a way to explore musical ideas by actually hearing something. I'd want to play with all sorts of microtonal scales and rhythmic stuff. Unquantizing the pitch relative to rhythm and vice versa to hear the rhythm of the scales (probably less interesting than it sounds in most cases, but I'd want to find out), playing with other MOS scales and their own circles of not only fifths...
This is super cool!
You could change the notes from the single rotating point on the smallest circle; to the dynamically moving points of intersections of circles
this was so fun... pretty sure that you just explained the Creation of the Universe and all other realities/dimensions 😁
I saw the video about classical music and Mobius grids years ago. So, I didn't wanna watch this one; Thinking it couldn't be topped. This is nice, too. Y'all should search for that other video. I can't remember the title. Edit: Should be a piano roll at the left-hand side, or bottom. We don't all have perfect pitch.
it would be interesting to combine this with some algorithm adjusting the generated notes to fit certain patterns, like returning to a root note or having a longer and softer pressed note when the time until the next note comes is large
When I saw the thumbnail I thought about the note being played whenever the point passes through any of the circles. Could be weird rhythmically, but still sounds like an idea to me!
You could use the circles themselves as pitch, for example, playing a note inside a certain circle changes the pitch or tuning. You could also use not only the distance from the middle circle, but all other circles as well
Underrated vid. It combines my two favorite thigns: music and coding
i love it
There had got to be an way to work out the pitch as a part of the mathematical function of the orbs. Maybe the speed of the ball represents an offset from the frequency, like the faster it moves toward the center the night the pitch grows but then it drops away when it moves away. The base mote could be based on the diameter of the circle so you could produce intervals like 5ths if one note is half the size of another, and you could track multi le circles at once to get chords. Then make it a local done with absolute speed affecting volume, faster getting louder.
You could also have different effects like echo, delay or vibrato that are effected by other circles that give powerups.
Then play it on a loudspeaker directly in tront of a metal guitar tuned to whatever chords you were playing and DI that into your recording software as whole mix reverb effect. Probably flange the di and add some analogue distortion, saturation
And a use 1st or 2nd order band pass filter somewhere between 220 and 440 Hz, to cut some low garbage and use a high pass at like 3k-5k to being back some of air.
Oh, and 5 band multiband compressors on EVERY output. I don't care if they only are compressing like 3-4 dB at the peaks it all adds up to make it sound was more professional when don right. Soft knees and low rations are where it is at. Attack hold and threshold you gust gotta get a feel for it.
The compressor on master output should be relatively fast and strong to keep and peeking under control and bring the good stuff up.
keep the good work soldier! Our lives are in your hands now.
There are so many possibilities with this. Each frequency could have it's own meaning like pitch, key, tempo, how many notes to play together, etc...
I am older now and my memory fails me at times, but if I recall correctly, the circle of firths is a feature of the well-tempered system, so to tune each key (if I get what you did right) diatonically and not within the well tempered system makes it sound more chaotic... More of an observation about how the circle of fifths does not really belong in a world of perfect tuning... This was a fun expriment to listen to, in part because it makes you wonder about improvisations and if there is some weird mind geometry behind it we are not aware of :D
Thank you so much for making this, the circle of fifths modulation in the end sounds absolutely heavenly!
Is there any way you could make this into a customizable application/vst? I am more familiar with making music than with coding, so that would be incredible. I would also spend some money for it :)
You could have it so when the dot crosses a circumference, a note plays.
For chords, you could decide if the third and fifth based on whether the dot is inside or outside one of the circles.
This is so beautiful! I would love to hear a version of your final melody in 12tet, as I have trouble appreciating Just Intonation due to it being acutely uncomfortable for me to listen to 😅
(Also, while I love pi, I feel like tau would be a more properly circle-related number, as it traces the complete circumference instead of just half of it. But pi is delicious, so until someone comes up with a tau food, I gotta go with March 14th!)
Wait got to the outro and realized this is the same guy who made music with fibonacci! Love these kinds of vids!
Can we download this program/code so that we can mess around with the frequencies and amplitudes ourselves? I loved the second last example!
This sounds great! Is there anywhere that we can maybe get our hands on the software that you used for making the circles into the sound?
It might be interesting to map popular or well known music to your circular maps to visually show what patterns we use all the time (the converse of your process).
I often use visual curves to compare and arrange
here's an idea: instead of controlling all musical parameters via different aspects of one rotating circle structure, have multiple of them: one for pitch, one for speed, one for how loud it is, one for scale and so on
So interesting
It'd be interesting to see if this is reversable, to take any piece of music, and find the circles and the speeds that matches them closest.
Probably NOT, but still a cool idea.
I wish the rounding of the notes to the scale (and when a note is being played prior to 3:26 ), was visualised on the diagram!
It would be cool to see this done with multiple sets of circles where each one is a different instrument so it makes an orchestra
It might be interesting to have the dot change circles whenever it arrives at an intersection. It could continue in its current direction around the next circle, or reverse clockwise/counterclockwise, or alternate every nth time.
P.S. This is lovely stuff!
Would be neat to see what you get from flipping the orbiting circles so that the smallest is between the two bigger. Change nothing else.
I suggest this only because of the change of tempo using arc length instead of milliseconds. That smaller circle is just... too small.
I think that by swapping the two outer circles only, you'll get a neat difference.
That last one though, that was very nice. You definitely got in the right direction with it.
that first one got me closing my eyes fr at 0:32 and when the beat changes up with the second circle is just perfect 0:35
Now this is making me wonder how good (or bad) it would sound to use the positions on the larger circles together as a chord. The first one would just be a constant tone like you mentioned, so, maybe omit that one.
That's interesting! I mean, the larger one might make a good drone anyway
That's interesting, the first one (or two) circles could be part of the rhythm section.
you are a true PI-oneer!
If you divide the circle. in four parts You have four seasons. and a sequence of 4 chords you can for example. take inspiration from the circle of the cycle of fifths in order to have a profession of four chords
This is such an original idea.
Another way to do it would be to make the center be 'north' and the outer most perimeter be 'south', then use the circle of fifths to adjust the notes in and out. The north would be faster and higher while the south would be slower and lower. The aspect of octaves could be introduced per circle and then have eight circles. One circle for each octave for each planet. This should result in some interesting effects.
I think it would be interesting to incorporate more music theory into this because I bet you could make some absolutely beautiful atmospheric melodies with some chord/key planning.
Something I would like to see would be to perhaps do an actual chord progression instead of a pure circle of fifths, or alter it so that occasionally it resolves naturally before going back to the slightly more atmospheric, constant motion.
Or you could do a partial circle of fifths and then it switches to circle of fourths so it kind of ping pongs between a few keys.
Use the circle of fifths relative to the position of more than one circle to create chords.
Or two of these circle groups, one for each hand
Gosh I love microtonal. It is a shame there is not more of it.
Nice
You could generate notes from both ends of the diameter of the outermost circle, with different arc length rates. Might create some interesting harmonies.
I'd love this to be an app
What values would you need to assign to represent an existing melody? I'm sure that the resulting trail would reveal a different perspective on the music.
Months ago I was experimenting with graphics for music inputs, I just learned some basic stuff but I had this intuition of using Fourier transform. I was following you already, so happy to see you achieved this! Such an exciting field
Check out in this account here some results
the jazz pianists dream of playing this last example
Man this is amazing! Can you share the sourcr code for the animations and audio?
5:20 is so beautiful
If we could turn that circle into a tajweed mouth. 20 heavy letters, 7 light letters, 1 stop letter. With 3 levels available on each letter with doubled intensity, and one merger between two letters. For combinations of single (as suffix/prefix, inter), dual, tripple and quad forms.
wow
This should be used to generate video game music! Tempo, key, pitch, volume etc could all be determined by the player's direction, velocity, altitude, maybe instrumentation is determined where in the world they are
Really beautifull sounds a little like Stanchinsky!
You are smart
Neat. If you want to try something like this yourself, might be interesting to give VCV Rack a try. There are some epicyclic LFO modules there, and with sample and hold and quantization you could keep to notes like in the video. The main difference is I'm not sure if the modules go as far as this video when it comes to iterations of circles. Another difference is that it seems the modules only show the point's path, rather than the circles that the point follows which would be generating the path.
Different approach to the same thing, that could also allow other math related approaches to generative music. Software is free at the base level (paying adds features rather than unlocks - nothing gimped in the free one), and you get a whole bunch of neat plug-n'-play bits to experiment with in an expansive library of (mostly free) virtual modules.
If anyone wants specifics for LFO's in the library it's "Roulette" and "Polar equation" that are the obvious ones. Some others may do similar, but they don't have the visual feedback in their UI.