The Coltrane Fractal
ฝัง
- เผยแพร่เมื่อ 1 ต.ค. 2024
- What do 200k notes in 6 seconds sound like? No, the result isn’t Black Midi - it’s way cooler than that. if you use the right math, you can create recursive melodies that rely upon the fact that your ears are incredible sophisticated judges of frequency ratios.
Join me in exploring the Coltrane Fractal!
MUSICAL FRACTALS:
• Musical fractals
HARMONIC POLYRHYTHMS:
• Harmonic Polyrhythms E...
WATCH THIS if you want to learn about the ear and hearing!
• What is up with Noises...
8th octave overtone tuning (Johnny Reinhard’s Paper)
stereosociety.c...
The 12-tone Fractal Table
docs.google.co...
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Peace,
Adam
![[UNCUT] “บอสณวัฒน์” ลากไส้!! ใครหนุนหลัง "แม่ตั๊ก ป๋าเบียร์" I คนดังนั่งเคลียร์ I 30 ก.ย. 67](http://i.ytimg.com/vi/QlD7mU2KKRk/mqdefault.jpg)
"All musicians are subconsciously mathematicians.“
― Thelonious Monk, Jazz Pianist and Composer
Almost makes me think of certain spiritual patterns (sacred geometry). I have to wonder what the song would look like in terms of vibrations within water for example.
The same could be said about mathematicians, pretty much everyone I had class with played an instrument or had very serious opinions about music
@@rl1275 this is a good observation.
Adam Neely: the Vsauce of music.
Dang it, I was about to say that!
I expected a "and as always, thanks for watching" at the end
I agree, but in a bad way. Both are hacks and this nonsensical video that's really about a synthesis artifact proves it.
I was thinking just the same thing
Oohwee
2:54 cat arrives in shot
2:58 cat jumps
3:12 cat is asleep
3:18 cats ear twitches
5:08 cat is sleeping in a different place
7:41 cat is shocked
8:05 cat cleans its self
you could become a legend by doing this to every YT video that has a cat in it. Just sayin.
this is good information
this should be in the description
like dan & mick hasve in their that pedal shows videos
..but now watch what happens at 200x speed
Didn't even notice the cat
16x speed: pacman
32x speed: pacman about to drop the beat
64x speed: pacman got a gun, everyone get down!
128x speed: Your windows 98 computer that you use to play pacman crashed.
aka extratone
I laughed wayyy too hard at this
This was a very good cat video. The guy in the front talking all the time is a bit annoying though.
2:59.... An essential moment
yes indded sir
selphur ahaha
Yeah, he truly has a shitty voice!
I gave you the 1000th like.
So if my math is correct.
1 + 1 = 2
E= mc^2
Coltrane Fractal x64 speed = AK47
and hotel = trivago
6:48 from pacman to service in iraq
Yi Zong Ong your sense of humour is perfect
That sound like an aweosome title for a musical album
you must have a really messed up mind mah dude, courage
Yi Zong Ong what I thought
Yeah, "Pac-Man" that's what I was thinking.
This whole ear calculation thing isn't quite as mysterious as Neely makes it out to be. Sound waves with simple ratio frequencies combine in the air before they ever reach your ear. They make an interference pattern that repeats more frequently and thus makes a smoother sounding sound then frequencies in a complex ratio. Light works differently because, although light behaves physically very much like sound, we perceive it through an entirely different mechanism. Our eyes have three kinds of cones that each pick up a different range of frequencies. Every color we can see is based on just three samplings. That's why screens and printers only need three colors. Because of the very rough way our eyes detect light, there is no way we could detect the interference patterns in light waves, even though they do still exist. If we could though, we might see the colors of some objects undulate over time the way dissonant chords do. You can appreciate how much worse humans are at seeing color than hearing pitch by imagining if you could only hear three notes, and every sound you could possibly hear was just some combination of those three notes at different volumes.
> Only hear three notes…
So, when installing cochlear implants, they need to shave a number of the hairs in ones cochlea. They then use electric stimulation to activate those cochlear bands remaining. The very earliest cochlear implants could only give one, two or four or so hearing bands. It produced a marked lack of ability to distinguish a lot of features. And worse, this narrowing of hearing bands was a permanent change, which meant that even as technology got better and could offer more bands, you were already locked into the earlier bands.
There are some videos that demonstrate what this would approximately sound like th-cam.com/video/SpKKYBkJ9Hw/w-d-xo.html
Came here to say this, you said it way better.
You're right about light, but wrong about simple ratio interference "repeating more frequently". If you combine two frequencies f1 and f2 in roughly equal amounts you get an envelope frequency of f1-f2, and a carrier of f1+f2. Thats always what you get regardless of the ratio between the two frequencies.
So would we perceive visual harmonics if our eyes worked the same way as our ears?
Also, if everything is made of only three colours does that mean every complicated colour is made of several frequencies, thus a chord of light?
That's not really how sound works. Two waves will always just pass through each other by the superposition principle. They only combine while they are intersecting, and they simply add. It's not that simple ratios are "smoother," it's just that the waveform of a single period is less complex. If the two frequencies have a small gcd (relative to their size), the sum will repeat more frequently, so there is less complexity in a single period just because the period is shorter. The problem with light is just that we have a very poor frequency resolution (3, like you said). Some organisms have many more types of photoreceptors, but none can approach the frequency resolution of the ear.
I have no idea what to do with this information but it's a lot of fun.
John Horne This should be a pinned comment on every Adam Neely video
You can make elaborate shit posts with hidden melodies and songs inside the fractal. You could make the melody of “Resonance” by using MIDI clips of All Star 😂😂
I hope someday y’all can understand the profound truth in this video and apply it to real life situations
@@JespMusic how to do that
5:29 Oh, I get it! It's called an "Almost Major Sixth" because it's slightly out of tune!
5:32 THAT'S your favorite?!?! I HATE things being so close!!!!
Also, the video length is 9:11, my birthday. Yes. MY BIRTHDAY IS 9/11 LOL.
6:28-7:25
1x: I don't know what to say. It's the original song.
2x: Okay, the original was already pretty fast...
4x: What the...
8x: That sounds like a weird sound effect now.
16x: That sounds like a (faster) weird sound effect now.
32x: *helicopter noises*
64x: *more helicopter noises*
128x: Wait, is it changing?
256x: It sounds like... ...a melody?
512x: Okay, HOW did it go from a piano to a beeping instrument?
1024x: Wait! That's... ...The original song slowed down?!?!
2048x: Yep! Definitely the original song. This sounds a bit like video game music!
4096x: Cool! Does this work with every song? Also, the camera messed up, ROFL.
I need the almost major 6th in my life.
Then again, I'm so bad at tuning that I probably already play almost major 6ths.
On guitar, major thirds and sixths sound a bit sharp. Make them "almost" thirds and sixths, and they sound in tune. Oh, intonation!
Deeeeeeeep, very deep.
180k Coltrane solos per second? Yes please!
Imagine how pretentious that porpoise would be
Bebopopotamus porpentious!
We could make a religion out of this!
Jeff Irwin there is literally a church in San Francisco whose patron saint is john Coltrane. They cover his songs during service
my left ear would never recover
That bit about the wierd chords; the "Howling dominant", the "Hyper leading tone major seventh", and the ""Almost major sixth", just immediately lead me into a deliberately off-key impromptu singing session of John Lennon's "Imagine".
It was beautiful.
Its like Vsauce.. for musicians!
I'd consider Adam Neely to be more of an Idea Channel for musicians
Gabriel Shaw rip Idea Channel
he literally said once in a video that he wanted to be kinda of like "vsauce for music"
That's unfair
Neely didn't sell out to TH-cam Red
He is Vsaucing the wrong way, the video doesn't end in a positive thought.
It's almost like he's NEGATIVE Vsaucing ;D
Every time Adam starts to say “midi clips” I keep expecting him to say “midiclorians.”
The legend says that the almost major 6th is still trying to become an actual major sixth.
to this day, one can only hope...
Metashrew 😂😂😂 close enough
the way he played it in descending keys, though! 😂😂😂😂
I believe in him.
I have high hopes for the major 6th.
I love how at 512x it just starts to sound beautiful again. I wish I could sample that part, it’s like the calm after the storm.
Man... This is absolutely brilliant and must have taken a TON of work. Thank you for this and congrats on the 200,000 mark!
"their ears would need to be tuned to the same frequency as ours... otherwise it'll just be noise"
So my parents are aliens? Hm
It's not the ear that is calculating the ratios, it's the waves interfering in a short repeating pattern for consonant intervals and long patterns for dissonant ones. A simple integer ratio has a lower common multiple than a more complicated one, which means adding up waves with those frequencies results in a pattern that repeats itself with a smaller period, and the longer that period is, the less consonant the two notes sound when played together.
thats the basic physics of Beats (acoustics) but the small differences in freq ( 9Hz as in adams example ) are to little to explain the perception of consonance vs dissonance. And this is really not everything that needs to be considered .... try what happens if you use 3 different sources for each frequency, or what happens if you pan one frequency left one center and one right on a stereo system. than move your head or change amplitudes.... :-) ....
my mind is all over the wall behind me
lord thick nipples underrated comment
Kurt Cobain humour
Our sound systems aren't able to reproduce Coltrane's solo sped up that fast precisely. At some point it's just going to approximate it to a pulse and you'll just hear those intervals as rapid pulses which approximates a saw-tooth wave. You're not going to be able to hear a genuine musical fractal digitally.
Allan Bartlett
At 2048x speed though, I think a lot of the extra detail in the true waveform would be inaudible, as they'd probably require frequency content that goes way above our hearing threshhold.
Allan Bartlett I was going to say something similar, but you beat me to it. By changing the tempo instead of speeding up the audio, the waves get cut off at the end of a note. It may be possible to play accurately if the sine waves that make the original solo are at the lowest frequencies with whole number cycles in each note.
I love the transition from a square wave to a sine as it speeds up. And then it just gets faster and faster and those blips can recreate music instead of just pure tones
6:47 Pac-man 😉👻👻👻
06:52 WW2
I love these but i should also point out that there is a fundamental problem with the way you demonstrate this fractal. That is that the notes end up playing faster than the frequency producible by the hardware your playing it on. By the very design of the hardware and software being used your only sampling a faction of the total "waveform" your producing. at 48000Khz you can get a waveform of 24Khz max and even a 27hz A0 at 2048x is 55296Khz. basically even at half that your not getting any of the notes you have laid out being played back at you.
Basically while I can't deny your theory is probably right what your hearing with your demonstration is not a fractal of the notes being played its a set of consistent data points created by a sound processing algorithm to approximate what you intend in a way that is physically possible for a speaker to produce. The computer is broad stroking the intended pattern with a much simpler and more constant wave form taking a periodical sample of the original and just playing that. Which in a way still proves your point on rhythms fairly well but its not fractal.
TL:DR your brain isn't hearing a fractal as a note. The computer is making a note because it cant play the fractal.
Listen to this guy
Your reasoning is mostly correct, but the computer isn't making any notes. The range of reproducible frequencies is indeed limited by the sampling rate of the DAW. The lower frequencies that become apparent as pulsing changes in volume (see the 64x and 128x sped up part) move into the lower end of our audible range when the audio is sped up fast enough. There are no limitations on how low of a frequency can be represented by a sampled signal. The higher frequencies are lost as the audio gets faster, but we really aren't missing anything since those frequencies are out of our audible range anyway.
Well yes. Its the destruction of the high frequency that i was saying also destroys the fractal. As such my point was that the note we perceive is not because our brain and eardrum is doing the simplification (which it probably would regardless.) its because the computer is reducing it down to a cycle of samples that is producible.
I was wrong however for a different reason. The method used doesn't speed the tape up it speeds the playing up. So the frequencies stays the same but the notes are payed faster. The point still stands though as the number of samples used for each not becomes too small to be meaningful and you still get a repeating jumble of samples instead of a tune. It effectively reduces it down to a series of pulses instead of notes.
weigh in on this Adam?? Why not try slowing down the actual recorded audio instead of slowing down play speed in the DAW?
actually it might be an interesting experiment. how much of a waveform do you need to hear to recognise it as a note? if the frequency is 50hz and you only play it for .02 of a second (one complete wave) can you tell the difference between that and say 80hz also played that short? itd be interesting to find out.
6:46 from an overheating 32 bit game console to a machinegun in a couple of seconds
but is it really our ears doing the work here? dont the notes get compressed by the program you are using already?
Ohh, good point.
Regardless your brain performs the same temporal compression.
It's actually one of the things that mp3 compression types rely upon, that our hearing has blind spots so to speak.
Yep. Despite what vinyl purists will tell you, we hear things digitally.
It's still mixed via the DAW but Ye you have a good point
@paul love Yeah, well I still jerk off manually.
Hey, thanks for achieving my lifetime project pretty much delivered in a 9:11 video and leaving me a pointless human being . But hey, thanks.
I only listen to music with howling dominants now
3:43 was so funny I have no idea why
6:46 get ready for the Drop
still waitin 😢....
Skyzen Skyluke nah bro that’s packman
Adam, just thought I'd let you know that this is also something in imaging called "aliasing". It occurs when you increase the cycles per pixel (or your Modulation Transfer Function) to a certain level. It happens with shutter speed of video capture as well, known as the wagon wheel effect. Its all just aliasing, and is a trait of all wave signal (sound OR light!).
I wish this comment was higher and more recognised. This video is flawed and the end result is completely unrelated to the self-similarity used by Bach
"Hey, check out my music!"
=> "This is just noise!"
- an alien from outerspace
- also, my mom
I often wondered what it must be like for a bird or a squirrel to hear an orchestra in the park, but now I know that they won't hear what we hear. I'm not a trained musician, and all theory is lost on me, but the weaving of real world examples with historical, cultural, even anatomical knowledge makes this one of the best channels I've found. Instant sub.
Congratulations on hitting that milestone! Though in my opinion you deserve way more than just 200K
Every journey starts with one (giant) step.
He'll get there... great content on this channel
globular goblin Dude blood mountain is so good
meh..he's no Jake Paul
Blood Mountain is extraordinarily good. I wonder if good ol' Adam Neely listens to The Don.
I knew Coltrane was an alien,
I KNEW IT!
There's a double album that I once had with 2 songs on it that sounded so freaking alien.
I've been trying to remember the name so I can find it and buy it.
its all frequency vibration !! only few people
mastered this. Watch a video of Nikola Tesla about numbers 369 ( illuminati confirmed again lol )
@@hakimbrahimi1015
Ok your user name makes you esoterically authentic so,
2x3x5x7 is NOT exactly 369 but let's get even farther than that. These first 4 primes multiplied together totals 210,... ... ... .... ..... ...... ....
wait for it ,waaiiiiiit for iiiiiit!!!!!😁😁😁😁😁😁.
Be patient, beeeeee patient,...
Meditate before you medicate,
medicate before you meditate,
say ohmmm, say ooooooo,
say ohmmm,say ooooooo,
210 gets you half way to?
210 gets you halfway to?
What does 210 get you half to?
@@iamiwasthenaiiamnow6846 ????
Gotta admit that you lost me there at a certain point. I don't want to admit how early.
andrewnicorn lost me about 5secs in but I still watched till the end hoping my brain would wake up... it didnt :(
This isn't real. It's just a result of the bitrate of your audio software skipping the loop.
You can’t make that up though
huh,
neat
Σ 1/k. The harmonic series
Besides being interesting and a fun topic of discussion - I'm curious how musicians use this kind of information in their music.
it's like how novelists probably won't use technical knowledge of linguistics in their novels. neat stuff, interesting and informative that gives them insight into the tools that they use - but no immediate application whatsoever.
Glorious answer Adam! To add to that, people love using these techniques in their compositions. Algorithmic composition immediately comes to mind. Composers such as Brian Eno, Steve Reich, Frank Zappa, or Aaron Funk have used these kinds of techniques. I've taught them for years to people of all ages and music abilities at my school. I think it's amazing how well Adam teaches this kind of stuff, and of the amount of people who are interested in it. Still, I'd be interested to hear from those who do apply it to their music.
Stockhausen uses the Rhythm to Pitch idea in Kontakte.
www.robertworby.com/writing/notes-on-stockhausens-kontakte-and-oktophonie/
Love Kontakte!
As a gut reaction, you could write a song that uses fractals in some places but not in others. Then have really varied content running throughout the rest of the piece that when sped up doesn't register as anything other than a thin layer of background noise. Done carefully the end result could be a song that when slowed down enough would play an entirely different song that still recycles and references a lot of the same melodic material and hooks. The other primary details that aren't present at the lower level at all would just become those choppy drones you normally get from slowing things down. It's like progressive ambient music for theory geeks... the downsides being that writing such a piece would likely take an absurd amount of work and almost nobody would ever bother to truly experience the music you end up with since the hidden song would be exceptionally lengthy.
Adam Neely, I'm slightly concerned here that the carrier frequencies in the "fractal" are lost in the encoding. Of course, everything you say about taking signals and then speeding them up to make a fractal such that we have a sound at the carriers we want (the notes) come back after rescaling is correct. However if you take a A at 440 Hz which lasts enough cycles that the ear can recognize it and then speed up the triggering of the MIDI synthesizer by a factor of 4096, you end up with the whole audio signal being dominated by the transients of the notes clicking on and off (ASDR envelope) rather than any of the harmonic content of the actual notes. In other words you just manually created a wavetable (which is what you said) but the actual content of the fractal should be completely gone within only a few octaves of magnification: you should only be able to observe a few octaves of the pattern and the rest is physically not there.
A visual analogy is rendering the Mandelbrot set on a computer screen. There are only so many pixels so we can only observe self similarity at a dynamic range
I'm curious about what you intend to convey here, because the increased sampling rate and oscillator don't address the issue of the first half. The wave remains dominated by the envelope.
I also agree factually with everything you said, though my perspective is different in that this video is already exactly what I envision a "fractal" (pedantic point that not all self similar things are fractals) piece of music should be.
I wonder whether there was an actual envelope to speak of as opposed to something all sustain with no attack decay or relase, but even that leaves one with the question of whether a fraction of a cycle of a sine wave in a pedantic sense still counts as that note. I'm of the opinion that for the purposes of a ridiculous endeavor like this, it counts, because I just don't know what else a note played at over 4 thousand times normal speed can be defined as. Seems the only other option is that notes just don't exist at that scale like Adam talks about in the fastest music video, but that theoretical approach doesn't allow for something like this.
With sampling rates, while something more physically accurate would take this ti the next level, I'm also happy either way since human ears would still perceive the exact same sound. The point of the standard sample rate after all is that anything higher than the Nyquist rate would only record frequencies higher than human perception. It's the abstract philosophical position that the goal of digital audio in this case is to accurately record and reproduce sounds as phenomena perceived by the human ear, as opposed to the goal of accurately creating the waves of air pressure as a physical phenomenon without regard for human perception.
Really noticed the quality of editing in this one - very slick and appropriately used. Fantastic stuff Adam.
Coltrane brought me here
*you rode the Coltrain here
ask him to come in next time
9:11 long
illuminati confirmed in video
I think Adam Neely is hiding things
Sixela963 “9:11” so Illuminati and 9/11 are connected 🤔
@@anthonynichols9224 precisely
Why didn't this guy change his name to 'Vsauce4 Adam Neely'
This was very enlightening and opened my mind to how amazing sound and the way we perceive it really is.
Thanks!
well now i know why people in medieval times hated the 3rds lol
I think the perceptual difference between harmonic and non-harmonic tones has more to do with the physics of waves than subconscious mental math. Waves with simple ratios remain consistent in how they interfere with each other, while ones that aren't simple will fall out of sync and become discordant and chaotic.
That's what I was thinking while watching. Still a very interesting video, but it feels like when turn signals line up with the music in a car and our brain gets happy. My brain isn't calculating anything, it just sees the frequency (rhythm) line up. Same thing happens with printer dots (Moiré effect) and on the printer I used for work, solid fields of full color grays made with uneven ratios of CMYK looked blotchy because the patterns would occasionally line up perfectly, then scatter into noise and the difference between random scattered dots, and perfectly lined up dots was perceptible as a wave.
This was b e a u t i f u l. You've resolved/ explored something I stumbled on back in the days when step-programming arpeggios on a Sequential Circuits synth, was exciting. I thought the melody returning was a function of the synth NOT being able to keep track or reproduce all the notes. I also noticed the clicks would have an interesting contrapuntal rhythm when I programmed an odd time signature. I have some questions but I'll read the other comments. Any music & sound nerds like me must have already done so. Thanks for sharing your ideas & explorations
Congrats and awesome video! But the audio we are hearing can't actually contain all the distinct pitches of the musical fractal because of sample aliasing. 272553 notes / 6 seconds = 45425.5 notes per second which exceeds the Nyquist sampling limit of 24000 samples per second for 48Khz TH-cam audio. In theory 96Khz FLAC could do it, but you would need to verify the waveform to see what Ableton does in practice and an exceptional soundcard.
thank you Captain "Stuff That Not Everyone has thought about except a few people who think about digital audio"
True Captain. Obviously the aliasing did not entirely kill this amazing effect I was not aware of!
6:48 *So that's why the game Pacman was so freaking popular!!! All those coins I spent as a kid!!!!* 🤣😄🤣😄😃
Is the audio not synced to fuck with me?
wow a year later you have like 162.5% more subs... congrats man :)
Hi Adam! This was a cool idea, but there are a couple reasons that we probably aren't hearing what we'd like to think we're hearing.
Nyquist rate and digital sampling rate are probably dominant factors in how the sound is being saved in digital form on a computer, with vast amounts of the original information lost. (Assume 1 kHz * 4k = 4 Mhz, or at least 8 Mbps sampling rate to capture a mid range tone sped up 4k times. Props to you if you did this.)
Not only can the human ear not hear frequencies that get shifted over ~20 kHz, the actual speakers aren't designed to produce tones that high, since no one can hear them anyway. Sending the speakers frequencies faster than they can physically oscillate doesn't work.
I definitely agree on this; what we are hearing as a result of speeding up the solo is definitely some kind of artifact (as in: the sixth definition here www.dictionary.com/browse/artifact ) . The video has some information, but the conclusions that are jumped into, do not connect correctly with the facts. Firstly, using MIDI for something like this is the first error - a synthesizer, that correctly produces sine wave should be used, and make it to change the sequence of frequencies you give it to in a quicker and quicker succession. This is because it's fairly probable that any MIDI player will make errors given the task at hand, since they are not designed for such a task! But one way to demonstrate this makes no sense, is that playing 200 000 notes in 6 seconds means ~33 333 notes per second, which is above human hearing (which means: this does not make any sense!). We might hear harmonics, but it wont definitely be something that changes ~28 times in a few seconds of time! TL;DR: This does make an interesting video, although it is mostly bogus / baloney. You can always believe you hear what you want to hear!
It does make sense in demonstrating the relationship between rhythm and pitch, and yes, everything about the MIDI maybe true, but the very low rhythms at maybe 20k note intervals will turn into low pitch, which would not happen when played slower to hear the higher rhythms at 10 or 20 note intervals, imho.
This is soooooooooooo over my head. Yet somehow I keep listening. Adam, your intellect and understanding of music and things beyond it, or tangential to it, is utterly amazing. Keep on making these great videos on all kinds of things musical, and congrats on more than 200 thousand subscribers, of which I am one!
9:11 minutes long, I see what you did here
Coltrane fractals can't melt jet fuel
Yep, and the thumbnail is the illuminati symbol. There's obviously a major conspiracy here
6:46 ahh so that's how the Pacman sounds were created
*B A S S*
At first I thought that he was saying the whole solo sped up enough times eventually reproduces the solo, which would be awesome! But he basically just just programmed the solo using the corresponding ratio for each note. Did I miss anything?
Amazing content! Really well thought, researched and well put together.
Just a question... how do you know it's our ear recognizing the melodic patterns again at 1024x and 2048x and not your computer playing the audio that way? There are a number of serious limitations in resolution and speed when using digital audio, which deeply affect how your computer will manage audio, and you are definitely pushing those limits:
frequency sampling on your audio card, midi resolution in ticks, and I would add the speed at which your midi file is "calling" audio samples from ram. Don't take for granted that beacuse it's a computer it must be lightning fast... computers are far from lightning fast, and latency is a good example of how slow computers really are.
I'll try to make my point clearer: have you ever seen a car on TV drive forward while its wheels spin backwards? that's aliasing and it's got nothing to do with your eyes or your brain, in fact you'll never see that happen in real life with a real car. it's the 25fps or 30fps in video framing that mess up the direction of those wheels. But.... I could put on a video on youtube, let you watch it and tell you "see what your eyes and your brains do"? Ignoring the fact that the distortion happened in the medium.
I'm not saying you made a bad video, it's a very interesting idea, but I think your being tricked by the machine. I think your software is filtering out or simply "skipping" the data it can't handle, which by the way is something that is intentionally coded in softwares: "keep on working no matter how many mistakes you're making" is the mantra in programming, otherwise our computers would freeze every second or so.
This is all I could think about after watching this. I thought it might be an elaborate troll. But I want to believe it's possible.
Look at it this way; you set up a playback of the same recording over an over, you could find a playback speed where the sample time is just a tiny amount longer than 1 copy to recreate the original. The sample it needs is always there, you match the sample rate to the periodicity of the piece, it should work.
I think it could be done with any piece of music, if you had a knob to increase sample playback speed, you could "tune" it by the turning it up until it starts to become recognizable.
@@redcollard3586 This reminds me of how CRT TV's project images. Really cool stuff.
I was thinking about this topic but with the opposite conclusion because my signals class taught me why this exactly is not a problem because of the Nyquist-Shannon theorem forming the foundation of digital signal processing. And aliasing in video just has differences since eyes are different.
The human ear can only hear frequencies up to 20kHz, and with the sampling theorem that is very useful.
The theorem proves that given any waveform with a finite max frequency, you can perfectly reproduce it by sampling its amplitude at a finite rate equal to double the highest frequency.
Since the ear cannot hear frequencies above 20 kHz, sampling at 40 kHz already gives us a perfect representation of any human audible sound.
But that only deals with the time axis, and in general it's the big theorem everyone cares about, but it might leave questions about how to record the actual amplitude of the wave for a single sample at a given point in time.
That's addressed by the concept of quantization noise, which models any remaining error as some very quiet white noise. While it does prevent the otherwise mathematically perfect reproduction, with a high enough bitrate one can guarantee that the noise won't be any louder than some max level, and considering the ambient noise present in the world anyway that might be okay.
With video as I understand the human eye just works pretty differently from either ears or cameras, but it's just stuff I read online. Eyes don't necessarily have some max framerate even though 30 FPS is enough to be perceived as continuous motion.The demonstration being that if a bright light turns off for a fraction of a millisecond, it is pretty much imperceivable, but a dark room having a bright light suddenly flash on certainly is. On the other hand similar analogy between eyes and ears with max frequencies might be with colors where high and low frequencies like ultraviolet and infrared can't be seen, but since eyes don't sense colors as frequencies we don't record color that way.
For aliasing, given a flashing light or spinning wheel a human eye eventually just starts blending the motion together instead of it disappearing from view like a high frequency sound. But as I recall the wheel spinning and camera aliasing does get used as an analogy for aliasing in sound for low sample rates, but it just doesn't match the biology of eyes.
This isnt true... ive seen rims on cars look like they are going backwards
@@telaferrum I'm not sure what your point is, digital and analog systems are VERY different because all analog systems have a finite passband, whereas purely digital signals have an infinite passband unless you intently add a filter. In a digital system you can create a signal in the MHz or GHz range and sample it at 40kHz and it will alias into something between 0 Hz and 20kHz. In an analog system with a lowpass at 20kHz (like our ears) you won't measure anything at all if you try to record a MHz or GHz signal. Aliasing only happens in digital signals.
Basically what Adam is doing only works because the computer is sampling these crazy fast signals at 40kHz and aliasing them into the audible range. If you sampled the signals closer to their actual frequency and had a speaker that could somehow play MHz or GHz frequency "sounds", you would not hear anything with your ears.
hi adam
do you think the ear combines the different frequencies that constitute intervals by itself (therefore performing "math"), or do the waves reach the ear already combined, and the math then comes afterwards in order to analyze into smaller elements (thus making it more complex) that which was originally perceived as simple?
As determined by people who do binaural beats, what the ear hears when you listen to an interval or chord, is not a combination of these frequencies, but the difference between them. This is proved when you play two frequencies that the human ear is incapable of hearing where their difference is a frequency that you can hear.
but isn't the fact that our ear hears a difference of frequencies proof towards the statement that the soundwaves already come combined?
in other words, the difference of frequencies is the result of their combination which happens before they reach our ear, thus allowing us to perceive them as simple entities, rather than complex ones?
Zgembo Adislić I think CrimSun was talking about binaural beats, where separate tones in each ear produce an effect similar to combining them physically. Since these tones don't physically interact, your brain has to be what's mixing them.
You have to be kidding me. A FRACTAL!??? HOW THE FUCK DID COLTRANE MAKE THIS!?
Laughed my ass off with the little dolphin hahaha, Adam, your videos are better everytime, the craft and the quality really hits me every time
The human visual range is 430-770 terahertz, which is short of an "octave". So we're unable to perceive any "overtone" to a color. That may be one reason why humans wouldn't have any special affinity for color combinations just for having simple frequency ratios. It's nevertheless interesting that the two ends of of the visual spectrum -- red and violet -- do look related enough to give the impression of coming close to full circle.
This turned into a ted talk and it was good.
This Guy I was thinkingV sauce.
I'm sorry, but I'm having a hard time figuring out why you said in the beginning that 200,000 notes were played in a span of 6 seconds.. The clip you showed for an example just showed the numbers go up, but maybe 1 note was heard per 40,000 notes that were displayed..
Ok, so I'm not sure if I'm gonna be able to eloquently express what I'm trying to say, but I'm gonna give it a shot. I've come to understand that pitch is essentially the same thing as rhythm, but there's something I'm not sure if I quite understand. So if I'm not mistaken, 1Hz is equivalent to 60bpm, but we don't hear it as a pitch because human hearing doesn't start until about 20Hz. Similarly, 16th notes at 120bpm would be equivalent to 8Hz, but once again we would hear it as a rhythm as supposed to a really low pitch, right? So here's my question. I read that some whales can hear down to 7Hz, so does that mean that they would hear 16th notes at 120bpm as a pitch instead of a rhythm? Sorry if I'm completely misunderstanding this, it's just really messing with my head. How can other animals perceive something as a pitch that we perceive as a rhythm? I'm really hoping you can answer this in the next Q&A.
That low end of our hearing 20hz is for a sine wave - a perfectly smooth increase and decrease in air pressure throughout each phase. If someone played 20 notes per second (1200bpm) on say a piano, that would be 1200 repetitions of the particular frequency of that note. So if it was an A that would be 440hz and you'd still hear it as an A, not like some sub bass frequency if that's what you mean?
Not sure what your saying, if I play 16th notes on my bass at 110Hz (110 bps) it's still just a low A note 16 times a mesure. If it is recorded on analog tape and I play that 15 inches per second recorded tape in fast foreward (approxamately 120 ips), that would be 8 X faster or 8 X 110 equaling 880 bps/Hz. 1000bps is 1000Hz or 1KHz or 1K. Analog can playback way higher than 24KHz, digital can run at 48KHz and every sliver can reproduce a higher note, but one sample of 50K is not noticed every second by itself even if it is two times above our hearing range.
20 notes per second would be times 60 to get 1200 bpm
A rhythm of 120 bpm is also one note at 2 bps for one minute, (I know, 4 octaves below our hearing ;)) Ok, 4 bps for half a minute? - just as 440Hz could be 55 bpm, or 110 bpm
Guess what I'm saying is the math is there but the sound does not get reproduced above 24K anyway.
milamber319, our ear only hears up to 24KHz, our brain can sense 120KHz or the lack of it. Light is 10 X our hearing. 55,296Khz is a color. Fractals go way past our hearing right away. Just like octaves, we only hear 10 of them, no matter what the math does.
theking oface
Yes, because animals respond to sound the same, the difference is in range. The limits don't matter and shift around from species to species, the point is a distinction is made at some arbitrary limit between distinct and indistinct beats.
For me, pitch is a shorthand way the ear describes a really fast rhythm, and rhythm as a really low pitch. So pitch tells us how fast the rhythm is, and its timbre tells us what that rhythm is, such as violin vs piano, and/or C major chord.
To be clear, the sound pressure has not changed from "rhythm" to "pitch", it is the ear's response to the pressure changes that shifts between rhythm and pitch, physically the medium remains exactly the same (just faster or slower pressure changes). So for the same pressure changes the wale hears pitch while the human hears rhythm.
rhythm is a time measurement, pitch is a sound measurement/
+king, 8 Hz to humans sounds like a rhythm, and if you slowly increase the frequency it will start to morph into a very low pitch at around 13 hz., it will definitely be a pitch by 20 Hz. You can hear this for yourself, if you download an oscillator.
Late to the party but I just want to point out that it is not strictly true that going up in the harmonic series, even towards infinity, will eventually yield the pitches in the 12-tone equal tempered scale we commonly use (assuming the same fundamental). Why? Because the harmonic series produces intervals which are, by construction, rational numbers. 12TeT, on the other hand, or any equal tempered system, produces intervals which are by construction irrational numbers. So while you could get arbitrarily close while going up the harmonic series towards infinity, you would never actually achieve the same pitches and the harmonic number would become so absurdly high as to lose all meaning.
My brain... Not just the content, but the fact that it's coming form a bass player...
Quebec City, Canada
6:53 Coltrane's solo seems to be turning into a machine gun...
I think dissonance intervals between color frequencies don't seem as messy just because we can hear vastly more octaves of sound than we can see of pitch (only about one octave). When two pitches sound simultaneously, ALL the overtones in both pitches are interacting, creating many polyrhythms, When two colors of light show simultaneously, we only see the fundamentals interacting. Also, we only have a few different types of cone cells in our eyes for interpreting the visible spectrum, vs. many more "hair cells" in our ears for interpreting the audible spectrum.
Also, I have long been curious about how pitch and color line up across the many-octaves divide between the audible and visible spectra. This page (flutopedia.com/sound_color.htm) has a chart called "The Color of Sound" that may have mostly accomplished this, though I do not know all the math/physics necessary to double check for myself. For example, I don't know whether they correctly accounted for the fact that sound travels at different speeds through different media (air vs. water, for instance), or if that would even matter. They also could have used magenta or "minus green" to loop the ends of the octave like a color wheel does.
the reason why we can't see light differences as much and why they don't bother us as much is because the light source is constantly changing. whether in bright daylight, in candlelight in a dark cave, or in any one of the millions of colors in the LEDs in your room, we can always see different colors as the same in relation to each other.
The way I see this, polyrhythm is macroharmony.
At 2:54 I cracked up when he said the John Coltrane solo was a little bit harder to put together than all star (A traditional jazz standard for All star) SOMEBODY
Such an impeccably made video, every fits well into each other and though I had to watch twice through to grasp it, the concept of what you were explaining was not massively hard to understand.
Yet all I've learnt is the mum from the new Godzilla's method of making the orca.
Isn't the digital sample rate an issue? With the rate of x Hz you can only playback a finite number of notes during one second.
I'm more an engineer than a musician, and I can't even follow this.
Wow, Coltrane sped up to 16x sounds like Pacman :)
I gotta try this
i think the reapearence of the solo melody in high speed replay is not due to the ear and the brain, but a result of the computer using modular arithmetic to single out each n-th amplitude (because it can't really replay above a certain resolution).
If you think about this fractal idea as related to sight rather than sound: you get a good example looking at fan or helicopter blades - I'd like to see how the 'look of reverse spin direction when speeds are changed' comes into play audibly. Please investigate this if you have time.
frequency modulation synthesis moment
You should've enlisted the help of fellow mathemusician ViHart.
Adam Neely is giving me Taylor Mason vibes in this vid. In a good way. (I love "Giant Steps," btw.)
who else TH-cam notification squad here? Real Neely hours
en.m.wikipedia.org/wiki/List_of_pitch_intervals pretty sure this is close enough
There are those who use Ableton Live to make beats and then there's Adam ;)
But you play it with midi right? If so, all you hear are the multiple frequencies of Ableton's midi engine not being able to play midi note that fast. Otherwise the timbre of each note of the final result would be MUCH more complex than this... Maybe you could check with audio files instead?
My thought exactly. I'm meaning to test this; it won't be too hard when I have the time to get around to it.
It's also true that the initial phrase is just repeated and it's not the whole solo that is being looped. My guess is that this phenomenon is probably true of any MIDI melody played really fast (with Abelton's midi engine) and is therefore not a feature of Coltrane's solo. It would be a fractal if and only if the ENTIRE solo produced this phenomenon when repeated.
Great video Adam, as always! But it seems like the audio and video get out of sync at around 4:42, and the dichotomy progressively gets worse as the video progresses (it might start earlier, but I'm not sure). It could just be my phone, but I don't think so because other videos seem fine.
No, it isn't just your phone... :-)
My guess is a mismatched frame rate between the video as shot and the video as uploaded to TH-cam (or possible mismatched audio rate)
On my phone too.
my phone too, but even a little earlier than the time you mentioned
Like the video but it goes out-of-sync on my iMac as well.
Hey, quick question, what the fuck?
6:48
When the bass is about to drop.
6:52 when the bass dropped, and started a world war.
his cat chilling the background : 3
I want to add an engineering perspective to this, which gives another lens to explain this but should also address to some degree concerns that the hardware or software is compressing or aliasing away data. It is, but even if it weren't it would sound the same anyway (edit: if done correctly, see the correction from Daniel), which is proven by the Nyquist-Shannon sampling theorem and a little biology.
The sampling theorem is pure math and necessarily true divorced from the physical world, but what biologically makes it useful is that ears can only hear sounds within a limited band of frequencies, being about 20 Hz to 20 000 Hz for humans.
When we talk about frequencies, we're basically talking about sine waves, and we can do that because of the Fourier transform, another cool bit of math proving that any continuous function can be written as a bunch of, possibly infinitely many, sine functions added up together, or talking about sound, a bunch of sine waves playing at the same time.
Sampling theorem uses this, coming in when we talk about recording or playing back a sound digitally. That means changing something continuous like sound into 1s and 0s, a finite number of discrete bits, so if you think of the waveform of a sound which is a smooth curve and record digitally, the best you can do is record the height of that wave at specific points in time. Intuitively one might think that loses information, but when it comes to human audible sound, sampling theorem basically proves that intuition wrong.
Sampling theorem says that if our original signal's frequencies (as defined by its fourier transform) are limited to a finite band (as they are with human hearing), then as long as we take samples at double the rate of the highest frequency, that is enough to mathematically perfectly calculate that original signal again. No data lost.
Digital software and hardware take advantage of this, always digitizing sound with samples far beyond human hearing. If the midi notes went by so fast that the software or hardware lost some of the data, that is sound that human ears mathematically are not capable of hearing because the only difference in the resulting sound waves are frequencies beyond the human ear.
So when it comes to the idea that all these midi notes played very rapidly end up also sounding like a smaller number of notes played at more typical speeds, that's because that is in a sense what is going on.
As Adam says we start perceiving those rapid notes as just waveforms, but outside music theory it is also true from this engineering signals perspective. The incredibly rapid notes produce some high frequencies that get filtered out, if not by the hardware or software then by the biology of human ears. The perceived waveforms of the perceived notes are whatever waveform you would get by running those sped up notes through a low pass filter to remove high frequencies, which is also equivalent to sampling the waveform at double highest frequency humans can hear.
The highest frequencies created by so many rapid notes cannot physically be heard by ears. The audio software knowing this likely drops some of that data using a lower sampling rate (edit: again, this would only work accompanied by a low pass filter), because it knows the wires transmitting data can physically only transmit a limited rate of bits, which is also fine because the speakers physically cannot vibrate fast enough to reproduce the very highest frequencies, which is fine because those cannot be heard by human ears.
The Nyquist-Shannon sampling theorem is fundamental to the field of digital signal processing which makes all digital audio recording and playback possible, but surprisingly also images and video to a lesser extent. Any engineering class on signals would teach it very early on, certainly for many electrical engineers. I'm also curious whether audio engineers are taught the same thing.
Agreed. I think the computer is definitely dropping notes at the higher playback rates. If the speed was increased even further, we'd probably go through a very similar pattern as we heard in the existing clip.
That's a very long way to explain why the sampling rate of most music is 48KHz. But it made it clear to me, so thank you very much.
You have it the wrong way round. The Nyquist criterion means a system sampling at 40kHz can actually reproduce signals up to 20kHz, but it CANNOT accurately reproduce frequencies above that. So you can reproduce what humans do hear, but for frequencies above what humans can hear you can get aliasing. If you were to oscillate a speaker at 100 kHz you wouldn't hear anything, but if you have a 100kHz signal that you sample at 40kHz and then play through a speaker, you would hear a signal at 11.8kHz. If you lowpass a 100kHz signal to 20kHz, then sample it at 40kHz, then play it back, you will again hear nothing, because the low frequency content doesn't actually exist. That's the whole point of worrying about aliasing, it's not the same as a lowpass.
@@danieljensen2626 You're totally right, I completely missed the aspect of requiring a low pass filter for what I described to be viable and avoiding aliasing, and honestly got the concept a bit mixed up. I was mostly focused on the idea that you can in fact represent the human audible portion of such a high frequency waveform using a finite number of samples, and presumed a good piece of audio software would incorporate it into the final version, but that's not at all safe to assume. I should edit the comments I already made. Thanks for pointing it out.
muse > mathic
ET may be like: _Your room lighting is awfully dissonant. There must be electrical wires running behind the walls. Try a different wallpaper glue. I think its smell is causing your video to rotate by a millionth degree to the distant middle bottom every now and there._
To be fair, you have to have a high IQ to understand John Coltrane. His music is extremely subtle, and without a strong understanding of post bop and avant garde music most of his music will go over a typical listeners head. There is also Coltranes' advanced reharmonizations soloing techniques, deftly woven into the chord structure - his soloing technique often draws from polytonality, for instance. The fans can comprehend his music; they have the intellectual ability to truly appreciate his soloing technique, to realize that his music isnt just notes, they say something about LIFE. As a consequence people who dislike John Coltrane truly ARE idiots - of course they wouldn't appreciate, for instance, the usage of "the lick" frequently in his solos over the common ii V I progression, which in itself is a cryptic reference to the popular Wagner-esque leitmotif craze during the romantic era. I’m smirking right now just imagining one of those addlepated simpletons scratching their heads in confusion as John Coltranes genius wit unfolds itself on their Itunes or what have you. What fools, I PITY them.
chill Freddie. 😂😂😂
Interesting twist on a classic, like Coltrane and Favourite Things. Nice
What about the tattoo part of the copypasta?
I've never seen a smaller dick on the internet.
Musical preference as a predictor of intelligence...hmmm. In what culture? At what point in history? Etc., etc., etc.
6:40 you can hear that "sorting methods video" noice 👌
For didactic purposes, especially since I'm a Latin teacher, I pronounce ORAL and AURAL as different words. OR-ULL, and OW-rull, as in, OW that hurts. From Latin os, oris, and auris, auris