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

"All musicians are subconsciously mathematicians.“ ― Thelonious Monk, Jazz Pianist and Composer

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.

Adam Neely: the Vsauce of music.

This was a very good cat video. The guy in the front talking all the time is a bit annoying though.

I have no idea what to do with this information but it's a lot of fun.

16x speed: pacman 32x speed: pacman about to drop the beat 64x speed: pacman got a gun, everyone get down!

So if my math is correct. 1 + 1 = 2 E= mc^2 Coltrane Fractal x64 speed = AK47

Man... This is absolutely brilliant and must have taken a TON of work. Thank you for this and congrats on the 200,000 mark!

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.

Deeeeeeeep, very deep.

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.

180k Coltrane solos per second? Yes please!

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.

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.

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!

Really noticed the quality of editing in this one - very slick and appropriately used. Fantastic stuff Adam.

This was very enlightening and opened my mind to how amazing sound and the way we perceive it really is. Thanks!

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.

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!).

6:48 from pacman to service in iraq

The legend says that the almost major 6th is still trying to become an actual major sixth.

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.

Thank you for providing such a smart perspective on music and sound. I totally get what you're saying and I appreciate you for articulating it so well.

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.

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.

6:46 from an overheating 32 bit game console to a machinegun in a couple of seconds

Every time Adam starts to say “midi clips” I keep expecting him to say “midiclorians.”

Congratulations on hitting that milestone! Though in my opinion you deserve way more than just 200K

6:46 get ready for the Drop still waitin 😢....

Best 200k subscriber special ever

I remember watching this 200k subscriber video when it was first uploaded and now Adam has about 980k subscribers. Can't wait for the 1 mil!

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.

Its like Vsauce.. for musicians!

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

I have not seen anything so mind blowing in a LONG time!

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

Amazing content! Really well thought, researched and well put together.

3:43 was so funny I have no idea why

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.

"Hey, check out my music!" => "This is just noise!" - an alien from outerspace - also, my mom

This turned into a ted talk and it was good.

my mind is all over the wall behind me

this is one of those videos that really changes your thinking, now after 2.5 years it still surprised me

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 only listen to music with howling dominants now

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.

this video deserves more attention

Besides being interesting and a fun topic of discussion - I'm curious how musicians use this kind of information in their music.

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.

Super interesting video,Adam. And rather amazing result from speeding up those notes. Even as an engineer, and part time musician, this is going to take some digesting (a testament to the work you did in presenting it). Thanks for further opening my ears :-)

Thanks . Seems like orchestrating the triplets & sticking can add up to something very musical . Buddy was great at this .

huh, neat

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.

6:28 this part blew my mind clear out to the stratosphere

I love the visual creativity of this video. Props for all the hard work!

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 KZfaq 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.

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.

Brilliant, Adam. I hope to learn more of your research. Truly fascinating.

The cat appearance wins, great info brother. Thank you for your divine energy

"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

9:11 long illuminati confirmed in video I think Adam Neely is hiding things

dude, as a mathematician and amateur musician this just blew my mind. thank you so much, you just opened a whole world for me!!

Your videos and your instruction are gold. I say this with the highest esteem.

6:48 *So that's why the game Pacman was so freaking popular!!! All those coins I spent as a kid!!!!* 🤣😄🤣😄😃

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

Adam, you are my personal MVP of the internet!

Recently, working in a recording studio, an engineer brought in a brand new alto sax. Yamaha. None of the musicians could play alto sax, as the session wore on, we all had a crack at the new sax, now, once you get the breathing and the reed/mouth piece, somewhat together so as to produce a note, then moving the fingers over the keys very quickly, boom, sounds like Coltrane, more by accident than anything else. "Try it "

but is it really our ears doing the work here? dont the notes get compressed by the program you are using already?

I gotta try this

My ears blew bleeding due to so much calculating. Thanks Adam.

I am honored to be a Coletrane F# of your subscribers! I have learned a ton...

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.

6:47 Pac-man 😉👻👻👻

I just entered at University to studying physics, and its so easy to me calculate the ratios in equal temperament (couse you are doing it at pitegorean temperament)

I have been able to follow every single one of your videos, even if only a little. That record has been broken. Damn you, maths!!!

wow a year later you have like 162.5% more subs... congrats man :)

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.

I find your channel and it’s content exceptionally educational

I'm a piano player and I like this concept Very nice job

well now i know why people in medieval times hated the 3rds lol

6:53 Coltrane's solo seems to be turning into a machine gun...

We can go deeper though. Take a MIDI melody, record the audio, then put it into a sampler (for instance the one in Ableton), and pitch it up enough so that it plays back fast enough to match the pitch the original melody was played at. We have then created a sampler patch that will play any MIDI notes sent to it as a series of tuned, high frequency repeats of the original melody - no math needed. You can then use that sampler patch to play the original melody, record the audio from that, and progressively build up layers. Because we're using a sampler to do the math for us it becomes feasible to build up a lot of fractal layers without too much effort.

dude ...... dude ...... i appreciate your existence... much love ...

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

My brain... Not just the content, but the fact that it's coming form a bass player...

1:00 I love the honesty

"Crusty old jazz man" LOL. Very impressed by Adam's knowledge of the science of music, most of us would be clueless on this, let alone be able to make a great video on it!

Is the audio not synced to fuck with me?

Gotta admit that you lost me there at a certain point. I don't want to admit how early.

Dude this was super exciting. I’ve always said this. Like, we can’t be sure that we are all hearing the exact same thing. And then it dawned on me, perhaps that’s why people like different music. How can some people LOVE one song, and others HATE that song?

ONE OF THE MANY REASONS JOHN IS STILL THE GREATEST.

Σ 1/k. The harmonic series

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.

200 000? Congrats on the almost 1 million. Such massive growth in 2 years.

Dude your channel is awesome, and by the way that stuff is pretty incredible

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?

Coltrane brought me here

THAT IS FANTASTIC. Love it.