@Rob Scallon I watched this despite learning the harmonic series years ago because I knew he would come up with *something* I didn’t know. That same part was new to me and makes total sense.
@@CyclesAreSingularities I mean if you want to seperate such a complex subject like maths in "highschool" and "physics" maths go ahead but that still doesn't undermine the fact that physics can only be applied to the real world by the application of mathematics
Honestly this was the first thing I wanted to figure out when learning music theory. Learning WHY things sound good together is so much more important to me than learning HOW to put things together.
@@HORNGEN4 On the topic of wobbles I have found a video with additive synthesis imitating a Leslie speaker on a organ ruclips.net/video/NIe8H8D54IY/видео.html
Andrew, I've been teaching music theory for years and have taught the harmonic series to some of my high school classes. Usually unsatisfactorily. Ive never seen it presented well in a reasonable timeframe. I used to use Leonard Bernstein's 1973 Harvard Lectures series clip of him demonstrating it on a piano. Charming if you love LB but terribly, grossly out of date for students today. This is the BEST video resource on the harmonic series I've ever come across BY FAR. Thank you so much.
" terribly, grossly out of date for students today." I really worry about that attitude. Someone just one generation older seems 'out of date', superannuated. As though a haircut or accent or costume alters what a person is saying! Trivial, superficial people. Not necessarily a generational thing, just whether one has a sense of history.
@@smkh2890 I understand your dismay, 100%. And I agree with your sentiment. I dearly love Bernstein and I have watched his entire Harvard lectures series numerous times. But Bernstein explaining something is long-form poetry. It could take 20 minutes to an hour for him to make the point. Bernstein is too brilliant and too aesthetically minded to simply give the bare facts of something - he will weave the point into a tapestry of interconnected concepts and supporting metaphors. But here’s the thing - I first found those lectures as an undergraduate music student and I devoured them on my own time. They aren’t well suited to be a supporting material for classroom teaching at all, and that’s what I need for my HS theory class. In the past, even when I showed my HS classes preselected 10-15 minute excerpts of his lectures, they didn’t quite get it. Look at Andrew’s style by comparison. Utterly different pacing, among many other things. Style is a language, and modern students speak the language of his style.
@@brianmessemer2973 of course you are right. I don’t want to repeat cliches about attention span because my own attention span is not what it used to be. But how many now listen to a piece of music 40 minutes long or more in one sitting? How many read 1000 page novels? Even full length albums are gone . people listen to one track and buy single tracks . the 70s ‘concept’ album with a story development over an hour or more, Tommy by the Who would be a good example, seems to have disappeared.
@@brianmessemer2973 as for teaching I taught English language mostly to students who are paying so they were attentive. I’ve also taught English literature at college level but I am not yet at the point where I dare to teach music. Anyway talking about style of teaching, Andrew is very very good . I think he is sponsored by Reverb, so he has resources. I did some electronics in the ‘60s so the components he showed in a bag were not a mystery!
@@smkh2890 yeah absolutely sir. Your points about music and literature are well taken. There certainly seems to be less time for, less emphasis on, and less cultural value/appreciation placed on the study of large works. Funny coincidence - I also taught English language in Japan for several years before teaching music back here in the US. Thank you for sharing your thoughts and background a bit - what a pleasant conversation with a likeminded individual. Cheers to us 🍻 and cheers to art, literature and music that takes time 🍻
Other MIND-BLOWING facts: - The reason sometimes sounds start clipping after you EQ them subtracting harmonics (which seems absurd), is that the harmonics you removed were interacting with the others and they were actually lowering the peaks of the waveform! - Two waveforms may have the exact same harmonics with the the exact same intensity yet sound completely different, because the harmonics are phased differently (the sine waves do not "align" the same way), so with a bunch of harmonics you'll still be able to obtain infinite sounds! EDIT: I substituted the term "interfering", which was technically incorrect, with "interacting". EDIT 2: Editing the comment made me lose the Heart from Andrew 😭😭 what we do for science
I'm not sure that's *completely* true. It *is* true that adjusting the phase of the different harmonics would make a signal that looks really different on a scope... However, humans are *really* bad at hearing phase of different pitches in a sound. (I'm pretty sure it has to do with the way the cochlea breaks up sound into different frequencies, but I'm not a doctor). So if you have two signals which have the same frequencies but slid around in phase, they'll sound the same to a human. Then again, humans are really good at picking up different phases *between the two ears* so there might be some funky psychoacoustic stuff going on if you tried that. (Also, apparently there are some animals whose ears work differently so they might actually be able to directly hear phase.)
And that's why the fourier transformation has to be calculated in the complex space. Every frequency also has a phase. But analyzers usually do not show them.
@@scorinth They will sound the same to a human, but when played together, it's not about the brain, its about the vibrations and the physics of the real world. The waves literally cancel each other out in the air and thus those frequencies are lost or reduced in amplitude.
The coolest thing for me is that variations in harmonics is also how we pronounce different vowels. When we change the shape and position of the mouth and tongue, we create a different "instrument" that prioritises different harmonics. Basically different vowels are the result of filtering and boosting specific overtones.
If you haven't studied quantum yet you're in for a fantastic surprise when you get to the harmonic oscillator. Wave theory is ubiquitous throughout all of physics!
Just going down the music theory rabbit hole and was just unable to grock how the same pitch sounds different in different instruments and this finally cleared it up for me.
What if I already knew about it, *and* I'm still impressed? I knew theoretically if you EQ'd away the harmonics, it'd sound the same, but I never thought to try it out. It felt different to hear it actually work.
I already "knew" all this as a scientist. But now, as a beginner musician, you made the relationship to chords, notes, and instruments so clear for me!
Many folks out here are well familiar with this and many other concepts that are not scientists or engineers or anything like that themselves. Interestingly enough, these concepts in physics and other focused scientific fields are the shared connection between any other concept or endeavor. And funny enough you could be coming to understanding and awareness of technical concepts by actually practicing "science" and not even know it just by doing other work, craft or study. Now, a scientist may scoff at that bc the practice itself has a set of rigid formalities and standards to be consciously followed or its not credible as new theory, law or fact, but the process of discovery can be very similar and just as genuine to one's learning and comprehension of reality. I think its healthy, interesting and helpful to share such analogies.
When you play a harmonic on a string, you are actually physically stopping lower harmonics from ringing, while keeping the higher harmonics. For example your finger over the twelth fret, halfway across the length of the string, you prohibit the fundemental from sounding.
What I really love is when I mute one string after playing it, and I hear the exact same harmonic vibrating from a different string that I didn't touch.
And then there's that violinist who somehow got the violin to produce tones *under* the violin's range and we still don't know what the physics are exactly.
@@woofelator That's sympathetic vibration, which is what makes sitars sound so goddamn cool. My high school music teacher demonstrated this to the class by taking the front off a piano and using his clarinet to play a note directly at the corresponding piano wire. We could then hear multiple piano wires sympathetically vibrate relevant to the harmonic series of the fundamental being played on the clarinet.
I remember being introduced to harmonics through throat singing one day. I think my local radio had a little segment on it, and it blew my mind that you could shape secondary notes over the main ones. I recall standing in front of the mirror with my electric toothbrush and opening and closing my mouth to isolate the different overtones. Thanks for bringing that fun time back to me, Andrew!
You'll often still hear overtones with a sine wave actually, because you're hearing them through speakers which have their own ways of vibrating and their own resonant peaks and you're also hearing the room. I think it's more in theory that they don't have overtones, because in the real world I'm not sure how you'd listen to it without engaging overtones from something, even if just from your own ear canal.
Then you don't hear a sine wave. Once the tone is colored by your amp, speaker, cable, W/E it's no longer a pure sine. It has gotten harmonics injected in the wave. So in a way you're right that it can only exist in theory. But with decently tuned and chosen gear you can approximate that sine wave to a point where the overtones you speak of have no real world influence on what we're hearing.
Acoustics nerd/musician here! While overtones do not have their own overtones, they do "create" more notes! These notes are perceived when any 2 notes (including overtones) are present. The term for this phenomenon is a "combination tone" or more specifically in this instance a "resultant tone". Resultant tones are often sounded an octave below the fundamental, adding additional depth to a tone of a given instrument. This is one of the aspects that makes virtual instruments not as "real" as their real instrument counterparts. This goes into what is known as the undertone series which is a whole topic of it's own (your string player friends should be able to tell you more. "wolf tones").
@@XenoghostTV it's also why distorted triads sound nasty if you don't fudge the intonation. The difference tone from an equal tempered major third is a very out of tune minor second, two octaves down. Gnarly on it's own, nightmaremish in a mix
Former opera singer, now digging into instrumental music and music production, from orchestral to the 80s synths of my childhood. This video utterly blew my mind, and was even news to my wife who has a Masters in music performance. GREAT video, clearly, concisely, and enjoyably explained. And you can't ask for more than that when it comes to education.
This is also how most image compression works, like jpeg. Instead of storing the actual pixel values, it reduces each block to a sum of sine (er, cosine) waves which add up to something very similar to the original signal. It's a very effective way to represent the types of shapes which tend to occur in nature. It has a hard time with square waves though, since those are the sum of an infinite series of sine waves. It takes a lot of space to store an infinite list of all the harmonics needed to build a square wave, and the point of jpeg is to make things small, not large. So it usually stores only the first few harmonics and the error becomes pretty noticeable whenever the picture has sharp edges.
There are definitely more compact ways to store data representing square waves... but they tend not to be as good at storing smooth contours. The compression is basically optimized for what the creators expect the input data to look like... so it'll be less optimal for unusual data. Although jpeg was a big step up from what came before it, there are definitely some corner cases (pun intended) where it's not so great.
Sound and light aren't part of the same spectrum. They're different types of waves. Sound is a compression wave of particles transferring kinetic energy by bumping into each other, like how ripples travel across a lake after throwing in a rock. The water itself isn't travelling outward; it's mostly just vibrating in place. The ripples don't exist without the lake. Light, however, is actually pure energy travelling from one place to another. It's not cascading vibrations of some other material... it's photons moving across space. Light exists as individual particles, while sound is a side effect of the movement of many many particles. Sound is a domino effect and only exists if there are dominos to move through, while light is more like throwing a ball.
You make RUclips something else Andrew. The amount of work that has gone into this video for us to view for free. Damn dude... Mad respect. This is untouchable content.
"It's the foundation of all the chords and scales we use. It's the reason why certain notes sound good together. It wasn't just that someone back in the day decided on a scale they liked and we all agreed to it and are using it out of habit. It's that the physical laws of the universe determined what these note relationships would be, long before music existed, long before humans even existed. Any resonant body vibrating at a consistent frequency would also include harmonics, would include those integer multiples of that base frequency." This is absolutely profound to me. It confirms to me the idea that our relationship to music is innate and universal rather than cultural and relative.
I felt the same. It confirmed to me why music by default is therefore so powerful in terms of provoking emotion etc as it is so intrinsically linked with the universe as a whole and all living structures. Basically the universe is a construct formed by numbers and mathematical equations both biologically as well as physically and on every quantifiable level, in this case audibly too. Everything we both comprehend and don’t, consists of vibration and frequencies. If you are able to master the rate of this vibrations you are able to master life. Raise your vibrations and you raise your synchronicities. Raise your synchronicities and you create the ability to manifest.
I think it's more of a thougth to apply to science and math in general rather than just music, the fact that science and math are so accurate to describe our world despite being made by humans it's mind blowing
@delt Wow, I somehow said that Google was the keepers of the mathematical constants we use to describe the universe 🙄 No. You said that those constants would exist without someone to discover them, and I countered that the assertion is based in philosophy (specifically, epistemology) rather than the hard sciences. Thanks for strawmanning something that is only really debatable in philosophy, the field I mentioned, because 2 is how we describe that quantity of items, not an actual physical substance. You can hold two apples, but you can't hold 2. That's my whole point 🤦♂️
Most mind blowing thing that I learned recently in music is: Keys/Chords are only relevant to the most recent chord that you transitioned from. Think about that. That means chord number 3 can be totally bonkers from chord number 1 as long as chord 2 works to give you the feel you want when you transition from 1 to 2, and similarly works to give you the feel you want from chord 2 transition to 3. This is how great musicians use the circle of fifths to bounce around from literally wherever they are to wherever they want to be.
Fun fact: this is also why your voice sounds different to you than to everyone else. The sine waves making up your voice travel differently because when you hear your own voice, they're passing through both the air and the bones of your head to your ears. Low frequencies carry better through physical contact than the air. If you experiment a bit with EQ, you can make your voice on recording sound closer to how it sounds to you speaking.
It took me a while to find it but like a year or so ago I found a really good paper on this and how to reproduce the voice you hear aka about what eq you need to get it. Sadly I didn't save the link and haven't been able to find it since.
Cover your ears with your hands, fingers pointing up, then fold your hands forward, keep the sides of your hands tight to your head, shielding your ears from what comes from front. Tadaa, your sound! 🧸💕🦠🔨
@@Stiddo Can you put it on a google drive and send the link, please? I'd love to read up about this. Seems like it could be a very creative way to make use of vocals. I've been having some trouble with vocals so experimenting and finding the best way to do it seems smart to me.
This is so true tough, alot of newer producers always think you need expensive gear to make good music while really all you need is a computer and a headset. Sure, the expensive gear could theoreticaly help, but only if you know the fundamentals of how it actualy works aswell as how to use it in general. Expensive gear is not a nececity
Physics major here, I wanted to say that I love that you are going out of your way to teach this. But, I wanted to shout out the guy to first discover many of these effects and give credit to him as few people actually know of him, but his contributions mathematics and science have changed all our lives far more than the vast majority of people we do all know about. Joseph Fourier is the father or harmonic analysis and Fourier analysis. This mathematics is used to study everything from the musical concepts you’re discussing to electronics to thermodynamics. Even many of the physicists who use his work all the time don’t know this but, he is also credited with discovering the greenhouse effect. One could argue this would effectively credit him as being the discoverer of global warming.
As a physicist, do you know where the harmonic series came from, its origin? It's a question that I have thought about a bunch and have some ideas but I hope somebody who studied the subject has their ideas as well.
@@TiqueO6 This notion of the harmonic series essentially comes from the notion of a Fourier series or a Fourier Transform. The fundamental idea is essentially exactly what this guy is talking about in the musical context, but the idea has consequences that much wider reaching than that. For example, the same technique can be used to study how heat in some distribution will diffuse over time. Basically, it is possible to represent a surprisingly large amount of functions as a sum of sine and/or cosine waves. In fact, any continuous function on a finite region can be represented this way. Now I would explain how this works, but I think 3blue1brown explained it better than I ever could in this video here. ruclips.net/video/spUNpyF58BY/видео.html&vl=en
As an amateur musician and professional artist-designer, i see so many relations between sounds and colors, and visual and musical composition. Your explanation of chords and harmonic series makes me think of Impressionist paintings, of Monet and Renoir, and how our eyes naturally mix contiguous colors into one. And color afterimages as well, which is why when we fixate our eyes on a red dot and then look away, we see green, the complementary color of red - just like the harmonic series. Thanks for the amazing video!
When I was in a choir growing up, they trained us to listen to the harmonics, so we could use them while we sang to improve tuning. When voices are in tune they become less distinguishable, but the overtones get stronger. Really cool stuff!
Yeah, I always noticed that I can only tune this string using a chord, unlike all other strings that I can tune separately. I only did not know why. Great video, thanks for sharing the knowledge! (yes, I did know everything except this out-of-tune-equal-division-stuff).
This is truly the First time I’ve heard someone else say that tuning the B string is AWFUL!!! I’ve been saying this for Years, and people think I’m nuts!!! I’ll have to try tuning the string in a chord...that’s a great idea. I use a tuner and either adjust it by ear, or I just suck it up I’m actually a drummer for 40 years that is self-taught guitar.....so I’m not very good...but bro....that B string kills me!!! 😂😂😂
If you can get the harmonic pluck just right you can gently touch (not press) just above the B string on the 5th fret and the G string on the 4th fret. When you tune the B string with the G string this way and you don't hear any beading it should be in tune, at least with itself. I didn't learn this until I had been playing for 5 years. Worst 5 years of my life. B is now my favorite string.
@@ericchin739there is no note. it's due to the mind's evaluation that creates notes. every perceived note is a combination of every other note, but every other note is also made of every other other note. It only appears to be a wave due to the integration of the evaluation process of the mind. There are no waves in reality, only in the mind due to conceptualization/evaluation/interpolation due to linear approximation/assumption.
I remember this high school teacher who taught math and guitar class would always say that theirs two universal languages: math and music. Mr Nolan was such a chill hippie teacher ^_^ He would even bring his own drums in for a drum circle club once a week. It was him who made me realize how much math is related to music in a non negative way
Was his favorite band Dream Theater? lol. also, math is a tool but also language that can describe anything. spoken and written languages can be related this way. Software languages are no different, they just have their own systems and application where it makes sense. Your genetic code is kinda like firmware in a way, your personality and own awareness is like an algorithm. Brains are not computers though, well kinda like a router I would say and your consciousness resides in hyperspace, a bit like cloud computing. Electricity is pretty important lol and also needs math to be explained studied and manipulated. Everything is math, its the root. Not everything is music... We like music because of patterned harmony of sound waves and patterns in arrangement of events over a formatted time parameter. Our brains really only do one thing, notice patterns. Aesthetics are patterns pleasing our purpose.
"Overtones don't have their own overtones." Yes and no. While each overtone of a fundamental is its own sine wave (pure tone), each overtone has its own overtone scale within the original fundamental's overtone scale. For example: The partials (fundamental plus overtones) of a C fundamental: C - C - G - C - E - G - Bb* - C - D - E 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 Order of the first few intervals: C - C (octave 2:1) C - G (perfect fifth 3:2) G - C (perfect fourth 4:3) C - E (major third 5:4) E - G (minor third 6:5) Now let's look at G, the 2nd overtone (3rd partial) of C. To get its overtone series start with 2:1, G - G (oh look, the octave up of the first G is the 5th overtone (6th partial) of C) G - D (a fifth up (3:2) the D is the same D from the ninth partial of the C overtone series) D - G (a fourth up (4:3) the G is the third G in the C overtone series, or partial #12) You will find the G harmonic series within the C harmonic series simply because G was introduced. Every time a new note is "introduced" in the harmonic series, it too will have its intervals up to infinity (2:1, 3:2, 4:3, 5:4, 6:5, 7:6, etc.) So an overtone series is self containing of other overtone series. 🤯🤯🤯
Andrew is actually right when he says the overtones don't generate their own overtones. It's a standing waves problem--if your original C sounds off a string of length L, then the G would sound off a string of length 2L/3. Strings of these lengths may share a few harmonics coincidentally but for the most part will not mach up.
You literally just explained virtual instruments. And more importantly the basis for timbre and what bit really means. AWESOME !!!!!!! No matter how rich you get on youtube don't forget that creators like you still figured out how to make great content by being yourself and sharing your knowledge!!!!
Harmonics, the stuff of sound. I remember when I first started to learn about harmonics, it was mind blowing. As an organist, I feel that it's necessary to understand harmonics up to at least the 8th because it will determine what sounds you use and certain sounds to avoid and why certain sounds blend together while others do not. At 76, and having had a life in music, teaching, playing etc, I'm still blown away at how the physics of sound is so important in getting the sound that you want. Thanks Andrew for explaining this subject so well and so clearly.
Andrew my man, you are king. I’m a sound therapy practitioner, and your understanding of sound that you pull into your creation and producing is exactly what the world needs. When we look at everything in creation, EVERYTHING IS VIBRATION. Sound and music, using the laws of resonance is going to be HUGE in the near future for emotional and physical healing. (The physical body is a reflection of the emotional state, the more our nervous system is in a coherent state, the body functions in a homeostatic state.) the better we feel emotionally, the better our bodies function. Love all that you do!!!!!
I learned about this in college music theory, and listening to an additive tone generator my mind was officially blown. They also talked about how square waves vs sawtooth waves are all of the even overtones or all of the odd overtones. AND THEN my mind was blown further when realizing that all the brain can do is sense vibrations from tiny hairs inside our ears, meaning that (like you said briefly) the brain is constantly doing math to decide if it’s hearing a single timbre or multiple timbres. AND THEN my mind was blown further when realizing that the only difference in human vowel sounds is their timbre, meaning our understanding of language is all due to these lightning fast calculations done by the brain because one hair wiggled a little faster or a little harder than another one. Don’t even get me started on how it impacts our perception of three dimensional space...
The way waveshapes are built would've been a good addition to the segment in ableton with the additive synth, I thought he was leading there. Well presented video anyway though.
Can you explain how the only difference between vowel sounds is their timbre? Sorry its kinda making sense based on what I heard in this video but not fully
Sure, basically the way our bodies make different vowel sounds is by making shapes with the tongue and lips which dampen or amplify certain overtones. “EE” shapes highlight higher overtones, while “OOH” shapes highlight lower overtones.
i had to sample and additively re-synthesize a pipe organ for my sound design class this past semester, and it honestly still blows my mind how close it sounds. Understanding the harmonic series has really done so much to enhance my understanding of production and synthesis.
This is just a fantastic explanation of one of the most complex concepts in music, and it’s made complex because we aren’t taught this from the start, we are pre conditioned to accept the “rules” of music and intervallic relationships. Thank you so much dude, this vid is very helpful to people, I’ll be sharing with my students
Great work Andrew, very well elaborated and explained. Two things: the string cannot simultaneously be in different modes.That is a physical imposibility. Rather, i think, it passes in dt from one mode to another. And secondly, that was also mind bloiwing for Pythagoras, who first discovered this, that is why he said that all things are numbers .
The Fourier series video by 3blue1brown shows how it's probably the most important concept in sound, and physics in general. When you draw notes out in your DAW, then record it into a waveform it's exactly the same thing. We can extract all the drawn notes from the waveform by doing a Fourier transform. Conversely, we can create the waveform from the drawn notes by doing an inverse Fourier transform. It’s all just transformations from frequency domain to time domain (and back). This concept is the most important element in quantum mechanics. Math is the friggin best
It goes deeper than that. If string theory is to be believed, then all subatomic particles are on a fundamental level 'strings' vibrating at different frequencies. Mean literally everything can be broken down to nothing but sine waves.
@@JonasHamill Leaving aside string theory for a moment, just pointing out that not all *vibrations* are sine waves. A sine wave is a smooth periodic oscillation. Vibrations can be way more complex than that: www.testandmeasurementtips.com/basics-non-sinusoidal-waveforms/#:~:text=A%20non%2Dsinusoidal%20waveform%20is,sinusoidal%20(sine%2Dlike).&text=A%20cosine%20wave%20is%20sinusoidal,but%20is%20neither%20of%20these.
@@llaith2 All frequencies can be broken down to sine waves. More complex wave forms are just multiple sine waves. You don't have to take my word for it but I have a degree in Electronic Engineering and work with signal processing on the regular. If you wish to look into it more look up Fourier Analysis. You can even look at the following quote from the link you provided "A non-sinusoidal waveform can be constructed by adding two or more sine waves"
@@JonasHamill Dude its cool. I did electronics engineering in uni before having a career in software. I get you but I thought your comment was simplifying the matter, given the context of the video where he didn't go into detail about recreating the timbre of instruments with pure sine harmonics. He did mention about other aspects of the waveforms a bit later, but it didn't seem connected for people who don't know this subject. I thought you were saying that any timbre could be recreated with simple sine waves at different amplitudes on the harmonics. Mainly it came across that way because of the way he was clicking in the software to add those harmonics in. So no offense meant. Btw, I suck at math, so those kinds of problems nearly killed me at uni! I decided to focus in on digital circuits and the micro-architure of chips instead. The switch to software was inevitable as I enjoyed coding in machine language for the chips we used. I'd rather not read any more on the subject in case my brain starts melting again! :D
For those interested: Early Music Sources (here on YT) have a couple videos on how just intonation worked in the Renaissance-covering the concept of composing a piece whose general pitch slowly rises as it's all relative. Adam Neely more recently made a video exploring that musical notion, Benedetti's Puzzle. Anyone who liked this video might find that interesting.
Comparing those 2 major thirds is mind blowing. The fact that the one that we’re used to is “wrong.” But when we hear the just intonation version, it sounds a bit more subdued and calmed, and of course darker. It actually sounds less dissonant once you hear it more.
This is amazing. And what really blows my mind is when you start thinking about wave patterns in nature and the physical universe. Gravitational waves, electron waves, color spectrum, movements in the ocean, heart and brain waves. So much is oscillations and waves. I don’t mean any of this in some new age stoner way, just that what you are tapping into feels significant.
Same happened to me when talking about this. People generally get into ''new age'' chatting without getting into the real talk, and start to lead the conversation into ''energies''..and you try to redirect saying ''no no, not energies like spiritual and good & evil, but real energy, the one that happens every moment in daily life'', and they look at you as if you were high or psycho or just trying to look smart 🙄
@@VeronicaGorositoMusic Go to Santa Fe, New Mexico. I met a woman from the Pleides star system. She told me all about chakra energies at a party. And numerology. It was a great sociological observation until it got boring.
This is why I'm a microtonalist. 12 equal isn't bad, but it shouldn't be viewed as God-given, when it's really just a system of compromises for particular goals. If you're mostly staying in one key, meantone is better than 12 equal. Composers in the Romantic period started to modulate keys a lot, so it was important that there be a tuning system that could handle that. Of course, you can always divide the octave equally by a different number than 12. Each number is its own musical universe. Each can do some things better and some things worse than 12. 53 tone equal temperament is super accurate (at least for major and minor chords) but it's really complex. 17 equal is melodically better sounding than 12 equal, and it's also almost as easy as 12, but its harmonies are a bit off from what we're used to. 19 is harmonically more in tune than 12, but melodically worse. Different tuning systems are all about compromises between good melody, good harmony, and ease of use. There's nothing wrong with 12, but it shouldn't be the only system that's ever used.
This is crazy: something so obvious that it's overlooked, can be easily understood, which, in-turn, breaks open so much more to be experimented and appreciated when working with music. Music is truly amazing
9:36 As a brass player, it finally clicked for me when I realized that the partials are divided into these pitches. On trombone the partials go Bb1, Bb2, F3, Bb3, D4, F4, a very flat Ab4, Bb4, C5, D5...
And here I thought I was the only one who struggled to tune the B string lol. Great explanation of the harmonic series. It's really amazing how well music relates to itself in so many ways.
Wow. 🤯 indeed! Your explanation, complementary visuals / audio, and obvious enthusiasm for the material all add up to an incredible video. Also, hearing the harmonic series gives me chills and a general sense of something very mystical, yet incredibly familiar. Awesome
I learnt about this when i was looking at how to do overtone singing. It showed me that at all times when im singing, other notes are playing. In overtone singing, you subtly change the position of your tongue or lips to accentuate the different notes that are already there. And thats why the shape of your mouth is so important for how you want to sound with regular singing too. Also whistling with your lips is a form of overtone singing in a way.
Wow! I am an awful an singer, it is hard enough for me to even sing the right notes on key. Having to also pay attention to the shape and position of your physical mouth in order to regulate which overtones you are singing is a layer of skill I didn't even know existed!
4:15 yes I already knew about this but I'm still watching because I love getting a different way of talking about a subject because sometimes you get a new perspective on the subject matter and other time you knew about something but it wasn't something you deemed anecdote worthy in a party with friends and you get an all-new different way of looking at it that is enlightening.
and a square wave is a combination of sinewave + its odd harmonic (3,5,7, ) at 1/N amplitude (N being the harmonic number). And if you take the even harmonic instead, you get a sawtooth wave :)
Julia code to make it : plot(x -> sum(sin(n*x)/n for n in 2:2:200), -pi, pi, lab="saw") plot!(x -> sum(sin(n*x)/n for n in 1:2:200), -pi, pi, lab="square") the more harmonic you have, the sharper is the edge.
Great video - really inspiring actually and something I had not considered before. Hoping to apply this knowledge in my own music in the future. Respect dude
You are such a great teacher Andrew. Your channel alone is like Gold. I took your course a few months back and you really are just amazing at teaching. Wanted to let you know that.
I've been involved with music for my entire life, playing records (DJ), keys, doing some production, and now the Bass Guitar and I never studied really this level of music theory. Needless to say, I have a couple synth modules that I'll be playing with for an extended period of time TODAY. You totally blew my mind. I'm also a software engineer and something about the harmonic illustration looked so beautiful to me, I can't really explain it. Thank you.
You definitely blew my mind. Ive heard about this before and watched other videos about it, but still you told me things I didn't know, made me think of things I hadn't before. And your enthusiasm for how strange it is makes the video infinitely better. Thank you!
Terrific job, Andrew! This is a pretty thorny subject (potentially mind-blowing, as you say), so it's no wonder most music education studiously ignores this whole subject. I've been teaching about this since the early 70's as part of classes about the basics of of sound synthesis, and I've always been amazed by how many otherwise well-trained musicians were never taught this stuff in music school. So, thank you for helping to fill that gap! BTW, another cool demo is to turn what you did with the low pass filter (progressively filtering out the higher harmonics) upside down, by sweeping a high pass filter UP the harmonic series. Interestingly enough, the ear still perceives the fundamental pitch, even when it and some of the other lower harmonics are completely missing, since the ratios of the upper harmonics that are still audible "imply" the missing fundamental. The same thing happens with rhythmic ratios (which are just slower frequencies, but follow the same principles): if you play a 2 against 3 rhythm, the ear picks up on the missing "1", which is the rate at which the 2 against 3 pattern repeats itself.
@@Action2me Absolutely, I agree with you there. But that was not my point. What I meant was that I think it's strange that even if you're not interested in the physics behind music I would have thought that after a rew years you would inevitable pick up some knowledge.
@@electronicgarden3259 I think most musicians do even if they don't realize it. Every good musician knows their instrument (yes that includes DAWs), how it plays, what makes it sing, scream, bite, whatever. Every instrument has its own quirks and it's up to the musician to figure them out. Say for instance you handed Jimi Hendrix one of Steve Albini's guitars and told him to play Hey Joe it just wouldn't be right, y'know? Also most guitarists know about harmonics and that's just straight up physics.
I've actually tried tuning my guitar's distorted major and minor chords to their just intonated intervals (tune the major third 14-ish cents flat, minor third 14-ish cents sharp, perfect fifth just a hair sharp) and found they often sound marginally better. Of course then I have to re-tune for each chord I play.
@@not-on-pizza Power chords are actually just major chords. The 3rd is produced by the overtones and is easily audible, your brain just convinces you not to notice it out of habit.
Fun fact: any sound can be represented by a combination of sine waves, even inharmonious one. (actually to represent any sound with perfect accuracy you will need infinite amount of time, because of the guy named Fourier, but for us humans approximate results are fine)
I had a subconscious understanding of overtones for a while, when I was younger and sang a particular note I'd hear a 5th overtone in the back of my head and never really knew why. Later in precalculus my teacher showed us the sine waves of certain volumes and pitches using a DAW, and I was enamored by it. Then when I started playing guitar and discovered pinch harmonics I was fascinated by being able to hear 3rds, 5ths and 7th depending on how I hit the string. It feels great knowing that these patterns I noticed have a name and are prevalent everywhere 🙏🏾
I used to say "wooow" really slowly and notice how the harmonics of my voice would appear and disappear in "units." You can hear a distinct quantization of the harmonics. I thought it was really interesting and now I know why that happens.
@@weareallbeingwatched4602 the brain is doing the math, or rather, the brain, through many many successive evolutionary iterations, tended towards the most energetically favourable way of interpreting the natural geometry of sound waves in a manner that is beneficial to the various selective advantages and disadvantages
HELP MY!!! My muscles are too big! I am a big tall man and my muscles are even BIGGER! I use them to get views but they HURT so much!!! Because they are heavy. Do you have any advice, dear milo
Another cool thing about actual physical acoustic stringed instruments that is worth mentioning is that the vibration from a string excites nearby strings that have shared overtones (this may not be the most accurate way to describe it). The coolest way to experience this phenomenon is to hold down the sustain pedal of a piano and press any key in a very short burst. You'll hear a wonderful soundscape created by other (related) strings that get excited.
Other instruments effect stringed instruments the similarly, if you play a just note from lets say like a trumpet and it's note is tuned that to the same of the piano, the piano string should start vibrating. It is this reason why certain notes can make certain objects vibrate. Most objects have something called a natural frequency, the frequency is extremely specific to the object but it that frequency is played at the object, the object should start vibrating. This is what resonance is. If any of you have seen a live video taken by a camera on a stand and that camera vibrates for this one certain bass note, that was because the objects natural frequency was that note. A good example of this is ruclips.net/video/XwlZBJIp1AA/видео.html at 1:46 and a real scenario, this case a beatboxing tournament ruclips.net/video/DFk6aVSWo7s/видео.html at 9:28 - In this case the camera wasn't on a stand but the camera's natural frequency caused it to vibrate (Better example at 10:12)
Entire instruments are built around this concept too! The Sitar for example, has sympathetic strings that resonate with the strings you play, creating droning harmonics and that classic sound!
This makes so much sense. The sine wave explanation brought this home for me. I’m a mechanic and the hardest thing to diagnose for us is vibrations at speed. For example tire vibrations at 60-70mph. When the tires are rotating at beyond 70 mph the vibration frequency matches the rotational frequency and the vibration disappears! Great video!!!
8:44 slight correction to this which is kind of mind blowing in itself: the laws of the universe only imply that any repeating wave _can_ be represented as a sum of sine waves. So it's not that every resonant body's vibration necessarily _includes_ overtones, it's moreso that our brains _choose_ to interpret the vibration that way (as combinations of pure tones, i.e. sine waves). Otherwise it would just sound like random noise to us. But other alien species might have no concept of overtones at all - their brains might have some completely different way of analyzing complicated waves.
Disagree 100%.......you're confusing properties of math & physics with auditory perception. Math is rigorously defined and maps perfectly onto physics, so my brain doesn't "choose" for a complex waveform to be mathematically equivalent to a sum of sine waves. So yes, the resonant body's vibration indeed necessarily includes overtones, because that's how the math is defined and how the physics works. Neither does my brain decide the properties of a resonant object...even allowing that human hearing is subjective, that doesn't mean the vibrational qualities of that object would seem random, because they aren't random, they are quite clearly patterned. (Unless it's actual noise, which does sound like random noise because that's what noise is.) And "alien species" is just a proxy for saying "what if you remove a key aspect of perception?" which is saying the equivalent of "Wow, imagine if we didn't have eyes, everything would be black!" When you remove the meaning from something, it's not a surprise when it becomes meaningless.
@@j3ffn4v4rr0 Okay maybe you're right that saying the vibration must "include overtones" is correct. But it's like saying that the number 91 "must include 7 groups of 13". Like sure, it's a fact of the universe that 91=7*13, but there's lots of other very valid ways to interpret the number 91. When I look at a crowd of 91 people, my brain doesn't immediately analyze it as 7 groups of 13 people each. The only calculation it does is "wow that's a lot of people, maybe about 100". That's how my brain *chooses to interpret* the crowd of 91 people. My point is that overtones, while obviously a consequence of math/physics, aren't some universal concept. Some alien species might perceive pitch in a more naive way that doesn't account for overtones (e.g. just averaging the frequency every X ms). And if you told those aliens that they could represent a guitar pluck as a sum of sine waves they'd be like "ok cool, why tho". Which is the same reaction you would have if I told you "hey that crowd of 91 people is divisible into 7 groups of 13". It's true, but you don't perceive any difference. So yeah, I _am_ pretty much saying "if we didn't have eyes then we couldn't see", but I'm only saying this because andrew said something analogous to "the laws of the universe determined that all stars must be visible, since before humans even existed". Like, it might be true that stars have always emitted light, but _visibility_ is a uniquely human concept/perception that only existed once we existed.
Some additional cool facts about sin waves and overtones - One can remove the fundamental of a sound (keeping the overtones) and still hear the fundamental! - The way we encode music into audio files on a computer is basically measuring how much of each sine wave there is, thousands of time per second
Yea you would think that removing the fundamental would make the note sound an octave higher, but it doesn't. That's because the combined cycle lengths of the overtones are all relative to the fundamental. I.e- the 1st harmonic (2:1) and the 2nd harmonic (3:1) won't "meet up" (for lack of a better term) until they cover the same length in time as one cycle length of (missing) fundamental. Like an eight note and triplet played together... they meet up at every quarter note and we can hear that whether or not the quarter note is being played.
You explain this all very well. I have been sharing these mind-blowing facts with my students for about 30 years and always wondered why my own teachers didn't talk about this stuff...b/c it opens up way too many doors. It IS fascinating!
Wow! This takes me back to my undergraduate courses in Electrical Engineering (many moons ago) dealing with Fourier Transforms in Signal Processing. It's been always fascinating to me that music, a fundamentally artistic endeavor, is totally based on mathematical concepts. You do a great job at explaining this!
Well explained, though the animation of the waves in a bass guitar is misleading - it's a standing wave (2:00) so it doesn't travel longitudinally, only vibrates transversally in time (aka perpendicularly to the string)
I had this slow realisation after doing music production as a hobby for many years. You basically just confirmed what I discovered in theory and it truly is mind blowing.
I'm studying music every day, I don't have any fancy gear and stuff but I have a dream, thank you for your content.. it's always helpful and inspirational :)
Man, you killed this topic. This is not an easy topic for most people to get, and you didn't just explain it well--including great visualizations and examples to make it more than a bunch of complex ideas--but you also made it FUN. You have a real knack for _teaching_ things...way more so than most of the folks making a career out of music on RUclips / the intarwebs.
Dude, your explanation around 8:00 of why old guitar strings sound "dead", and why you need new ones... It *makes sense!* I've never understoon _why_ everyone repeated this (like a mantra), but the asymmetry from wear, corrosion, oxidation, etc, dampening the overtones... THAT clicks in my brain. I've been playing guitar for almost 30 years, and only just now did you explain this in a way that makes sense in my brainmeats. Thank you! =)
"Our ears are doing math" To be honest it's pretty amazing when you think about it that way, how our brain can process all of this information without we even knowing it. Really something we take for granted...
It gets weirder the deeper you go. The basilar membrane in the ear mechanically deconstructs the sound into the constituent sine waves and converts them to electrical signals. It's almost like the brain reconstructs them. There's a cool phenomena called Binaural Beats. The standard Beats phenomenon is the idea that when you play two similar notes with slightly different frequencies, you hear it as one note of the average frequency that's pulsing at a rate equal to the frequency difference. This is the pulsing you hear when you are trying to tune up, and is a physical phenomenon caused by the sound waves interfering in the air. Binaural Beats takes this further. If you play one tone in one ear and a slightly different tone in the other ear, you hear the same thing. The two waves never physically interact, but *your brain adds the interference back in!*
When I was in university, I was learning about this in my electronic music classes while also taking geology courses. At some point in my geology class, it all clicked: "Everything happens in cycles...circles are just waves and vice versa....all measured physical phenomena through time can be represented by a signal....literally everything is music." and I have never been the same since.
on a side note..as musicians and scientists alike, we can easily get sucked into what we perceive as great, grand and unifying theories. but they are so tempting.
THIS. people laugh at me for babbling on about Andrew Huang then he dOES THESE types of videos. I'm showing this to all my friends. Thank you for sharing so much of your knowledge, sensei *bows*
When you did the EQ wall that completely blew my mind. I don't know much about music yet, and I don't know how this would effect me, but if just feels like such a fundamental property of sound that i had to pause the video for a couple seconds to process
4:39 "What the [sine wave] is a sine wave?"
clever, Andrew, clever.
Maltalented Creator I didn’t notice lol
Ge also starts by saying this is one of the most fundamental aspects of music
7:45 I HAVE NEVER CONSIDERED THAT. That makes SO MUCH SENSE
Rob!! That's actualy realy cool.
Hello scob rallon, how are you doing this fine afternoon?
@Rob Scallon I watched this despite learning the harmonic series years ago because I knew he would come up with *something* I didn’t know. That same part was new to me and makes total sense.
It’s the first of October
Yeah
Me as a child: "I'll never need math, I'm gonna be a musician."
Math: "Get back here, you little sh*t"
it's physics ;)
@@marek2031 And math is the language of physics ;)
@@einprozent3738 nice checkmate lol
@@marek2031 Fun fact: I've never met a Physicist that didn't play some kind of stringed instrument.
@@CyclesAreSingularities I mean if you want to seperate such a complex subject like maths in "highschool" and "physics" maths go ahead but that still doesn't undermine the fact that physics can only be applied to the real world by the application of mathematics
Honestly this was the first thing I wanted to figure out when learning music theory. Learning WHY things sound good together is so much more important to me than learning HOW to put things together.
Part 2: Amount of overtones is important, but how their loudness changes over time and how the pitch wobbles is the other half of a timbre
With FM you get a really wobbli boi to the point a sine wave can sound like a walrus
@@christiantaylor1495 ...I'm going to hunt for walruses now
Exactly why simply re-pitching even the nicest real-world instrument in a sampler sounds synthetic
@@HORNGEN4 On the topic of wobbles I have found a video with additive synthesis imitating a Leslie speaker on a organ ruclips.net/video/NIe8H8D54IY/видео.html
Andrew, I've been teaching music theory for years and have taught the harmonic series to some of my high school classes. Usually unsatisfactorily. Ive never seen it presented well in a reasonable timeframe. I used to use Leonard Bernstein's 1973 Harvard Lectures series clip of him demonstrating it on a piano. Charming if you love LB but terribly, grossly out of date for students today. This is the BEST video resource on the harmonic series I've ever come across BY FAR. Thank you so much.
" terribly, grossly out of date for students today." I really worry about that attitude. Someone just one generation older seems 'out of date', superannuated. As though a haircut or accent or costume alters what a person is saying!
Trivial, superficial people. Not necessarily a generational thing, just whether one has a sense of history.
@@smkh2890 I understand your dismay, 100%. And I agree with your sentiment. I dearly love Bernstein and I have watched his entire Harvard lectures series numerous times. But Bernstein explaining something is long-form poetry. It could take 20 minutes to an hour for him to make the point. Bernstein is too brilliant and too aesthetically minded to simply give the bare facts of something - he will weave the point into a tapestry of interconnected concepts and supporting metaphors. But here’s the thing - I first found those lectures as an undergraduate music student and I devoured them on my own time. They aren’t well suited to be a supporting material for classroom teaching at all, and that’s what I need for my HS theory class. In the past, even when I showed my HS classes preselected 10-15 minute excerpts of his lectures, they didn’t quite get it. Look at Andrew’s style by comparison. Utterly different pacing, among many other things. Style is a language, and modern students speak the language of his style.
@@brianmessemer2973 of course you are right. I don’t want to repeat cliches about attention span because my own attention span is not what it used to be. But how many now listen to a piece of music 40 minutes long or more in one sitting? How many read 1000 page novels? Even full length albums are gone . people listen to one track and buy single tracks . the 70s ‘concept’ album with a story development over an hour or more, Tommy by the Who would be a good example, seems to have disappeared.
@@brianmessemer2973 as for teaching I taught English language mostly to students who are paying so they were attentive. I’ve also taught English literature at college level but I am not yet at the point where I dare to teach music. Anyway talking about style of teaching, Andrew is very very good . I think he is sponsored by Reverb, so he has resources. I did some electronics in the ‘60s so the components he showed in a bag were not a mystery!
@@smkh2890 yeah absolutely sir. Your points about music and literature are well taken. There certainly seems to be less time for, less emphasis on, and less cultural value/appreciation placed on the study of large works. Funny coincidence - I also taught English language in Japan for several years before teaching music back here in the US. Thank you for sharing your thoughts and background a bit - what a pleasant conversation with a likeminded individual. Cheers to us 🍻 and cheers to art, literature and music that takes time 🍻
Other MIND-BLOWING facts:
- The reason sometimes sounds start clipping after you EQ them subtracting harmonics (which seems absurd), is that the harmonics you removed were interacting with the others and they were actually lowering the peaks of the waveform!
- Two waveforms may have the exact same harmonics with the the exact same intensity yet sound completely different, because the harmonics are phased differently (the sine waves do not "align" the same way), so with a bunch of harmonics you'll still be able to obtain infinite sounds!
EDIT: I substituted the term "interfering", which was technically incorrect, with "interacting".
EDIT 2: Editing the comment made me lose the Heart from Andrew 😭😭 what we do for science
Holy 🦆 I've wondered why that is thank you!
I'm not sure that's *completely* true. It *is* true that adjusting the phase of the different harmonics would make a signal that looks really different on a scope...
However, humans are *really* bad at hearing phase of different pitches in a sound. (I'm pretty sure it has to do with the way the cochlea breaks up sound into different frequencies, but I'm not a doctor). So if you have two signals which have the same frequencies but slid around in phase, they'll sound the same to a human.
Then again, humans are really good at picking up different phases *between the two ears* so there might be some funky psychoacoustic stuff going on if you tried that. (Also, apparently there are some animals whose ears work differently so they might actually be able to directly hear phase.)
And that's why the fourier transformation has to be calculated in the complex space. Every frequency also has a phase. But analyzers usually do not show them.
@@scorinth They will sound the same to a human, but when played together, it's not about the brain, its about the vibrations and the physics of the real world. The waves literally cancel each other out in the air and thus those frequencies are lost or reduced in amplitude.
They wouldn't technically harmonic if they were out of phase. The phases should line up with the fundamental.
The coolest thing for me is that variations in harmonics is also how we pronounce different vowels. When we change the shape and position of the mouth and tongue, we create a different "instrument" that prioritises different harmonics. Basically different vowels are the result of filtering and boosting specific overtones.
And my mouth talking ass still can't figure out how to EQ shit, i'll be damned
That's pretty rad though
What the fuck
WHAT
"All musicians are unconscious mathematicians" -Thelonius monk
But I hate math 😂
@@hannahboesen1647 then I hate u
Math haters = 🤢
I’ll change my statement, I don’t really like math lol
I was listening to Andrew and all I could think of was he's like a doctor but with music.
I've had this explained several times but your pacing and visuals are extremely helpful
Literally just finished harmonics in physics 😂😂 this is really helpful for that actually, cheers!
Same but Andrew does it cooler
@@ethanyoung4629 yeh😂😂, my physics teacher could never be as cool as Andrew😂😂
If you haven't studied quantum yet you're in for a fantastic surprise when you get to the harmonic oscillator. Wave theory is ubiquitous throughout all of physics!
@@denglish5 we just started quantum, I finished the photoelectric effect yesterday and my head still hurts😂
Just going down the music theory rabbit hole and was just unable to grock how the same pitch sounds different in different instruments and this finally cleared it up for me.
tambre b like
@@MsStevieFernandez*timbre
"or you already knew about this, in which case, why are you watching" because you're Andrew Huang
🥰🥰🥰
Exactly... Lol
Synthesis Music absolutely relatable
yes!
What if I already knew about it, *and* I'm still impressed? I knew theoretically if you EQ'd away the harmonics, it'd sound the same, but I never thought to try it out. It felt different to hear it actually work.
I already "knew" all this as a scientist. But now, as a beginner musician, you made the relationship to chords, notes, and instruments so clear for me!
Omg same!
(not a scientist but a physics student)
@@harmitchhabra989 and me as a JEE student is visualising these things. and its mindblowing.
@@thehealingguy1503 same mai bhi jee21 ka hu
@@harmitchhabra989 isn't physics a branch of science?
Many folks out here are well familiar with this and many other concepts that are not scientists or engineers or anything like that themselves. Interestingly enough, these concepts in physics and other focused scientific fields are the shared connection between any other concept or endeavor. And funny enough you could be coming to understanding and awareness of technical concepts by actually practicing "science" and not even know it just by doing other work, craft or study. Now, a scientist may scoff at that bc the practice itself has a set of rigid formalities and standards to be consciously followed or its not credible as new theory, law or fact, but the process of discovery can be very similar and just as genuine to one's learning and comprehension of reality. I think its healthy, interesting and helpful to share such analogies.
When you play a harmonic on a string, you are actually physically stopping lower harmonics from ringing, while keeping the higher harmonics. For example your finger over the twelth fret, halfway across the length of the string, you prohibit the fundemental from sounding.
What I really love is when I mute one string after playing it, and I hear the exact same harmonic vibrating from a different string that I didn't touch.
🙀 too genius
And then there's that violinist who somehow got the violin to produce tones *under* the violin's range and we still don't know what the physics are exactly.
@@woofelator That's sympathetic vibration, which is what makes sitars sound so goddamn cool. My high school music teacher demonstrated this to the class by taking the front off a piano and using his clarinet to play a note directly at the corresponding piano wire. We could then hear multiple piano wires sympathetically vibrate relevant to the harmonic series of the fundamental being played on the clarinet.
No man, you'll get an entirely new fundamental that has a wave length starting from the fret you pressed the string at.
The way you visualized it on the guitar was brilliant. That edit made it so clear and easy to understand! 1:53
I remember being introduced to harmonics through throat singing one day. I think my local radio had a little segment on it, and it blew my mind that you could shape secondary notes over the main ones. I recall standing in front of the mirror with my electric toothbrush and opening and closing my mouth to isolate the different overtones. Thanks for bringing that fun time back to me, Andrew!
You'll often still hear overtones with a sine wave actually, because you're hearing them through speakers which have their own ways of vibrating and their own resonant peaks and you're also hearing the room. I think it's more in theory that they don't have overtones, because in the real world I'm not sure how you'd listen to it without engaging overtones from something, even if just from your own ear canal.
maybe feed them directly into the brain somehow hehe
overtones are all around us
we cant escape them
not sure if that puts me in awe of the universe and its sheer beauty or puts me in fear of it
Maybe the closest possibility is a tuning fork on ones forehead..?
Then you don't hear a sine wave. Once the tone is colored by your amp, speaker, cable, W/E it's no longer a pure sine. It has gotten harmonics injected in the wave. So in a way you're right that it can only exist in theory. But with decently tuned and chosen gear you can approximate that sine wave to a point where the overtones you speak of have no real world influence on what we're hearing.
I was just thinking of that
The limitations of the world are amazingly weird
Acoustics nerd/musician here!
While overtones do not have their own overtones, they do "create" more notes! These notes are perceived when any 2 notes (including overtones) are present. The term for this phenomenon is a "combination tone" or more specifically in this instance a "resultant tone". Resultant tones are often sounded an octave below the fundamental, adding additional depth to a tone of a given instrument. This is one of the aspects that makes virtual instruments not as "real" as their real instrument counterparts.
This goes into what is known as the undertone series which is a whole topic of it's own (your string player friends should be able to tell you more. "wolf tones").
And that's why fifth chords sound so damn good on a distorted electric guitar
@@XenoghostTV it's also why distorted triads sound nasty if you don't fudge the intonation.
The difference tone from an equal tempered major third is a very out of tune minor second, two octaves down. Gnarly on it's own, nightmaremish in a mix
@@gonzoengineering4894 That's quite some nerdy stuff there. ;)
@@benjaminschallwig43 it gets headspinningly more nerdy when you realize that, unlike overtones, difference tones DO make more difference tones
Wut
Former opera singer, now digging into instrumental music and music production, from orchestral to the 80s synths of my childhood. This video utterly blew my mind, and was even news to my wife who has a Masters in music performance. GREAT video, clearly, concisely, and enjoyably explained. And you can't ask for more than that when it comes to education.
This is also how most image compression works, like jpeg. Instead of storing the actual pixel values, it reduces each block to a sum of sine (er, cosine) waves which add up to something very similar to the original signal. It's a very effective way to represent the types of shapes which tend to occur in nature.
It has a hard time with square waves though, since those are the sum of an infinite series of sine waves. It takes a lot of space to store an infinite list of all the harmonics needed to build a square wave, and the point of jpeg is to make things small, not large. So it usually stores only the first few harmonics and the error becomes pretty noticeable whenever the picture has sharp edges.
Now you got me reading about DCT lol. Things get kinda wacky with compressive sensing/ whatever field it falls under in that context.
My fairly basic understanding is that there are other bases/kernels that would be able to do better with square waves, no?
There are definitely more compact ways to store data representing square waves... but they tend not to be as good at storing smooth contours. The compression is basically optimized for what the creators expect the input data to look like... so it'll be less optimal for unusual data.
Although jpeg was a big step up from what came before it, there are definitely some corner cases (pun intended) where it's not so great.
And when one end of the sound waves in the spectrum ends- light waves begin. They're all connected.
Sound and light aren't part of the same spectrum. They're different types of waves. Sound is a compression wave of particles transferring kinetic energy by bumping into each other, like how ripples travel across a lake after throwing in a rock. The water itself isn't travelling outward; it's mostly just vibrating in place. The ripples don't exist without the lake.
Light, however, is actually pure energy travelling from one place to another. It's not cascading vibrations of some other material... it's photons moving across space.
Light exists as individual particles, while sound is a side effect of the movement of many many particles. Sound is a domino effect and only exists if there are dominos to move through, while light is more like throwing a ball.
You make RUclips something else Andrew. The amount of work that has gone into this video for us to view for free. Damn dude... Mad respect. This is untouchable content.
"It's the foundation of all the chords and scales we use. It's the reason why certain notes sound good together. It wasn't just that someone back in the day decided on a scale they liked and we all agreed to it and are using it out of habit. It's that the physical laws of the universe determined what these note relationships would be, long before music existed, long before humans even existed. Any resonant body vibrating at a consistent frequency would also include harmonics, would include those integer multiples of that base frequency."
This is absolutely profound to me. It confirms to me the idea that our relationship to music is innate and universal rather than cultural and relative.
I felt the same. It confirmed to me why music by default is therefore so powerful in terms of provoking emotion etc as it is so intrinsically linked with the universe as a whole and all living structures. Basically the universe is a construct formed by numbers and mathematical equations both biologically as well as physically and on every quantifiable level, in this case audibly too. Everything we both comprehend and don’t, consists of vibration and frequencies. If you are able to master the rate of this vibrations you are able to master life. Raise your vibrations and you raise your synchronicities. Raise your synchronicities and you create the ability to manifest.
I think it's more of a thougth to apply to science and math in general rather than just music, the fact that science and math are so accurate to describe our world despite being made by humans it's mind blowing
@@MRtecno98 ruclips.net/video/FY74AFQl2qQ/видео.html
@delt That gets more into philosophy than math and science. There's a lot to be said for the question of was math invented or discovered?
@delt Wow, I somehow said that Google was the keepers of the mathematical constants we use to describe the universe 🙄 No. You said that those constants would exist without someone to discover them, and I countered that the assertion is based in philosophy (specifically, epistemology) rather than the hard sciences. Thanks for strawmanning something that is only really debatable in philosophy, the field I mentioned, because 2 is how we describe that quantity of items, not an actual physical substance. You can hold two apples, but you can't hold 2. That's my whole point 🤦♂️
Most mind blowing thing that I learned recently in music is:
Keys/Chords are only relevant to the most recent chord that you transitioned from. Think about that. That means chord number 3 can be totally bonkers from chord number 1 as long as chord 2 works to give you the feel you want when you transition from 1 to 2, and similarly works to give you the feel you want from chord 2 transition to 3. This is how great musicians use the circle of fifths to bounce around from literally wherever they are to wherever they want to be.
Fun fact: this is also why your voice sounds different to you than to everyone else. The sine waves making up your voice travel differently because when you hear your own voice, they're passing through both the air and the bones of your head to your ears. Low frequencies carry better through physical contact than the air. If you experiment a bit with EQ, you can make your voice on recording sound closer to how it sounds to you speaking.
It took me a while to find it but like a year or so ago I found a really good paper on this and how to reproduce the voice you hear aka about what eq you need to get it. Sadly I didn't save the link and haven't been able to find it since.
Cover your ears with your hands, fingers pointing up, then fold your hands forward, keep the sides of your hands tight to your head, shielding your ears from what comes from front. Tadaa, your sound!
🧸💕🦠🔨
Perrin Silveira I studied a bit of this and have a few papers written up on my old hard drive, super interesting topic
@@Stiddo Can you put it on a google drive and send the link, please? I'd love to read up about this. Seems like it could be a very creative way to make use of vocals. I've been having some trouble with vocals so experimenting and finding the best way to do it seems smart to me.
@@Stiddo bro i need this whats your email?
Fools out here buying 10k worth of gear while I'm creating the perfect tone by meticulously layering sin waves on top of eachother entirely for free
I laughed so hard
This is so true tough, alot of newer producers always think you need expensive gear to make good music while really all you need is a computer and a headset.
Sure, the expensive gear could theoreticaly help, but only if you know the fundamentals of how it actualy works aswell as how to use it in general.
Expensive gear is not a nececity
Which also gets expensive time- and learning curve-wise. Wendy Carlos has a lot to say about additive synthesis. A LOT.
And then I put an 0TT on it
@@Scyriate While this is true, making music only by overlapping sine waves manually would take a *ridiculously* long time.
Physics major here, I wanted to say that I love that you are going out of your way to teach this. But, I wanted to shout out the guy to first discover many of these effects and give credit to him as few people actually know of him, but his contributions mathematics and science have changed all our lives far more than the vast majority of people we do all know about. Joseph Fourier is the father or harmonic analysis and Fourier analysis. This mathematics is used to study everything from the musical concepts you’re discussing to electronics to thermodynamics. Even many of the physicists who use his work all the time don’t know this but, he is also credited with discovering the greenhouse effect. One could argue this would effectively credit him as being the discoverer of global warming.
As a physicist, do you know where the harmonic series came from, its origin? It's a question that I have thought about a bunch and have some ideas but I hope somebody who studied the subject has their ideas as well.
@@TiqueO6 This notion of the harmonic series essentially comes from the notion of a Fourier series or a Fourier Transform. The fundamental idea is essentially exactly what this guy is talking about in the musical context, but the idea has consequences that much wider reaching than that. For example, the same technique can be used to study how heat in some distribution will diffuse over time. Basically, it is possible to represent a surprisingly large amount of functions as a sum of sine and/or cosine waves. In fact, any continuous function on a finite region can be represented this way. Now I would explain how this works, but I think 3blue1brown explained it better than I ever could in this video here. ruclips.net/video/spUNpyF58BY/видео.html&vl=en
As an amateur musician and professional artist-designer, i see so many relations between sounds and colors, and visual and musical composition. Your explanation of chords and harmonic series makes me think of Impressionist paintings, of Monet and Renoir, and how our eyes naturally mix contiguous colors into one. And color afterimages as well, which is why when we fixate our eyes on a red dot and then look away, we see green, the complementary color of red - just like the harmonic series. Thanks for the amazing video!
Comments like this are why I look into the comment section.
Thank you CZ 👍🏻
Do you have synesthesia?
When I was in a choir growing up, they trained us to listen to the harmonics, so we could use them while we sang to improve tuning. When voices are in tune they become less distinguishable, but the overtones get stronger.
Really cool stuff!
"It's why tuning that b string is so annoying" I feel that.
Yes man! I need to like this twice 😅
Yeah, I always noticed that I can only tune this string using a chord, unlike all other strings that I can tune separately. I only did not know why. Great video, thanks for sharing the knowledge! (yes, I did know everything except this out-of-tune-equal-division-stuff).
Totally - makes more sense now (as a keyboard player who occasionally tunes a guitar and feels ... weird on that string)!
This is truly the First time I’ve heard someone else say that tuning the B string is AWFUL!!!
I’ve been saying this for Years, and people think I’m nuts!!!
I’ll have to try tuning the string in a chord...that’s a great idea.
I use a tuner and either adjust it by ear, or I just suck it up
I’m actually a drummer for 40 years that is self-taught guitar.....so I’m not very good...but bro....that B string kills me!!! 😂😂😂
If you can get the harmonic pluck just right you can gently touch (not press) just above the B string on the 5th fret and the G string on the 4th fret. When you tune the B string with the G string this way and you don't hear any beading it should be in tune, at least with itself. I didn't learn this until I had been playing for 5 years. Worst 5 years of my life. B is now my favorite string.
"fundamental" pun in the first 10 seconds
It’s wild to think that each note is essentially a chord on a micro level🤯
Even crazier, because a sine wave is basically a rhythm, every chord is a basically a giant polyrhythm
@@lemonsyswtf
@@lemonsys Yuuup.... and the polyrhythm with odd intervals are why they sound dissonant
@@ericchin739there is no note. it's due to the mind's evaluation that creates notes. every perceived note is a combination of every other note, but every other note is also made of every other other note. It only appears to be a wave due to the integration of the evaluation process of the mind. There are no waves in reality, only in the mind due to conceptualization/evaluation/interpolation due to linear approximation/assumption.
I remember this high school teacher who taught math and guitar class would always say that theirs two universal languages: math and music. Mr Nolan was such a chill hippie teacher ^_^ He would even bring his own drums in for a drum circle club once a week. It was him who made me realize how much math is related to music in a non negative way
In a way math and music are the same language
@@IntrepidInfinity 🤯
Was his favorite band Dream Theater? lol. also, math is a tool but also language that can describe anything. spoken and written languages can be related this way. Software languages are no different, they just have their own systems and application where it makes sense. Your genetic code is kinda like firmware in a way, your personality and own awareness is like an algorithm. Brains are not computers though, well kinda like a router I would say and your consciousness resides in hyperspace, a bit like cloud computing. Electricity is pretty important lol and also needs math to be explained studied and manipulated. Everything is math, its the root. Not everything is music... We like music because of patterned harmony of sound waves and patterns in arrangement of events over a formatted time parameter. Our brains really only do one thing, notice patterns. Aesthetics are patterns pleasing our purpose.
"Overtones don't have their own overtones."
Yes and no.
While each overtone of a fundamental is its own sine wave (pure tone), each overtone has its own overtone scale within the original fundamental's overtone scale.
For example:
The partials (fundamental plus overtones) of a C fundamental:
C - C - G - C - E - G - Bb* - C - D - E
1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10
Order of the first few intervals:
C - C (octave 2:1)
C - G (perfect fifth 3:2)
G - C (perfect fourth 4:3)
C - E (major third 5:4)
E - G (minor third 6:5)
Now let's look at G, the 2nd overtone (3rd partial) of C.
To get its overtone series start with 2:1,
G - G (oh look, the octave up of the first G is the 5th overtone (6th partial) of C)
G - D (a fifth up (3:2) the D is the same D from the ninth partial of the C overtone series)
D - G (a fourth up (4:3) the G is the third G in the C overtone series, or partial #12)
You will find the G harmonic series within the C harmonic series simply because G was introduced.
Every time a new note is "introduced" in the harmonic series, it too will have its intervals up to infinity (2:1, 3:2, 4:3, 5:4, 6:5, 7:6, etc.)
So an overtone series is self containing of other overtone series. 🤯🤯🤯
Mind blown
Bro...
Andrew is actually right when he says the overtones don't generate their own overtones.
It's a standing waves problem--if your original C sounds off a string of length L, then the G would sound off a string of length 2L/3. Strings of these lengths may share a few harmonics coincidentally but for the most part will not mach up.
The Fundamental generates all partials, period.
this man waves
You literally just explained virtual instruments. And more importantly the basis for timbre and what bit really means. AWESOME !!!!!!! No matter how rich you get on youtube don't forget that creators like you still figured out how to make great content by being yourself and sharing your knowledge!!!!
Mind BLOWN- from MSU brass at 7 pm
Harmonics, the stuff of sound. I remember when I first started to learn about harmonics, it was mind blowing. As an organist, I feel that it's necessary to understand harmonics up to at least the 8th because it will determine what sounds you use and certain sounds to avoid and why certain sounds blend together while others do not. At 76, and having had a life in music, teaching, playing etc, I'm still blown away at how the physics of sound is so important in getting the sound that you want. Thanks Andrew for explaining this subject so well and so clearly.
Andrew my man, you are king. I’m a sound therapy practitioner, and your understanding of sound that you pull into your creation and producing is exactly what the world needs. When we look at everything in creation, EVERYTHING IS VIBRATION. Sound and music, using the laws of resonance is going to be HUGE in the near future for emotional and physical healing. (The physical body is a reflection of the emotional state, the more our nervous system is in a coherent state, the body functions in a homeostatic state.) the better we feel emotionally, the better our bodies function. Love all that you do!!!!!
I learned about this in college music theory, and listening to an additive tone generator my mind was officially blown. They also talked about how square waves vs sawtooth waves are all of the even overtones or all of the odd overtones.
AND THEN my mind was blown further when realizing that all the brain can do is sense vibrations from tiny hairs inside our ears, meaning that (like you said briefly) the brain is constantly doing math to decide if it’s hearing a single timbre or multiple timbres.
AND THEN my mind was blown further when realizing that the only difference in human vowel sounds is their timbre, meaning our understanding of language is all due to these lightning fast calculations done by the brain because one hair wiggled a little faster or a little harder than another one.
Don’t even get me started on how it impacts our perception of three dimensional space...
The way waveshapes are built would've been a good addition to the segment in ableton with the additive synth, I thought he was leading there.
Well presented video anyway though.
Can you explain how the only difference between vowel sounds is their timbre? Sorry its kinda making sense based on what I heard in this video but not fully
Sure, basically the way our bodies make different vowel sounds is by making shapes with the tongue and lips which dampen or amplify certain overtones. “EE” shapes highlight higher overtones, while “OOH” shapes highlight lower overtones.
Any ideas on the origin of our harmonic series? I have my theories but would love to hear others'!
Fascinating science and I thought you explained it in a really approachable way. Thank you!
i had to sample and additively re-synthesize a pipe organ for my sound design class this past semester, and it honestly still blows my mind how close it sounds. Understanding the harmonic series has really done so much to enhance my understanding of production and synthesis.
As a physics nerd, I think this video is perfect! I love Harmonics!!
:D
This is just a fantastic explanation of one of the most complex concepts in music, and it’s made complex because we aren’t taught this from the start, we are pre conditioned to accept the “rules” of music and intervallic relationships. Thank you so much dude, this vid is very helpful to people, I’ll be sharing with my students
Great work Andrew, very well elaborated and explained. Two things: the string cannot simultaneously be in different modes.That is a physical imposibility. Rather, i think, it passes in dt from one mode to another. And secondly, that was also mind bloiwing for Pythagoras, who first discovered this, that is why he said that all things are numbers .
The Fourier series video by 3blue1brown shows how it's probably the most important concept in sound, and physics in general. When you draw notes out in your DAW, then record it into a waveform it's exactly the same thing. We can extract all the drawn notes from the waveform by doing a Fourier transform. Conversely, we can create the waveform from the drawn notes by doing an inverse Fourier transform. It’s all just transformations from frequency domain to time domain (and back). This concept is the most important element in quantum mechanics. Math is the friggin best
Where is this video? 10 yrs ago I wanted to be able to do an FFT fromwaveform|drawn_notes
like they said, look up 3 blue 1 brown. you wont miss it.
@@midinerd ruclips.net/video/spUNpyF58BY/видео.html
3blue1brown is incredible.
You DIG IT. Cool to have someone who actually watches 3b1b and Andrew. Bet You watch Adam N and Anton P...as well?
Yes, as a someone with physics background harmonic series in music was very quickly digestible and intuitive.
me: I'm bored...
Andrew Huang: Single pitches in your area!
The note told me she was single
HBERRGCCH
This deserves more likes seriously
"Wait, it's all sine waves?"
*Cocks gun* "Always has been"
It goes deeper than that. If string theory is to be believed, then all subatomic particles are on a fundamental level 'strings' vibrating at different frequencies. Mean literally everything can be broken down to nothing but sine waves.
@@JonasHamill Leaving aside string theory for a moment, just pointing out that not all *vibrations* are sine waves. A sine wave is a smooth periodic oscillation. Vibrations can be way more complex than that: www.testandmeasurementtips.com/basics-non-sinusoidal-waveforms/#:~:text=A%20non%2Dsinusoidal%20waveform%20is,sinusoidal%20(sine%2Dlike).&text=A%20cosine%20wave%20is%20sinusoidal,but%20is%20neither%20of%20these.
@@llaith2 All frequencies can be broken down to sine waves. More complex wave forms are just multiple sine waves. You don't have to take my word for it but I have a degree in Electronic Engineering and work with signal processing on the regular. If you wish to look into it more look up Fourier Analysis.
You can even look at the following quote from the link you provided "A non-sinusoidal waveform can be constructed by adding two or more sine waves"
Fourier intensifies
@@JonasHamill Dude its cool. I did electronics engineering in uni before having a career in software. I get you but I thought your comment was simplifying the matter, given the context of the video where he didn't go into detail about recreating the timbre of instruments with pure sine harmonics. He did mention about other aspects of the waveforms a bit later, but it didn't seem connected for people who don't know this subject. I thought you were saying that any timbre could be recreated with simple sine waves at different amplitudes on the harmonics. Mainly it came across that way because of the way he was clicking in the software to add those harmonics in.
So no offense meant. Btw, I suck at math, so those kinds of problems nearly killed me at uni! I decided to focus in on digital circuits and the micro-architure of chips instead. The switch to software was inevitable as I enjoyed coding in machine language for the chips we used.
I'd rather not read any more on the subject in case my brain starts melting again! :D
You explain this superbly and mind IS BLOWN!!!
Let us just appreciate Andrew for a minute
💖
Yeah!!
@@andrewhuang
woah you replied 😱
But seriously your content is amazing
Is it bad that I have actually started to hi-five the air whenever an Andrew Huang video starts?
It’s unequivocally good 😊
Don't worry, I've done this for every single video he's posted for the last 4 years (except the ones where there is no high five of course)
I DO TOO!!!! LMAO!!
think of it like the musical fluffy unicorn version of the brofist
It is good and fitting
For those interested:
Early Music Sources (here on YT) have a couple videos on how just intonation worked in the Renaissance-covering the concept of composing a piece whose general pitch slowly rises as it's all relative.
Adam Neely more recently made a video exploring that musical notion, Benedetti's Puzzle.
Anyone who liked this video might find that interesting.
And Early Music Sources have just released a new video on temperaments. It's been a good week to explore pitch!
Comparing those 2 major thirds is mind blowing. The fact that the one that we’re used to is “wrong.” But when we hear the just intonation version, it sounds a bit more subdued and calmed, and of course darker. It actually sounds less dissonant once you hear it more.
This is amazing. And what really blows my mind is when you start thinking about wave patterns in nature and the physical universe. Gravitational waves, electron waves, color spectrum, movements in the ocean, heart and brain waves. So much is oscillations and waves. I don’t mean any of this in some new age stoner way, just that what you are tapping into feels significant.
Same happened to me when talking about this. People generally get into ''new age'' chatting without getting into the real talk, and start to lead the conversation into ''energies''..and you try to redirect saying ''no no, not energies like spiritual and good & evil, but real energy, the one that happens every moment in daily life'', and they look at you as if you were high or psycho or just trying to look smart 🙄
Have a Google of electron orbitals. It's like this in 3(+)D
It's funny because "I don’t mean any of this in some new age stoner way" sounds exactly like a harmless version of "I'm not racist, but..." 😉
I instantly thought about a 3D sound wave oscillating in a medium.
@@VeronicaGorositoMusic Go to Santa Fe, New Mexico. I met a woman from the Pleides star system. She told me all about chakra energies at a party. And numerology. It was a great sociological observation until it got boring.
This is why I'm a microtonalist. 12 equal isn't bad, but it shouldn't be viewed as God-given, when it's really just a system of compromises for particular goals. If you're mostly staying in one key, meantone is better than 12 equal. Composers in the Romantic period started to modulate keys a lot, so it was important that there be a tuning system that could handle that.
Of course, you can always divide the octave equally by a different number than 12. Each number is its own musical universe. Each can do some things better and some things worse than 12. 53 tone equal temperament is super accurate (at least for major and minor chords) but it's really complex. 17 equal is melodically better sounding than 12 equal, and it's also almost as easy as 12, but its harmonies are a bit off from what we're used to. 19 is harmonically more in tune than 12, but melodically worse.
Different tuning systems are all about compromises between good melody, good harmony, and ease of use. There's nothing wrong with 12, but it shouldn't be the only system that's ever used.
I strongly agree
This is crazy: something so obvious that it's overlooked, can be easily understood, which, in-turn, breaks open so much more to be experimented and appreciated when working with music.
Music is truly amazing
9:36 As a brass player, it finally clicked for me when I realized that the partials are divided into these pitches. On trombone the partials go Bb1, Bb2, F3, Bb3, D4, F4, a very flat Ab4, Bb4, C5, D5...
tbh this whole whole number ratio thing makes a whole lot more sense than anything else i've heard in music theory
Love how you censor "what the beeep is a sine wave?" With the the sound of...a sine wave 👏😂
I also noticed it and came to the comments to see if anyone else had noticed it too xD glad to find out I'm not the only one
Lol I thought the exact same thing
@You're fake and gay The regulatory TV censorship sound in the US is a 1000hz sine wave
You're so smart. I didn't get that!😂
I'm also pretty sure that sine wave is an 'F'
And here I thought I was the only one who struggled to tune the B string lol. Great explanation of the harmonic series. It's really amazing how well music relates to itself in so many ways.
What about the G string tho?
@@boazcohen7992 ;)
Music is basically relations of frequencies
Just remove the B string 🎸
You're welcome 🤣
Wow. 🤯 indeed! Your explanation, complementary visuals / audio, and obvious enthusiasm for the material all add up to an incredible video.
Also, hearing the harmonic series gives me chills and a general sense of something very mystical, yet incredibly familiar. Awesome
I learnt about this when i was looking at how to do overtone singing. It showed me that at all times when im singing, other notes are playing. In overtone singing, you subtly change the position of your tongue or lips to accentuate the different notes that are already there. And thats why the shape of your mouth is so important for how you want to sound with regular singing too. Also whistling with your lips is a form of overtone singing in a way.
your profile pic is one of my favorite videos of all time
Wow! I am an awful an singer, it is hard enough for me to even sing the right notes on key. Having to also pay attention to the shape and position of your physical mouth in order to regulate which overtones you are singing is a layer of skill I didn't even know existed!
I've already knew this thing, but each time I hear about that, it doesn't getting less mindblowing
This was knews to me too, buddy.
Same what i wanted to write
4:15 yes I already knew about this but I'm still watching because I love getting a different way of talking about a subject because sometimes you get a new perspective on the subject matter and other time you knew about something but it wasn't something you deemed anecdote worthy in a party with friends and you get an all-new different way of looking at it that is enlightening.
and a square wave is a combination of sinewave + its odd harmonic (3,5,7, ) at 1/N amplitude (N being the harmonic number). And if you take the even harmonic instead, you get a sawtooth wave :)
Julia code to make it :
plot(x -> sum(sin(n*x)/n for n in 2:2:200), -pi, pi, lab="saw")
plot!(x -> sum(sin(n*x)/n for n in 1:2:200), -pi, pi, lab="square")
the more harmonic you have, the sharper is the edge.
Great video - really inspiring actually and something I had not considered before. Hoping to apply this knowledge in my own music in the future. Respect dude
You are such a great teacher Andrew. Your channel alone is like Gold. I took your course a few months back and you really are just amazing at teaching. Wanted to let you know that.
Music teacher here. Can confirm everything you said. Seconded ✅
I've been involved with music for my entire life, playing records (DJ), keys, doing some production, and now the Bass Guitar and I never studied really this level of music theory. Needless to say, I have a couple synth modules that I'll be playing with for an extended period of time TODAY. You totally blew my mind. I'm also a software engineer and something about the harmonic illustration looked so beautiful to me, I can't really explain it. Thank you.
You definitely blew my mind. Ive heard about this before and watched other videos about it, but still you told me things I didn't know, made me think of things I hadn't before. And your enthusiasm for how strange it is makes the video infinitely better. Thank you!
Terrific job, Andrew! This is a pretty thorny subject (potentially mind-blowing, as you say), so it's no wonder most music education studiously ignores this whole subject. I've been teaching about this since the early 70's as part of classes about the basics of of sound synthesis, and I've always been amazed by how many otherwise well-trained musicians were never taught this stuff in music school. So, thank you for helping to fill that gap! BTW, another cool demo is to turn what you did with the low pass filter (progressively filtering out the higher harmonics) upside down, by sweeping a high pass filter UP the harmonic series. Interestingly enough, the ear still perceives the fundamental pitch, even when it and some of the other lower harmonics are completely missing, since the ratios of the upper harmonics that are still audible "imply" the missing fundamental. The same thing happens with rhythmic ratios (which are just slower frequencies, but follow the same principles): if you play a 2 against 3 rhythm, the ear picks up on the missing "1", which is the rate at which the 2 against 3 pattern repeats itself.
It always blows my mind everytime I realize that so many musicians don't have a clue of even the most fundamental physics behind sound and music.
Honestly you don’t need most of it to make good music. Music is more about the emotion.
Action true, but if you have emotion, and can combine that with intelligence in a meaningful way, damm, then maybe you got something?
@@Action2me Absolutely, I agree with you there. But that was not my point. What I meant was that I think it's strange that even if you're not interested in the physics behind music I would have thought that after a rew years you would inevitable pick up some knowledge.
@@electronicgarden3259 I think most musicians do even if they don't realize it. Every good musician knows their instrument (yes that includes DAWs), how it plays, what makes it sing, scream, bite, whatever. Every instrument has its own quirks and it's up to the musician to figure them out. Say for instance you handed Jimi Hendrix one of Steve Albini's guitars and told him to play Hey Joe it just wouldn't be right, y'know? Also most guitarists know about harmonics and that's just straight up physics.
Don’t need to. Just need to know what sounds good.
Andrew Huang slowly entering the domain of Adam Neely :D
If this becomes the new trend in electronic music... I wont be bothered at all. :D
More Xen stuff please.
Ade WE WANT XENHARMONICS
Andram Hueely
@@alderankorym everyones gonna get into fm synthesis, then proceed to slowly rip their hair out while screaming in frustration.
Excellent video, Andrew - clear explanations and no wasted time. Top class stuff!
As a 3rd year engineering student learning the Fourier series theory before music theory, this is still just as awesome.
Thats also the reason why distorted Major chords sound better than distorted Minor chords!
And probably also the reason why Power Chords sound better still.
I think Paul Davids went deeper into this once. I think it was about chord progressions in classic rock.
I've actually tried tuning my guitar's distorted major and minor chords to their just intonated intervals (tune the major third 14-ish cents flat, minor third 14-ish cents sharp, perfect fifth just a hair sharp) and found they often sound marginally better. Of course then I have to re-tune for each chord I play.
Adam Neely blew my mind when he talked about why power chords have a major flavor somehow.... I should find that video.
@@not-on-pizza Power chords are actually just major chords. The 3rd is produced by the overtones and is easily audible, your brain just convinces you not to notice it out of habit.
Fun fact: any sound can be represented by a combination of sine waves, even inharmonious one.
(actually to represent any sound with perfect accuracy you will need infinite amount of time, because of the guy named Fourier, but for us humans approximate results are fine)
To be fair, Fourier may seem like a mathematical god, but he too was merely a human.
well thats what he said in the video
I had a subconscious understanding of overtones for a while, when I was younger and sang a particular note I'd hear a 5th overtone in the back of my head and never really knew why. Later in precalculus my teacher showed us the sine waves of certain volumes and pitches using a DAW, and I was enamored by it. Then when I started playing guitar and discovered pinch harmonics I was fascinated by being able to hear 3rds, 5ths and 7th depending on how I hit the string. It feels great knowing that these patterns I noticed have a name and are prevalent everywhere 🙏🏾
I used to say "wooow" really slowly and notice how the harmonics of my voice would appear and disappear in "units." You can hear a distinct quantization of the harmonics. I thought it was really interesting and now I know why that happens.
"Our ears are doing math..." Love it!
Except they aren't... it's the natural geometry. No math. Just sound.
@@weareallbeingwatched4602 the brain is doing the math, or rather, the brain, through many many successive evolutionary iterations, tended towards the most energetically favourable way of interpreting the natural geometry of sound waves in a manner that is beneficial to the various selective advantages and disadvantages
Me: Sees Andrew posted another video
Also me 30 seconds into the video:
“Mom!!! Could you grab the mop my brain is on the floor!”
HELP MY!!! My muscles are too big! I am a big tall man and my muscles are even BIGGER! I use them to get views but they HURT so much!!! Because they are heavy. Do you have any advice, dear milo
Another cool thing about actual physical acoustic stringed instruments that is worth mentioning is that the vibration from a string excites nearby strings that have shared overtones (this may not be the most accurate way to describe it). The coolest way to experience this phenomenon is to hold down the sustain pedal of a piano and press any key in a very short burst. You'll hear a wonderful soundscape created by other (related) strings that get excited.
Other instruments effect stringed instruments the similarly, if you play a just note from lets say like a trumpet and it's note is tuned that to the same of the piano, the piano string should start vibrating.
It is this reason why certain notes can make certain objects vibrate. Most objects have something called a natural frequency, the frequency is extremely specific to the object but it that frequency is played at the object, the object should start vibrating. This is what resonance is.
If any of you have seen a live video taken by a camera on a stand and that camera vibrates for this one certain bass note, that was because the objects natural frequency was that note. A good example of this is ruclips.net/video/XwlZBJIp1AA/видео.html at 1:46
and a real scenario, this case a beatboxing tournament
ruclips.net/video/DFk6aVSWo7s/видео.html at 9:28 - In this case the camera wasn't on a stand but the camera's natural frequency caused it to vibrate (Better example at 10:12)
Entire instruments are built around this concept too! The Sitar for example, has sympathetic strings that resonate with the strings you play, creating droning harmonics and that classic sound!
This makes so much sense. The sine wave explanation brought this home for me. I’m a mechanic and the hardest thing to diagnose for us is vibrations at speed. For example tire vibrations at 60-70mph. When the tires are rotating at beyond 70 mph the vibration frequency matches the rotational frequency and the vibration disappears! Great video!!!
8:44 slight correction to this which is kind of mind blowing in itself: the laws of the universe only imply that any repeating wave _can_ be represented as a sum of sine waves. So it's not that every resonant body's vibration necessarily _includes_ overtones, it's moreso that our brains _choose_ to interpret the vibration that way (as combinations of pure tones, i.e. sine waves). Otherwise it would just sound like random noise to us. But other alien species might have no concept of overtones at all - their brains might have some completely different way of analyzing complicated waves.
Is that why my cat is never impressed by my music?
Non-repeating wave can be deemed as repeating wave with infinite periodicity.
Disagree 100%.......you're confusing properties of math & physics with auditory perception. Math is rigorously defined and maps perfectly onto physics, so my brain doesn't "choose" for a complex waveform to be mathematically equivalent to a sum of sine waves. So yes, the resonant body's vibration indeed necessarily includes overtones, because that's how the math is defined and how the physics works. Neither does my brain decide the properties of a resonant object...even allowing that human hearing is subjective, that doesn't mean the vibrational qualities of that object would seem random, because they aren't random, they are quite clearly patterned. (Unless it's actual noise, which does sound like random noise because that's what noise is.) And "alien species" is just a proxy for saying "what if you remove a key aspect of perception?" which is saying the equivalent of "Wow, imagine if we didn't have eyes, everything would be black!" When you remove the meaning from something, it's not a surprise when it becomes meaningless.
@@j3ffn4v4rr0 Okay maybe you're right that saying the vibration must "include overtones" is correct. But it's like saying that the number 91 "must include 7 groups of 13". Like sure, it's a fact of the universe that 91=7*13, but there's lots of other very valid ways to interpret the number 91. When I look at a crowd of 91 people, my brain doesn't immediately analyze it as 7 groups of 13 people each. The only calculation it does is "wow that's a lot of people, maybe about 100". That's how my brain *chooses to interpret* the crowd of 91 people.
My point is that overtones, while obviously a consequence of math/physics, aren't some universal concept. Some alien species might perceive pitch in a more naive way that doesn't account for overtones (e.g. just averaging the frequency every X ms). And if you told those aliens that they could represent a guitar pluck as a sum of sine waves they'd be like "ok cool, why tho". Which is the same reaction you would have if I told you "hey that crowd of 91 people is divisible into 7 groups of 13". It's true, but you don't perceive any difference.
So yeah, I _am_ pretty much saying "if we didn't have eyes then we couldn't see", but I'm only saying this because andrew said something analogous to "the laws of the universe determined that all stars must be visible, since before humans even existed". Like, it might be true that stars have always emitted light, but _visibility_ is a uniquely human concept/perception that only existed once we existed.
@@NadavKoller if we didn't have eyes, we might not be able to see, but that doesn't mean color doesn't exist
Some additional cool facts about sin waves and overtones
- One can remove the fundamental of a sound (keeping the overtones) and still hear the fundamental!
- The way we encode music into audio files on a computer is basically measuring how much of each sine wave there is, thousands of time per second
Yea you would think that removing the fundamental would make the note sound an octave higher, but it doesn't. That's because the combined cycle lengths of the overtones are all relative to the fundamental. I.e- the 1st harmonic (2:1) and the 2nd harmonic (3:1) won't "meet up" (for lack of a better term) until they cover the same length in time as one cycle length of (missing) fundamental. Like an eight note and triplet played together... they meet up at every quarter note and we can hear that whether or not the quarter note is being played.
You explain this all very well. I have been sharing these mind-blowing facts with my students for about 30 years and always wondered why my own teachers didn't talk about this stuff...b/c it opens up way too many doors. It IS fascinating!
Wow! This takes me back to my undergraduate courses in Electrical Engineering (many moons ago) dealing with Fourier Transforms in Signal Processing. It's been always fascinating to me that music, a fundamentally artistic endeavor, is totally based on mathematical concepts.
You do a great job at explaining this!
Well explained, though the animation of the waves in a bass guitar is misleading - it's a standing wave (2:00) so it doesn't travel longitudinally, only vibrates transversally in time (aka perpendicularly to the string)
I had this slow realisation after doing music production as a hobby for many years. You basically just confirmed what I discovered in theory and it truly is mind blowing.
I'm studying music every day, I don't have any fancy gear and stuff but I have a dream, thank you for your content.. it's always helpful and inspirational :)
this music thing is a journey
Persevere no matter how many challenges you are faced with and that dream will become a reality. Beleive you can and you will!
@@camt3787 Thank you, I won't give up
Years later, I watch this video once a year and STILL it blows my mind
Man, you killed this topic. This is not an easy topic for most people to get, and you didn't just explain it well--including great visualizations and examples to make it more than a bunch of complex ideas--but you also made it FUN. You have a real knack for _teaching_ things...way more so than most of the folks making a career out of music on RUclips / the intarwebs.
The thing that is the most insane out of all of this is that music is infinite and always will be.
I showed my mom one of your songs and she asked; “why isn’t THIS on the radio?”
Dude, your explanation around 8:00 of why old guitar strings sound "dead", and why you need new ones... It *makes sense!* I've never understoon _why_ everyone repeated this (like a mantra), but the asymmetry from wear, corrosion, oxidation, etc, dampening the overtones... THAT clicks in my brain. I've been playing guitar for almost 30 years, and only just now did you explain this in a way that makes sense in my brainmeats. Thank you! =)
I am so happy you mentioned that percussion doesn't follow the same harmonic rules as strings and wind instruments.
"Our ears are doing math"
To be honest it's pretty amazing when you think about it that way, how our brain can process all of this information without we even knowing it.
Really something we take for granted...
It gets weirder the deeper you go. The basilar membrane in the ear mechanically deconstructs the sound into the constituent sine waves and converts them to electrical signals. It's almost like the brain reconstructs them.
There's a cool phenomena called Binaural Beats. The standard Beats phenomenon is the idea that when you play two similar notes with slightly different frequencies, you hear it as one note of the average frequency that's pulsing at a rate equal to the frequency difference. This is the pulsing you hear when you are trying to tune up, and is a physical phenomenon caused by the sound waves interfering in the air.
Binaural Beats takes this further. If you play one tone in one ear and a slightly different tone in the other ear, you hear the same thing. The two waves never physically interact, but *your brain adds the interference back in!*
When I was in university, I was learning about this in my electronic music classes while also taking geology courses. At some point in my geology class, it all clicked: "Everything happens in cycles...circles are just waves and vice versa....all measured physical phenomena through time can be represented by a signal....literally everything is music." and I have never been the same since.
"everything under the sun is in tune, but the sun is eclipsed by the moon" - PF
on a side note..as musicians and scientists alike, we can easily get sucked into what we perceive as great, grand and unifying theories. but they are so tempting.
That's pretty much what ancient Greek philosopher's meant by "music of the spheres" (viewing the planets' cycles in a musical context)
@@faselblaDer3te and this was passed onto the new religions that popped up 2000 years ago and into its songs.
After several years this is still one of the best music theory videos I've ever seen. I even understand most of it!
THIS. people laugh at me for babbling on about Andrew Huang then he dOES THESE types of videos. I'm showing this to all my friends.
Thank you for sharing so much of your knowledge, sensei *bows*
When you did the EQ wall that completely blew my mind. I don't know much about music yet, and I don't know how this would effect me, but if just feels like such a fundamental property of sound that i had to pause the video for a couple seconds to process
The "what the [bleep] is a sine wave" is a good example of the kind of throw away little detail that sets Andrew's videos apart. 🙇♂️
I'm a teacher, and wish I could have done that as well as you did...one of the best-spent 15 minutes of RUclips time ever!