The most mind-blowing concept in music (Harmonic Series)

hey it's Andrew Huang today's video is about the number one most mind-blowing thing I've ever learned about music it's absolutely fundamental to how sound works and why we like the music we like but a lot of people never learn about it even people like me growing up in a musical family learning lots of different instruments studying music theory I never even encountered this concept until I was 18 and went to university for music what we're talking about is the harmonic series have a listen the pitches in this series occur in nature they're completely consistent and they're quietly audible almost anytime you hear a musical note so every note is actually a whole bunch of tiny notes put together with one exception that we'll also take a look at I guess it's really notable note whenever you play a note you'll be hearing a mix of these higher quieter notes along with it which we call harmonics or overtones and I should clarify it that it's not necessarily the exact pitches you heard in our example the harmonics are all going to be relative to whatever note you're playing and there's a very simple pattern behind that basically every time you play a note you're also going to be hearing a little bit of the frequency that's twice as fast and a little bit of the frequency that's three times as fast and the one that's four times as fast five times as fast six times seven times eight all of the integer multiples of that original notes frequency theoretically to infinity but in reality only the first handful are really audible so let's take a look at this bass guitar the whole length of this string is vibrating and that's what determines what note we hear but it's also simultaneously vibrating in other modes here's a little diagram to illustrate so you've got the main loudest note that you hear the fundamental and that is vibrating the whole length of the string so if you picture this string wobbling back and forth that wave is traveling all the way down the length of the string and all the way back what we're also hearing quieter is the integer multiples of that wave so we're hearing the wave that's twice as fast and we're hearing the wave that's three times as fast and so on the same thing happens in wind instruments where it's a certain length column of air that's resonating so these additional waves are the harmonics and depending on your instrument on its design on its shape and size also on the way that you play it the volume of these different harmonics can be quite different that's why plucking a string towards its ends different than plucking it closer towards the middle by plugging it in different places the additional modes of vibration the harmonics may be strengthened or weakened that's also why two different instruments playing the exact same note can sound completely different the main note that they're playing the lowest one the fundamental is actually completely identical and it's just the mixture of harmonics that give each instrument its own unique character so for example check this out I've got a clarinet and a guitar both playing an F here very easy to tell which is which even though they're playing these tiny little notes let's check them out in a spectrum analyzer firstly I hope you're noticing all the harmonics showing up there all these distinct points above the main note there are more and more of them and they get closer together as you go higher but also once you get past a certain point they start to tail off notice that what the guitar sound a lot of the lower harmonics are stronger than in the clarinet actually the guitars first harmonic no wait its first overtone the fundamental counts as a harmonic and that's the one difference between the terms harmonic and overtone the guitar is first overtone technically the second harmonic is stronger than the fundamental it looks like but now let's see what happens if I put a brick wall EQ curve there and start sweeping down now both of them sound basically identical we're just hearing that pure fundamental F tone if your mind isn't blown yet I don't know what to tell you your your difficult to impress or you already knew about this and why are you watching now here's an interesting thing overtones don't have their own overtones unlike the fundamental they are pure tones without their own harmonic series they'll sound kind of like our guitar & clarinet did when we filtered all of the harmonics away down to just the fundamental it's a very simple dull plain tone a tone that has no harmonics is a sine wave therefore all harmonics are sine waves now what the is a sine wave a sine wave is the purest tone possible it truly is just a single pitch it's one perfect wave visualized amazingly in video about Fourier analysis by smartereveryday if we were to turn this circle on and watch you go up and down and up and down and trace that motion out you get what's called a sine wave fascinating video I highly recommend it if you want to understand more about waveforms and how they interact so if we have a musical note and we strip away all the overtones and are just left with the fundamental that is a sine wave we've also learned that overtones don't have overtones themselves because they're all also sine waves so that means that any consistent pitch played on any instrument can be recreated just with the right combination of sine waves once again let's quickly hop back into Ableton here I've got the operator synth open which is an FM synth but it also lets you do what's called additive synthesis which is adding sine waves together so let's play a C and it's just gonna do a sine wave here now what operator lets you do here in this kind of graph looking area is add individually any of the first 64 harmonics so I'm gonna hold down this note and then I'll add the first few overtones and you can hear what that sounds like [Music] now here's an interesting phenomenon the first bunch of harmonics make up a major chord and so when you add them one by one like that it sounds like you're making a chord but if I now play a scale with this sound where all the harmonics are moving along with each note you don't really notice it anymore it sounds like an individual note with some overtones let's try again just adding harmonics at random and making a really weird dissonant chord like that doesn't seem to sound good when you're just listening to the sine waves individually being added on but if you again play a melody with it it just sounds like a synth with a particular Tambor so using different combinations of harmonics is one way that through synthesis we can approximate real-world instruments that's like kind of trumpet e obviously would need a bit more work but you can hear the beginnings of that what if we have very few lower harmonics and then add a bunch of higher ones you know really buzzy sound do some other stuff at random so these can be the starting points for so many different timbres which you can then further shape with other filtering or envelopes you know affecting how things change over time affecting how the volume changes find blown if I'm blowing your mind right now please leave a comment because I just remember what I learned about this is a little baby student and my brain was on the floor there are of course plenty of things that don't vibrate at a consistent pitch so the sounds that they make don't invoke the harmonic series and with any real-world object there will be imperfections that may contaminate the harmonic series so for instance that's why old guitar strings sound worse than new ones when they're worn or damaged in different places it means the string can't vibrate perfectly symmetrically and so instead of getting the pure harmonic series the sound will be a little bit noisier I hope you're still with me because we've only covered the first reason why the harmonic series is so mind-blowing so musical notes are just collections of interacting sine waves doesn't matter what instrument you're playing if it's a pitched instrument it's a complex sine wave generator it might also be making some other sounds like for instance on a guitar before the note actually sounds you'll probably have a bit of the click or the scrape of the pick against the string those are in harmonic sounds and all those little details add to the unique character of any given instrument but the second mind-blowing thing about the harmonic series is that it's the foundation of all the chords and scales that 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 that they liked and we all agreed to it and are you 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 let's have a listen to the series again [Music] as you can hear and see in this notation the pitches of the harmonic series correspond with the notes and intervals used in the vast majority of music if this low C is our fundamental then the first overtone the vibration that's twice as fast as that is this C and octave up and then the vibration that's three times as fast as that is the G above that four times faster is another C five times faster is an E and so on so first we're going up by an octave and then from that note we're going up by a fifth from there up by a fourth then a major third a minor third another minor third and then switching clefts here we go up a major 2nd major 2nd major 2nd so for instance if we play a C look at how many C overtones we have if we play an e with a C well there's a bunch of E's in the overtone series on C and then in the overtone series on E there's gonna be all those octaves so you've got a lot of a lot of alignment that sounds good to us and the reason why these intervals sound good together is because our ears are doing math an octave is two notes vibrating at a two to one ratio the next simplest whole number ratio is a perfect fifth three to two a perfect fourth is a four to three ratio notes sound consonant they sound nicely harmonized to us when the math is the easiest not only that but when two notes related by this series are played together they will share a lot of overlapping overtones now there is just one little wrench to throw in the equation let's get this diagram to see these numbers across the top those represent how many cents sharp or flat the notes underneath them are compared to equal temperament that's why some of the notes were colored the bluer they are the flatter they are the redder they are the sharper they are now let me be clear harmonics occur naturally and they sound like that example we've been playing throughout this video what this diagram is showing is notes that are slightly out of tune compared to a human-made tuning system called equal temperament what we found is that if we transposed the most audible harmonics the first 30 or so overtones into one octave they would correspond pretty closely to twelve equally spaced divisions of that octave closely but not perfectly when you tune everything to 12 perfect divisions of an octave that's equal temperament and it's what most of the music you hear nowadays will be tuned to the reason for this is consistency with overtones every note that isn't an octave of the fundamental is slightly out of tune compared to its equal temperament counterpart that means that once you start making even slightly complex music if you're tuned to the perfect ratios of the harmonic series then some of your intervals will be out of tune with each other for instance let's look at the first major thirds that occur in the harmonic series on C we have a see - an e here so the fourth and fifth harmonics a five to four ratio the C is perfectly in tune because it's an octave of the fundamental the Evo is $0.14 flat compared to what it would be an equal temperament let's have a listen to the subtle difference between these two thirds [Music] the next major third is this b-flat going to this D now this B flat which is a perfect seven to one ratio going to our C fundamental is already 31 cents flatter than equal temperament B flat so if we want to pure 5/4 ratio major third up from this B flat it should be a d that is 14 cents even flatter than this so a D that is 45 cents flat but this D which is a perfect 9 to 1 ratio from our fundamental is four cents sharp so look what's happening with these ratios on our first major 3rd this C and E we have a five to four ratio the b-flat to the D is a 9 to 7 ratio it's similar but it's slightly off if it were ten to eight of course it would be perfect because that's an exact doubling of five to four and as you can see here on our eighth and tenth harmonics we again have that C and E so if you were writing a piece that went from a C major chord to a B flat major chord you would have two different sounding major thirds there you'd also have a completely different interval moving the whole tone from the B flat to the C where the first note is thirty one cents flat then you would moving from the C to the D also a whole tone but the second note is four cents sharp equal temperament divides the octave equally so that every whole tone is the same as every other whole tone any given major third is the same spacing as any other major third it's a tuning system of compromise so that every possible interval or chord change in any key sounds equally in tune or depending on how you want to look at it equally out of tune and now that I've made this video I realize why so many music programs probably skip over it because it just opens so many cans of worms now I feel like I gotta explain how much we're culturally trained to hear equal temperament how live musicians often naturally make adjustments to get certain notes closer to just intonation it's the reason why very professional highly trained choirs will still sometimes end up a little sharper or flatter than where they started is by tuning a guitars B string is so annoying that major third man you should definitely look more into all this if it's piqued your interest but at any rate I hope now you know if you didn't already why music is the way that it is love to hear your comments subscribe and turn on notifications to keep up with my music content and I'll see you next time [Music]

Channel: ANDREW HUANG

Views: 684,466

Rating: 4.9775319 out of 5

Keywords: andrew huang, andrew, huang, music, musician, producer, song, canadian, canada, toronto, ontario, AndrewHuang, producing music, how to, how to make music, music producer, making music, ableton, songwriting, learn music, harmonic, harmonic series, overtone, concept, operator, synthesis, series, fundamental, music theory, theory, education, explained

Id: Wx_kugSemfY

Length: 15min 6sec (906 seconds)

Published: Thu May 07 2020