9. The Overtone Series and Timbre

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For more information check out my website: www.thejazzpia...
When you pluck the A string on a guitar, it vibrates back and forth 110 times per second (or at 110 Hz). The vibration is then passed on to the hollow body of the guitar which vibrates at the same rate as the string, and amplifies the sound. But when you pluck the string, it doesn’t just vibrate back and forth at that one frequency. Actually, it vibrates at many different frequencies all at the same time, the lowest of which is 110 Hz - this is called the fundamental frequency.
But because the string is fixed at both ends, it can only vibrate in multiples of the fundamental frequency:
The whole length of the string vibrates at the fundamental frequency of 110 Hz (this is AKA the 1st harmonic)
The string can vibrate in halves = second harmonic (or the first overtone) at 220 Hz
The string can also vibrate in thirds = third harmonic (or the second overtone) at 330 Hz
The string can vibrate in quarters = fourth harmonic (or the third overtone) at 440 Hz
And so on…
This is called the Overtone Series or the Harmonic Series - and it’s the basis of how we structure music, as we discover over the next few videos.
Some of the animations in this video were sourced from the below websites. A big thank you to them.
Title: Vibration_corde_trois_modes_petit.gif
Author: Christophe Dang Ngoc Chan
Link: commons.wikime...
License: Creative Commons Attribution-Share Alike 3.0 Unported
Title: Vibration_corde_trois_harmoniques_combinees_petit.gif
Author: Christophe Dang Ngoc Chan
Link: commons.wikime...
License: Creative Commons Attribution-Share Alike 3.0 Unported
Title: Bowed violin string in slow motion.gif
Author: ViolinB0W
Link: commons.wikime...
License: Creative Commons Attribution 3.0 Unported

[@a_bush]

This is the one most useful video on overtones and its topics I have found. Seeing the clip of the irregular string vibrating changed my idea on music in all. This video helped me understnd overtones and timbre really well, thanks

[@brendanschwarz]

Oh my god dude, I've been thinking/reading about this stuff for a long time and this is the first time I hear about the overtones arising from being unable to pluck the string starting at a perfect curve. That makes so much sense!

[@vincentl7007]

Man, you are the best I found yet on youtube to explain musics math in details. I'll listen eagerly each and every part. You got a sub and as many likes as you have videos. Thank you so much!!!!!

[@elementz018]

Really helpful. Especially gives me inspiration to "forge" an instrument digitally through wave tables and oscillators.

[@Maxim_Corp]

Yo saaaame

[@atriagotler]

Wow, I know nothing about music but I was doing a math class about harmonic series. Suddenly a video of overtone singing from 5 years ago popped up in my mind and I wondered if it is, in fact, a harmonic series thingy stuff... and well, that rabbit hole very soon brought me here! Awesome video

[@dilippawse9898]

Thanks. Very well explained. Understood the physics behind the musical instruments ...A perfect blend of an musician and a Physicist.

[@ylonmc2]

Really enjoying this series. Thanks

[@WalkThatBass]

Glad to hear it :) Thanks for the comment.

[@Charlie-e9k]

Thank you so much for sharing knowledge, I read a book on music theory but don't fully understand it . After watching your overtones diagram, I can understand a little more what I just read. I will watch again your video until I really understand what you're talking about.

[@rhythmharmony2923]

Wow! I learned a lot in this video! It goes more in depth than my intonation class or other videos on harmonics.

[@abrogard142]

never knew that before. so beautifully simple when you see it illustrated. the harmonics are 'waves on the wave'. You can even see it on a skipping rope I reckon. Get it going round - there's your fundamental - and then with a bit of flick of the wrist you can send a wave along the length of it to the other person - that'd be the mixture of harmonics. That's what that shot of the guitar string revealed. Beautiful, entirely.

[@totfosk]

this video is gold with gold and sugar and gold again

[@elvirjade4742]

This was super helpful. As someone who just picked up music theory I have countless questions, but they are rarely answered. Thank you

[@someone6429]

This was really useful for my physics subject

[@JetBob84]

Wow!! This is EXCELLENT! You put a lot of time into this, and I want to thank you very much....it was time very well spent.

[@aku7598]

Very good physics explanation on musical notes production. The pitch is seemed to be determine between the points where ALL the waves are at zero amplitude.

[@kykwan49]

Thank you. Excellent lecture. Even though the materials in this video are quite fundamental, but the way you explained it really help me to have a better understanding of sound and music.

[@WOHEI62X]

The best animation I´ve ever seen

[@WalkThatBass]

Thanks :) Very nice of you to say...though perhaps a slight exaggeration.

[@stoneandpithos]

Wonderful video!

[@nbecnbec]

This answered basically all my questions about overtones, thank you

[@peterwood-jenkins3634]

BRILLIANTLY EXPLAINED Many Frequencies playing at once on any note ,of the fundamental Most here will find that difficult to take in , but its a fact Some better singers have more overtones in their voices making a richer sound

[@taliesinmusic]

brilliant video. But "the sound of a violin" sounds like a church organ

[@eliascorrea8573]

The violin has vibrato and many other dynamics naturally. You can't accurately recreate the sound of a violin only by changing what harmonic sounds the most but you can recreate it's timbre like he did in the video :)

[@jackh6534]

Thank you so much. This is so fascinating to learn about, and I can't appreciate enough the way you're able to present it in a way that is so easy to understand. You are such a fantastic teacher!

[@LAM1895]

Very interesting. I was wondering how it could be possible to recognize an instrument based on a spectrogram of its sound. You said violin had certain predominant harmonics, is there a comprehensive list of characteristic harmonics for every instruments out there? I would appreciate any pertinent links.

[@MusicOscillations]

Your Videos were my wish and you made my wish come true. A wish of understanding and to find answers to my Questions. Thank you.

[@6hypnone]

Awesome. So this is why, all other things equal, no 2 voices sound the same.

[@samcarsonx]

I learned about this a few years ago but I needed to touch up on my knowledge and this helped tremendously! Thank you :)

[@justaperson1812]

this is absolutely fascinating

[@sunimod1895]

Great video! I am self-studying overtones because I am interested why my open cello strings vibrate even when I don't play them.

[@jellybean2619]

i play the cello too! it's called synthetic vibration, when you play the same note on another string:)

[@joaoomar3613]

Yeah, synthetic vibration is also why drums don't have notes, because one side of the drum is tuned to onde note and the onther side tuned to a different note, which makes the sound "die" inside the drum. Sometimes when I'm talking with someone that's distant from me, i can hear one of my guitar strings vibrate, probably because I sad something in the same pitch very loudly.

[@ivankorablev-dyson8281]

thank you so much! one of the best videos i've seen about overtones! and all slo mo vids and software demos were very helpful for deeper understanding!!!

[@praveenabeysinghe6038]

soooo perfect, i really understood about the notes and everything through this video. Thanks a lot❤️❤️❤️

[@RoseEyedBlackDRagon]

What an awesome tutorial. Well-explained and well-animated.

[@haripanditparanjpe30]

Wow amazingly simplified explanation 👌

[@Ginge2820]

What an excellent video! I've been wondering about this stuff for a long time and you explained it very well :)

[@mikeguitar-michelerossi]

Great video! I'll make a serie on my channel on Home Recording next weeks and I'll surely recomand this video to the people who want to learn more! Thank you!

[@innocentoctave]

A very clear explanation.

[@WalkThatBass]

Thanks, Paul :)

[@StevenWallerstein]

Fantastic! Just what I was looking for. I've wondered for some time: How do we know it's Frank Sinatra singing a middle C and not a piano playing Middle C. Overtones I guess. At about 5:35 the video shows the Synth Oscillator which is some kind of overtone graphic equalizer thingie. Is there one of these that we can play with somewhere online? And/or can we see the differences between instruments and voices on a Synth Oscillator somewhere? Thanks

[@drdca8263]

Very nice! This answered many of my questions!

[@johnmullaney3724]

Thanks, made it easy to understand, fun to watch

[@gillianomotoso328]

5:26 - So a violin is periodic in its harmonics while very concentrated at the fundamental, while a flute has very few overtones, with exception to a little whiff sticking out at the 3rd harmonic! Pure & robust vs. pure & sinewy :)

[@Tracks777]

Lovely content! Keep it up!

[@WalkThatBass]

Cheers, will do.

[@kori4580]

Thank you...this helped me with studying for the MCAT!

[@evoluti0n09]

Perfectly clear and concise, great work!!

[@JohnSmith-iu3jg]

The relationship between string length and frequency is not direct; it's inversely proportional.

[@methandtopology]

And that is because the string length is proportional to the wavelength, and given a specific string acting as a medium for the wave, the speed is constant. Therefore, to satisfy v=fλ, any change in the string length inversely changes the frequency.

[@tejabommireddy5665]

@@methandtopology h

[@kukitoo22]

You are really good at explaining dude, thanks a bunch!

[@aaron9296]

This was excellently explained thank you very much.

[@chandanonline]

Great video 👏👏👏

[@mylesfranco3545]

wow, this is the best explanation iv seen

[@jonnyhotchkiss9522]

Wow. Amazing videos and explanation. 6mins in, wondering with the flute vs the violin, and the dominant harmonic being the fundamental or the 2nd, and the subsequent harmonic series (248 for violin vs f+3 for flute) is that common across instrument types, or inferable in anyway? Similarly with the selected amplitudes were they calculated? Really great presentation and explanation 👍🏻👍🏻

[@palashmyaccount]

Brilliantly explained. Keep up the great work!

[@uzaydan]

thanks a lot !

[@Pajonear]

i have no music theory background, just fidling in my pc and i always wondered about overtones on basses for example, like how can bass in F# have overtone A# that doesnt fit into my F# minor scale and sometimes it made me to stop in progress because i was so confused and thought that it will sound ,,not in scale" and bad (ye i dont really trust my ears about ,,music being correct")...after years i wanted to find out and this was sooooo helpful man. thank you so much

[@TorkilZachariassenTZNG]

It might be worth mentioning that the first nine harmonics starting from A are exactly, or very close to, the tones A A E A C# E G A B which might be described a particular voicing of the chord A9 even if only one low A I'd actually played. Í other words: The A string contains an A, A7 and a A9 chord. It works the other way around as well. Play A E C# E G A B and your brain might choose to fill in an extra lower, subharmonic, A in order to complete the pattern above.

[@ThePi314Man]

Torkil Zachariassen As well, the ascending ratios of notes follow the Fibonacci sequence.

[@alexshih3747]

Not to be pedantic, but C# and G are quite noticeably different from the true harmonics that come from the overtone series.

[@ffhashimi]

Well done! this is a very interesting and useful series

[@tomlavelle8518]

Thank you for the clear explanations!!

[@TheRealUncleScar]

I know this video has been out a while, but another reason piano timbre changes up the scales is because the ratio of string length to where the hammer hits is also different. A few inches on a 5' string is a much smaller ratio than a single inch on a 10" string. The hammer hits much closer to the end of the string on the longer one and much closer to the middle on the shorter one, even if raw distance is smaller. Those are not exact numbers but I hope they show the point.

[@hugoponssegovia3987]

Best explanation

[@TheBlazinAsian96]

Comprehensive and concise, thank you very much for this!

[@johnm5321]

How does the shape of motion in the slowed down recording of a violin string vibrating (2:54) or the gif of the combined harmonics (2:39) resemble/relate to the wave shape? can you see the wave shape from the behavior of the string? Are they different because of the visual demonstration of the longitudinal wave?

[@annschwaar5772]

Super clear and helpful! Thank you!

[@WimBlock]

Hi, my music teacher tell's me that B and G string are more often out of tune than other strings on a guitar. I hope to know something about stress in materials and things like that and hopefully one day able to build my own guitar. I've never heard this before and at this point I'm unable to match this in my technical background. I'm not sure if this is true or based on some of his personal experience... Is it just a coincidence? If truly so, whats the reason for this? (I don't mean any bridge or tuning machine's issue's here)

[@ogorangeduck]

That's because the equal temperament system (the tuning system Western music uses nowadays) makes the third fairly sharp, and B and G are a third apart, so that third is harder to make sound right (it's also psychological, as the two strings can be perfectly in tune and still sound off compared to the other strings)

[@NcMuggets]

Strings going out of tune have nothing to do with temperament.

[@MelloCello7]

Excellent video my friend!

[@wiegraf9009]

Just to get this straight, if I pluck middle C and then one octave up the shorter string will translate the same amount of kinetic energy into a higher pitched frequency because the rate of oscillation is higher, but the timbre will generally be identical because the materials of the instrument are identical and the string lengths are geometrically proportional to each other. In this way we get the same harmonics at a higher or lower pitch and therefore it makes sense to call both of these notes "C." Is this correct?

[@Anuradha-lb3le]

Really informative series

[@camelectric]

On a natural resonant signal, the intensity (amplitude) of the overtones tends to decrease exponentially.

[@oboealto]

A question on the harmonic series. So we know that if we start at 110 Hz, the third harmonic is 330 Hz (i.e. 1/3), but what about the mirrored node (i.e. 2/3) at 165 Hz? Same goes for the 4th harmonic. 440 Hz (i.e. 1/4) is OK, but why not also 146.67 Hz (i.e. node 3/4)?

[@JamesAGuitar]

Fantastic explanation and examples!

[@Maratusvolans]

Cool video! Just one thing, at 9:44, I believe the reeds of woodwinds and the lips of brass players are the things that cause the air to vibrate in those instruments, like the strings. Maybe you were thinking about flutes?

[@martaabadtorrent4263]

Brilliant! Thank you so much!

[@abhishekbijlwan5324]

Thanks a lot.. was looking just for this :)

[@siwulf7539]

holy cow your videos are so good!

[@HuyLe-hl7qp]

How do you find the favored harmonics of different instruments?

[@NoChrReq]

That was a wonderful, clear and straight to the point explanation.

[@abrogard142]

I would like to know where we can get this ADSynth software he's using. Google seems very shy of revealing any info on it to me... though I got the impression it should be freeware...

[@dariountama1784]

Great video!

[@JBrooksNYS]

How does 1 string vibrate in multiple frequencies at the same time? This is the part I dont understand.

[@IS_CBR_2763]

2:39

[@lordviewer7305]

Pretty awesome video thanks

[@crrs2332]

the Angels numbers. you explained it finally . timbre tambor - it how things go out of tune and frequency .

[@zhouryan6960]

best tutorial

[@fredashay]

What would happen if you create several sine waves that are harmonic to each other (110 Hz, 220 Hz, 440Hz, etc) but shift the nodes so they don't line up? Will it sound different?

[@hidgik]

Please also do a video about overtones in a flute. Thanx. This video was an eye (ear) opener .;}

[@davidcorning1738]

I got the software you said at 5:36, but I don't find anything that looks like what you have at 5:36. How do I get that so I can see a frequency and the various over tones as I add them?

[@WalkThatBass]

It's an instrument called ZynAddSubFX in LMMS. Found a short tutorial of it online. Try that. kzbin.info/www/bejne/g5DSfYaYaql8pq8

[@JorgeTabaresMusic]

Incredible video! Very well and methodically taught! Could you recommend some good books to read about this? A small blibliography we could also read? Thank you!

[@WalkThatBass]

Hi Jorge. The following are both good resources: How Music Works ~ John Powell The Physics of Sound ~ Richard E. Berg

[@JorgeTabaresMusic]

Thank you! I appreciate it. I just discovered your channel and am enjoying your videos very much.

[@overtonefinds6385]

when you pluck the A string on a "GEETSAAAAAAHHHHHHHHH"

[@sydneeicloud247]

is the overtone basically the aura of that note?

[@malexmartinez4007]

How will it sound if we stack overtones using just sine waves?

[@MelloCello7]

Could you by any chance explain why some harmonics get softer and die off eventually?? My thinking is that since they have smaller amplitudes, they may be bullied out by the larger amplitude ones, but i could be very wrong, some help would be great thankyou!

[@rameezwaniii]

what sets up the string to fundamental frequency?

[@josephjeon804]

6:30 you mean a viola* right

[@kariknudsen9058]

Hi! I am looking for a way to measure wich overtones are more or less dominant when I am bowing in different ways on a violin. I want to know what I hear. Can you help? Any app or other tool? ❤

[@matis2317]

Spectroid shows the loudness of frequencies, shown as a graph. But it doesn't show which note or overtone series it is, you have to write down the numbers of the graph peaks, and find that out based on which note you play.

[@kariknudsen9058]

@@matis2317 thank you!

[@abhijeethnair2052]

sir which software are you using to generate tones. Please do tell i want to use it my research topic

[@damoon57]

So the fundamental is only the A 110 or it can be the first note everywhere on the piano or guitar ?

[@Sonder_stoic]

I’m doing a project on this in math. What app/ website did you use to show the frequency?

[@davidfrankelguitar]

Brilliant!!!

[@lomasck]

This is what I think is going on in my Pulse Jet Engines.The fundamental frequency is about 140hz plus a about 5 other higher frequencies.Gasoline powered organ pipes I call them.

[@mitalkansara2804]

Why does overtones only vibrate in integer multitude of fundamental?

[@linco011235]

Let y(x,0)=2g(x). And let g be 2L periodic with odd symmetry. If y(0,t)=y(L,t) for all t (node) then the solution of the wave equation is y(x,t)=g(x-ct) + g(x+ct) where c=sqrt(Tension/linear density)

[@__________hugo]

Thanks

[@laurastackmusic]

Awesome. Thanks!

[@matteo8931]

MINDBLOWN

[@ZERMELOmusic]

The overtone and harmonic series are slightly different -- the harmonic series starting with the fundamental and the overtone series starting on the second harmonic -- right? I just got a little confused when at 1:45 you said "This is called the overtone series or harmonic series" which seemed to suggest they could be interchangeable. Thanks man!

[@innocentoctave]

They are interchangeable, though any given person will tend to use one or the other. The difference lies in what the lowest frequency component is called. In the overtone series, it's called the fundamental, because it generates all the others. The higher overtones can then be called 'first overtone', 'second overtone' and so on: they are literally 'the first tone over the fundamental' and so on. In the harmonic series, the lowest component is called 'the first harmonic': so the next one up must be 'the second harmonic' and so on. So: fundamental = 1st harmonic first overtone = 2nd harmonic second overtone = 3rd harmonic and so on. I agree that it's confusing, but so long as you understand that historically there are these two different descriptive systems for the same set of acoustic phenomena, you should be okay.

[@WalkThatBass]

Hi Zermelo, Exactly what Paul said. The terms are both referring to the same thing (a vibrating string) but just use a slightly different naming convention (either starting from the first or second frequency). You can use them interchangeable.

[@parkerault2607]

I'm not a signal processing expert by any definition but I was under the impression that harmonic frequencies are a subset of overtone frequencies; that is, an overtone is any frequency above the primary, but a harmonic frequency is always an integer multiple of the primary frequency.