The Phenomenon of the Missing Fundamental
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- เผยแพร่เมื่อ 6 ก.ค. 2024
- Why do some higher frequencies sound like they have lower pitch than lower frequency sounds? Engineer and music lover Shaun Fitzgerald explores the phenomenon of the missing fundamental.
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Shaun Fitzgerald is a Royal Academy of Engineering Visiting Professor at the Department of Engineering at Cambridge University. Dr Fitzgerald was previously also the CEO of Breathing Buildings Ltd, a leading technology company pioneering hybrid ventilation systems. He was appointed a Fellow of the Royal Academy of Engineering in 2014.
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As someone who has played several instruments over the course of my life, got a degree, and took a few physics classes, I never truly understood this until watching this video. This was extremely well presented and easy to understand, thank you!
This effect is often used in pipe organs.
It's most commonly used to produce a vibrato-like effect, using a rank of pipes that are deliberately a few hertz off pitch (and fairly quiet). When combined with another similar-sounding rank, the result is that the small difference in frequency is heard as the vibrato. (The _Vox humana_ is one example of such a stop. This shouldn't be confused with the _Tremulant_, which actually varies the air pressure to produce the effect.)
The other way it's used is more similar to the effect that was demonstrated here, generating a lower tone that isn't present in either of the original tones. This can be done "roughly" by the organist choosing a few suitable stops (or simply playing appropriate chords) but some instruments have a dedicated stop that either has a specially-tuned rank of pipes that combines with another "normal" stop or actually has multiple dedicated ranks of pipes tuned to the appropriate intervals. It's useful for getting very low pitches which would normally require very big pipes. (It might be called something like _Harmonic Bass 32'_, meaning that the pitch it produces would normally need pipes up to 32 feet long.)
(Apologies to any organists reading this - I know I've simplified and glossed over things here horribly. I just didn't want it to be too excessively wordy.)
Beats between two close frequencies don't produce true vibrato (frequency modulation), it produces tremolo (amplitude modulation).
Hey! Do you think this is used in Meshuggah‘s „The Faultless“?
After this super disorienting guitar solo it launches into 03:08 and I‘m pretty sure they‘re using a dissonance between one guitar and the other guitar and bass to create this effect.
Don’t be shocked if it’s not your type of music / you’re not used to hearing tones this low and distorted. They’re music nerds so it wouldn’t surprise me if they used this technique in full awareness of what they‘re creating.
@@ShitmanDerBarbari don't think that's what's going on. I'm pretty sure both guitarists play 8 strings which puts them in bass territory. It sounds to me that they're just playing a unison chug with the bass. The combination of crunchy guitar playing unison with bass gives you that beef that your hearing.
At least that's what i think I'm hearing.
These short-form videos really enrich this channel, add a certain panache alongside the lectures.
For the hearing impaired, that was a fascinating explanation of sound. Thank you for this.
Brilliantly clear and simple explanation of something that's been taxing me for ages. Thank you.
This is a great way to help understand how synthesizers generate sound. I'd love to see more videos on this subject.
Perception of pitch, properly handled, is a topic that could easily turn into a semester course.
Many of the sounds used in this video to demonstrate the missing-fundamental effect don't actually have a missing fundamental frequency, because after the waves were added together the sound was clipped.
Yeah that explains it actually, it was doing me a headache thinking of why it didnt work thise two times
Glad someone else caught this! The clipping started when they added more than two sine waves. The result is even more harmonics being added. I don’t know how this would affect the missing fundamental, I think I still heard it(?)
0:58 All I heard was the 2:3 (“perfect 5th”?) chord.
You can imagine it is a single note which has a new timber. If you are still trying to find the sine wave timber, you would separate it into two notes.
Do so e people perceive a 5th as sounding lower than the root? I hear the same as you
Adam Neely intensifies
You may be able to here a difference tone if you listen closely
Try turning up your speakers; it’s much easier to perceive when the pitches are loud.
That. Was. Incredible. The clearest explanation I’ve heard yet, def sending this one to my classmates for reference! Thank you!
I watched this several times trying to hear the phenomenon you are describing and I can only hear the separate tones. I would really like to know why.
Same.. I'm listening on some decent studio monitors too so it's not a speaker problem. To me it just sounds like chords and then a note is taken away or added but I don't hear a new frequency.
Honestly same, I'm a little confused
Well, it is a video about the combination of sound waves. The behaviour described can be explained mathematically and experimentally. Nobody need to _hear_ anything. When it comes to human perseption of sound, that will vary a lot from person to person in many ways. I'm sure you'll find many videos on the subject. But this one is not one of them. Hope this was a bit helpful.
You need to turn up the volume. You’ll still hear the higher pitches, but you should start to perceive a lower, much more “grainy-sounding” pitch as well.
3:56 When you removed the 110 Hz fundamental I still heard that pitch, as you described, but the timbre was noticeably different. This why I don't like resultant stops in organs. They just don't sound quite right. But, I suppose if it's a choice between a 32' resultant stop and no 32' stop at all, I can live with the resultant.
The very first example didn't sound much lower to me, although I was willing to accept it for the sake of argument. However the one with 770 added clearly went up. I'm a musician, and immediately realised I was hearing multiple notes, which I couldn't help but distinguish, as if looking for a chord. Mind you, isn't there a load of physics about what happens when you combine two waves - can't remember the details, but it produces a counter-intuitive reduction in frequency or something.
I don't seem to be hearing what you are hearing. It's pretty clear when you remove the lower frequency or add the higher frequency.
Fantastic, thank you for positing!
0:57 I don’t hear a resulting pitch, I just hear two frequencies.
Same here!
Same here. Maybe this is part of why I prefer lower instruments, since they actually produce low tones for real.
Brilliant explanation. Thanks for the video.
Very eloquently explained, thank you!
maybe its me but I think I can hear each "component" when the "fundamental" is missing. So for example with the 220/440/660/770 I can hear two dissonant frequencies which I guess would be 220 and 770. when you mentally combine them they sound lower, 110, but I can definitely hear two if I want to.
Same
Typically when an instrument is played, only the first few harmonies have strong vibrations, and they are just octaves or octaves + fifths, which are not easy to separate by ears. But this 770 Hz is the 6th harmony of 110 Hz, which usually has a small percentage in the instruments or voices, and also it is the minor 7th note of the base frequency. So you can clearly hear a 770 Hz which has the same intensity in this case.
Maybe this means you're one of those rare people who can tell all notes from a random smash chord.
Fantastic explanation! 👏
This just blew my mind. Thank you so much!
I was taught that our eardrums have asymmetric damping which, in the presence of multiple tones, creates the undertones and overtones we perceive. Thanks for a great video!
i think that's helmoltz's theory
VERY good explanation.
good stuff. this guy looks like what i envision Dewey from Malcolm in the Middle will look like when he's miiddle aged
Exactly what I needed to see. Thank you 💚
Good illustration. The pitch may also be determined by the brain's detection of the spectral pattern of harmonics rather than temporal periodicity of the composite waveform.
Philips used this principle a few decades back to create small bass speakers, they called it the baribass. It actually produced very high pitched interfering tones to create deep bass sounds.
In the 1930's radios were built that would distort the bass so as to produce harmonics that would cause people to "hear" bass that wasn't actually produced by the speakers. It was called synthetic bass.
Cool video to explain the periodicity pitch theory. It's been around for a while, though. Actual pitch is determined both by the locations on the basilar membrane that vibrate and periodicities in the time domain waveform that cause periodic spike groups in the auditory nerve.
Wow, that was really good.
when the fundamental is removed or a higher harmonic added, i hear/perceive a higher frequency not lower ... am i the only one? i am "bothered" by higher frequency noise more than most people, if that makes any difference or explains anything, lol :-) maybe i'm more sensitive to the harmonics?
the volume of the harmonics that were generated are equal, correct?
No, there are plenty of people with the same perception. I only percieved this effect in the last example, in other examples I heard higher pitch when fundamental was missing.
I was about to comment the same thing about the addition of 770Hz (the "flat 7th". It didn't sound lower to me, although the quality of the sound seemed rougher, less pure than the others. I definitely heard a lower notw in the first example, though.
I believe for the last example 110hz is just really quiet to hear so the additional 770hz made it sound higher. However, for the first one I definitely heard it as lower.
Surprise to hear Prokofiev at 2:05
Honestly the right one sounds much higher to me. Also I cannot experience the combination of 220Hz and 330Hz to be higher together. I might have some hearing problem? I also cannot hear the 110Hz anymore when you remove it from its harmonics.
Same.
This is the correct explanation for "Tartini's Third Tone"
what the... other than arguably the first example (which hardly sounded "lower", more like "twisted" or "wider", but around the same region) I didn't hear any those pitch differences. When they added the two pure pitches I just heard... both pitches =/
When I saw the preview of the film before playing it, and saw a trumpet, I thought this was to be about a different "missing fundamental". If you play (almost any of) the brass instruments, you can usually play the fundamental, if you get your lips loose enough and use a slow airstream. I've never been able to get it, nor do I believe that I've ever heard it on a trumpet (which I play professionally btw). If anyone could point me in the direction of an explanation of this, or footage of someone comfortably playing a fundamental on a trumpet, I would be grateful :) EDIT: No need, I just found a bunch!
Its simple heterodyne effect.
A few bassoonists can make use of this phenomena and actually play “lower” than the acoustical length/range of the instrument by a 4th
Wait that's actually really cool
Intriguing!
I get what the video is saying but how come a Fourier transform missing the fundamental won't show it even though it apparently is there in the time domain?
Also i had heard of this before and remember it indeed was explained with out brain "filling in the gaps" and that is also what seems to be the stance of other sources when looking for this online
In this case, the Fourier transform is able to discern what is really happening more cleanly than time-domain analysis. As you state, the fundamental frequency is apparently happening in the time domain, but it doesn't exist in the actual physics. So approximate frequency-domain analysis (for example, our hearing) identifies the missing fundamental. But less approximate Fourier analysis is not fooled, and identifies the actual physics involved.
Even though the 110 Hz wave is not part of the waveform, adding the 770 Hz wave changes the _period_ of the waveform from 220 Hz to 110 Hz. This is because the greatest common divisor (GCD) of 220, 440 and 660 is 220, so the period of that waveform is 220 Hz - but the GCD of 220, 440, 660 and 770 is 110, so the period of that waveform is 110 Hz.
The point of the video is: what we perceive as *pitch* of a sound is not the lowest vibrating frequency, but the *period* of the vibration.
Mathematically, the former would be the lowest component in the Fourier transform, while the latter is the GCD of all the frequencies involved.
The thing to remember is that as far as a Fourier transform is concerned, a "fundamental" is a SINE wave with that frequency - which is not part of the "removed" tones; however, those tones are still waveforms that are strongly periodic at the frequency / period of the fundamental sine wave that isn't actually part of them.
neat af, thanks
It's like the quantum double-slit experiment, but with sound perhaps? The waves (highs and lows) are canceling each other and changing the perceived sound making you hear a lower tone. The real question is... would the sound change if no one was there to hear it?
Cool video:)
I'm a bit puzzled though, how comes 'the *royal* institution' is asking for patreon support..
We wish the Royal name would come with royal amounts of cash to splash, but in reality we are an independent charity, without any governmental support, so rely entirely on funds we can raise ourselves. Our charitable mission is to encourage everyone to think more deeply about science and its place in our lives. A key part of that is making our digital content (talks, explosive demo films, podcasts, blogs, etc.) available everywhere for everyone for free. We think it's important, and therefore explore all avenues of funding to make sure we can continue doing this, and keep our independence.
The Royal Institution you are guys are amazing.
In the example of the 110, 220 and so on, why don't we hear 55 for example? why 110?
Just try playing two notes very close to each other, such as when tuning a guitar. A frequency of 440 Hz (concert pitch A) played alongside a frequency of 420 Hz, gives a beat frequency of 20Hz which is heard as a variation in volume, commonly called vibrato, but the 20 Hz component is there and much lower than the frequencies producing it.
This is of coure not wrong, but I think it is treated as a different phenomena since you usually don't hear beating as a pitch but rather as fast changes in volume.
Do an FFT to see on a Bode plot what frequencies are at a maximum. Even though sounds come from different frequencies there will be some added component that will combine the two
To make an additive pitch. Take some electrical engineering courses. This stuff is pretty simple.
Are you guys doing a music themed Christmas? There's been so many sound-y things coming my way.
Err, yes, sure, let's go with that.
The Royal Institution err-ed you.
It just doesn't work. The first example with the first sound sounding higher worked. But combining the notes did not let me hear a lower tone that is lower than each of them. In the second example with the two tones I just heard the 220Hz one as the perceived pitch. And in the last example, I heard either the lowest or the highest as the perceived pitch. But I could not hear a tone that is not one of these, that is lower. That didn't work with me.
I had a violin with a “wolf” note. What’s up with that?
maybe it is forming beat frequency and needs to be tuned.
Isn't this just an example of beat frequencies which are simply the frequency generated due to constructive and destructive interference and are given simply by modulus (f1-f2). I learned this in O or A level physics. This is why all higher frequency harmonics sound like the fundamental.
I hear each of the pitches, but not this phantom lower one. It is so odd to trying to convince me to hear something that is plainly not there.
but it is and the lack of real time spectral analysis may make this confusing to an untrained ear. its fallacious to call it a phantom as it is literally there.
the fundamental is also the difference tone of those harmonics
I don't get it, I hear both notes?
Hmm. I need to watch/listen tothis again on other speakers. I did not percieve everything as described.
No no, you can't fool me! You're a wizard and that's magic. 🙈
The waves automatically calculate their greatest common factor!
What happens if they aren't in phase, though?
Only thing I heard with 220 and 330 was the same pitch plus a third component (which indeed was deeper in pitch). I know I hear things in a weird way but I doubt I'm THAT strange.
Anyone else?
The second tone obviously sounds higher
Am I the only one who thinks the second pair of sounds was high pitched instead of being lower when they were summed
if your watching on a laptop, or have poor speakers, 220hz is below the minimum frequency response, innaudible
This is pure algebra. The base frequency is always the same because every higher frequency is a multiple of the base number. Its like searching a common divider.
In the last example the lowest frequency is 220, already has 110 as common divider, which is now the only option as common divider after adding 770Hz.
yes but why does it change if you add EXACTLY 770 Hz?
Is that a small man or a viola?
Synth and Sound Design 101
because 770 isn’t a natural harmonic of 220 but is a harmonic of 110?
For me it was reversed, second sounded way higher
You could have hearing loss at specific pitches. Might want to get it checked out.
I'm tone deaf and thought the same thing.
Very interesting! We hear the greatest common factor as the pitch? Makes sense because at that frequency all the components are adding to each other. Thank you
this is gold
Best TH-cam channel ever.
I was so expecting close encounters of the third kind reference here.. but alas I shall be the one to make it. :)
Not too far to go now. let a little time pass... . .WooF.
Lots of confused people no doubt. This all relates to Fourier analysis and how combined wave-forms add up and more importantly how you can break any random waveform that is repeating into pure sine waveforms usually ass in a relationship with "a" fundamental but with different multiples and amplitudes.
When randy Travis teaches you music
That's not the brain playing tricks. The low frequency is there physically, as an interference.
odd as I heard both and they sound dissonant. I can mentally combine them and create a deeper sound, but not at first.
They clearly stated that at 5:36
short form educational content is the most effective, 2-5 minutes i think. Thanks
Beat Crazy!
This is a truly amazing video...
1:30 - "We're going to use a violin"
Viola player: squirms
Actually, the were relived that they didn’t have to play in front of an audience.
No, I don't hear a lower pitch when you combined 220 + 330 Hz (00:55)
This explains how you can hear bass with small loudspeakers, so they don't sound as terrible as they should.
This reminds me of how different wavelengths of light are used in combination to increase the bandwidth of fibre-optics.
I just hear a perfect 5th between 200Hz and 330Hz lol. No change in pitch
Very interesting!
Isn't this just a "beat frequency" effect? 770Hz - 660Hz = 110Hz beat signal.
It shows up in the math to analyse the result, so its not missing nor a psycho-acoustic phenomenon.
This is also used in trios for 2 flutes. Two pitches form a differential pith almost octave lower.
Seems like whatever set of pitches you add up, you'll hear the LCM (lowest common multiple) to a certain extent.
Huh, not being a trained musician this had always baffled me. As soon as you said "and a bit of math", it all clicked for me and made so much sense! Pretty damn awesome video mate :)
Because it’s creating a lower beat frequency. 770 minus 660 = 110.
Sounds like fractality.
But the second sound sounded higher...
I don't think we are hearing the same pitch, mister.
It is not like that for me sir.
So in the end, it's down to the LCD, i.e., maths. "When will we ever use this stuff outside of school?" ¬_¬
GCD you mean
I get it !!!!!
For those of you who aren't hearing things as described, first try to wear over the ear, decent quality headphones in a quiet environment, or with noise-cancelling on?
I heard the second as higher, but i do audio forensics. :P
A certain Christian Valentin Brunn has brought me here.
This is silly but a useful video in understanding sound. When I close my eyes and see light or colour correspondance with the sound as if it generates light frequency within the brain. But I'm a total mess so what do I know? Nothing.
Six years of music theory (all at first grade) and nobody told me. This is how it works.
Um, I couldn't hear 220, is it my ears, my speaker, or was it a joke?
OK, Google says it wasn't a joke, I should have been able to hear it
at 0:39? must be on your end
You're not alone. I'm watching on a cheap cellphone. I could feel the 220hz but it was barely audible.
It's your end. Cheap sound systems, or headphones are barely or unable to create such low frequencies. That is mainly an effect of size and geometry. There is a reason bass boxes have huge speakers and in-ears very little bass.
@@FreeOfFantasy In ears actually don't have to have the problem. On normal speaker size is needed to prevent acoustic short circuit. (The pressure equalizes around the edge of the speaker membrane.) With in ears, if the ear canal is completely plugged, the small membrane still can transmit the low frequencies.
Yes please, Moiré :)
Ok, th-cam.com/video/cvWF_Q5-Kt8/w-d-xo.html 😃
In summary waves interfere either constructively or destructively
Universal balance! Pain and fear are necessary but too much pain or fear can be a problem.