Audio Illusion – do you hear the missing fundamental?

Listen to these two sounds:

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Is the second sound higher or lower than the first sound? (let us know in the comments). Play it again if you're not sure.

Ask a few other people to do the same. You'll find that some people hear the second note as higher and some hear it as lower!

(mini update: so far 5 commenters hear the second note as lower and 8 hear it as higher)

That's because it's an audio illusion. And just like an optical illusion an audio illusion can tell us something about the way we perceive the world around us.

The explanation is all to do with resonance and harmonics.

What is resonance?

When you pluck a guitar string the note it produces is the resonating frequency of the string. So you can think or resonance as the tendency of a system (like a tight string) to oscillate at a particular frequency when you put energy in it in the right way.

But it turns out that systems can have more than one resonating frequency. They can have a whole series of harmonics.

What are harmonics?

If you pluck that guitar string again but this time rest your finger gently on it right at the centre you'll hear a new note. This is also a resonating frequency of the string and it's twice as high as the first.

If you then rest one finger a third of the way down and another two thirds or the way down and pluck the string (with your third hand presumably) you'll get another resonating frequency. The pitch of this one will be three times that of the open string.

The points where you rest your fingers are called nodes. The places where, for that resonating frequency there is no movement. You could continue adding nodes and getting new frequencies along the way.

These are called harmonics. The first harmonic, or fundamental harmonic, is what you hear with an open string. The next one up is the second harmonic and so on. Here's what they look like:

Audio Illusion – do you hear the missing fundamental?

Now in reality when you pluck an open string you're actually getting a mixture of all these harmonics but you only hear the fundamental. The other harmonics don't register as distinct notes but instead make the whole sound richer. Here's an illustration of the sound produced by a guitar string being plucked:

Audio Illusion – do you hear the missing fundamental?

You only hear that lowest frequency but the other harmonics are there.

How does all this relate to the audio illusion?

Natural systems like the guitar string or human vocal cords tend to vibrate in this way, they vibrate at a fundamental harmonic and all the other harmonics on top. So our senses have evolved to interpret these mixtures of harmonics as a single tone coming from a single entity.

Here are two notes side by side:

Audio Illusion – do you hear the missing fundamental?

As you can see the second note is lower. And this is exactly what you're hearing when you play the sounds at the top of this post except for one important difference. The fundamental frequency of the second note has been taken away so it looks like this:

Audio Illusion – do you hear the missing fundamental?

That gap is "unnatural" and the way you interpret that depends on how your brain works.

It turns out that the way we perceive pitch isn't just to do with the tones we hear but also the pattern of tones. So for some of us our brains would receive the pattern of frequencies of the second note, ignore that fact that the pattern is broken, and interpret the sound as being lower. In other words your brain is hearing the fundamental harmonic that isn't there.

On the other hand, if you heard the pitch go up, that's because the pattern of frequencies is less important to your brain than the absolute lowest frequency.

Most people are a mixture of the two and depending on how you engineer the two sounds you can get anyone to hear or not hear the missing fundamental.

Did you hear it? Let us know in the comments.

You might also like the optical illusion in this post.

Update: Some interesting insight from Martin Coath who first told me about the effect: "The predisposition to hear one or the other is correlated with a volumetric asymmetry in Hesch'ls Gyrus - ie one of the auditory parts of your brain is bigger on the left or the right. (Schneider, Sluming et al Nature Neuroscience 8, 1241 - 1247, 2005)"

Another update: Awesome commenter sci ran my sounds through a frequency analyser and got this:

Audio Illusion – do you hear the missing fundamental?

I've attempted to anotate this image to show what I think is going on (am I getting it right sci?):

Audio Illusion – do you hear the missing fundamental?

So my original illustrations are a bit off. The sounds have fewer harmonics than I thought. But it does show the missing fundamental which I'm very excited about Audio Illusion – do you hear the missing fundamental? Thanks sci.

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  • http://twitter.com/TimMacQueen Tim MacQueen

    higher-lower

  • http://wizkidsound.com Wizkid Sound

    lower!

  • http://twitter.com/camwood2011 Cameron Wu

    Second note is lower.

  • aramisgm

    Interestingly, I hear two tones, as part of a descending arpeggiated chord (i.e., not independent tones at all).

  • http://twitter.com/mmaarrow Gemma Arrowsmith

    Higher to lower. I checked on my piano and it’s E above middle C down six semitones to B flat. Why, no, I don’t have a life. Interesting post, Steve.

    • Anonymous

      Nice! Of course it’s only B flat if you’re the type of person who hears the missing fundamental. Which is turning out to be most people!

    • guest

      surely you mean half steps, not semitones.

  • Anonymous

    I tested this in from of about 700 kids today. I’d say at most 10% heard the second sound as higher. So I might need a few more commenters before we find one of those!

  • Gregwoollaston

    I got Llower-higher. To be fair, I was using the crappiest computer speakers known to man. I’m pretty sure they have a average frequency of (nasty) 1kHz and a standard deviation of about 4 Hz. I’ll try with some good headphones at work.

    • Anonymous

      Well you’re the first low to high so far. Would be interesting if it was down to some sort of clipping. When you try it with good headphones try to go with your first instinct. I find that I can persuade myself that it’s going lower or higher if I listen enough times. Actually it would be interesting to test whether bias has an effect. Would saying something like “I’m about to play you two sounds, the second is higher than the first” would have any influence on how they were perceived.

      • Wendy Thorburn

        I’m hearing the second note higher, as I did in Bristol on Thursday.I really enjoyed your talk.Can I make a Rubens tube for the science department at school?

        • http://stevemould.com Steve Mould

          Thanks Wendy! What percent would you say heard it go higher? I’ll drop you an email with instructions in how to build the Rubens’ tube.

  • Laura Donelly

    I initially heard it go higher. Like you said in your last para, I can pretty much make myself hear it either way, but I have to concentrate to hear it go lower.

    • Anonymous

      Weird isn’t it!

  • Sarah

    I heard low-high: E to F# – same as you’d get with first finger on the E string on a violin.
    I listened loads of times, and while I feel like I should be able to hear E to C#, I can’t pick out the C#
    Really interesting!

  • http://rags.wordpress.com/ raghu

    Low-High. Very interesting…Really enjoy reading your posts – Do keep it coming :)

  • http://www.youtube.com/scibot9000 sci

    Stand back, I am a musician! *listens*
    lower to higher. kind of. It sounds like two notes, and only one changes (and it goes up).
    plugging it through my spectrum analyzer thingie agrees: http://i.imgur.com/ARF2e.png

    • http://stevemould.com Steve Mould

      Sci, that’s awesome. I’ve added it to the post. Have a look, I think I’ve annotated it correctly.

  • Crazyhannah12

    Wow! It was definately lower! I loved your talk

    • http://stevemould.com Steve Mould

      Thanks Hannah! It goes lower for me too. That’s cos we hear the missing fundamental harmonic that isn’t there.

  • Guest

    I came to watch GCSE Science Live today at Colston’s when you were testing this.
    - I heard lower to higher the first time, but the second time I could sort of hear it either way (in that it sounded like it was supposed to go down).
    By the way, the demonstration with the Ruben’s Tube was awesome and very interesting!

    • http://stevemould.com Steve Mould

      Thanks! That’s really interesting that you could hear it either way the second time.

  • http://dullhunk.myopenid.com/ Duncan Hull

    hello, saw you demo this at GCSE science live – very cool! Can you tell me what the name of the metal tube and the resonating metal square was called, they had scientific names but I can’t remember them. Thanks

  • Holy John

    I heard low to high. E to F

  • Celestial

    Second note is definitely lower

  • Ross

    Loving this blog, great stuff. Adding it to my list of regular reads :)

    • http://stevemould.com Steve Mould

      Thanks Ross!

  • Colonel

    I heard both…eventually. I heard the second as being higher initially then really wanted to hear it as lower so I tried a few things but none seemed to work. Then I tried whistling the first note and holding it as the second note played. I then heard the second note as lower, now I hear both at the same time. Don’t know why this worked, but quite cool.

    • http://stevemould.com Steve Mould

      It’s weird, it really is possible to hear either way. Though I’ve never heard both at the same time! Can’t imagine what that would be like.

  • Cody Long

    I here two tones in the second note, one higher and one lower than the original. When I first looked I was like “Audio File! MUST LISTEN!” When I heard the second note I knew it sounded weird so I listened again and I heard one tone higher and one tone lower than the original. Then I read your post and realized we talked about this in my AP Music Theory class.

  • Robin

    I hear higher-lower, but the second note has an odd noise behind it which could be slightly higher.

  • Jen

    second tone is lower for me!

  • Cam

    Second tone is clearly higher.

  • JuuS

    Second tone higher

  • Will

    I’m a musician, if that makes any difference. But I heard 2 note pairings (harmonies) in succession, instead of two tones in succession. I heard the higher tone staying the same, and the lower one raising a half step. After reading reading further, I get the physics of it…but I’m still at a loss as far as the psychology behind it. I’d love to know more about what this says about me, if you have any insights on that. Thanks, and great blog entry!! Yay stumbleupon!!

    • http://stevemould.com Steve Mould

      That’s weird! Not sure what it means. I think maybe musician listen more actively. They analyse the sounds more closely. They notice there’s something fishy with the sounds and that gets interpreted in musical ways. Like hearing a harmony for example. That’s a total hunch though.

      Yay stumbleupon indeed! It’s where all my traffic comes from and I have no idea why :)

  • Guest

    I heard the second note lower, but my mom and brother both heard it as higher

  • Anthony

    I’m also a musician and heard the same thing as Will up there ^^^. I hear two pairs of notes. In the second pair of notes, the higher note stays the same, and the low note goes up in pitch. Just like the picture shows from the frequency analyzer above.

  • Martysec

    so i was confused at first. i heard the second as higher. then read through and thought, “surely it’s not an illusion if you’re taking out the fundemental – because you’re actually making it higher” but then i realised it’s only an illusion if you hear the second as lower. right?

    • http://stevemould.com Steve Mould

      I’d agree with that yes!

  • Ben London

    I have a fairly non-standard and possibly synaesthetic audio sense; I heard/saw basically the equivalent of sci’s spectrogram. This was before I saw his images of course. I was confused because you asked which was higher and I thought, “well they’re the same note, just different chords. Well, I suppose it’s higher, because it’s compressing the two tones with the upper tone anchored.” If I listened really hard, I could almost hear the “lower” version, but since I heard/saw that there wasn’t a tone descending, just an interference pattern at the frequency of where the lower note would be.

    • http://stevemould.com Steve Mould

      That’s really interesting. Thanks Ben!

  • http://profiles.google.com/petryk.steven Steven Petryk

    Yeah, I’m hearing what all of the other musicians hear on here too. It sounds like an interval whose top note stays the same while the bottom note moves up.

  • http://jimsjournal.blogspot.com Jeeemeister

    Second sound was higher for me.

    Fascinating site Steve!

    Jim from Southern Thailand

  • Ed

    From a nerdy musical analysis, sounds like 2 notes both times. The interval between which is first a maj3rd then a min3rd.. so top note stays same and lower goes up a semi-tone. Basically 2nd sounds higher (considering the lower part ‘goes up’). Fascinating though, keep up the good work Steve!

  • http://plivesey.myopenid.com/ plivesey

    I heard this at one of your FOTSN shows and tried it again here. The second tone is simultaneously both higher and lower than the first. What I hear is one chord (almost DTMF maybe?) followed by another. On repeat listenings I can ‘make’ it go higher or lower at will but naturally I hear it as both.
    In my defence I’m a EE♭ and string bass player and so therefore tone deaf.