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Introduction

We are all used to the idea of optical illusions, but auditory illusions also exist. One such is the 'Zwicker tone', first characterised by Eberhard Zwicker at Bell Labs in 1964.

The illusion is created by playing a subject (for a few seconds) broad spectrum white noise that contains a frequency gap, i.e. if you were to play it through a spectrum analyser all the bars would be at maximum, except one. Then sound is then turned off, and even though there is complete silence, the subject hears a very faint, pure tone of about equal frequency to the frequency gap in the noise. In essence the effect is like brief tinnitus lasting only a few seconds. Various configurations of noise, silence and the addition of a pure tone can give differing, or indeed no Zwicker tone. Various configurations, and their effects are shown below (reproduced from reference 1)


(a)                  (f)
 ^                     ^
 | Low-Pass            |     High-pass
 | Noise               |     noise
 |                     |
 |                     |     
 |####                 |         ####             
 |#### @               |         ####
  -------------->       ------------->

(b)                  (g)
 ^                     ^
 | Noise with          | Noise with 
 | wide gap            | tiny gap
 |                     |
 |                     |
 |####      ####       |###### ######             
 |#### @    ####       |###### ######
  -------------->       ------------->


(c)                  (h)
 ^                     ^
 | Noise with          | White noise 
 | small gap           | 
 |                     |
 |                     |
 |#####   #####        |#############             
 |##### @ #####        |#############
  -------------->       ------------->

(d)                  (i)
 ^                     ^
 | Noise with          | Pure Tone 
 | pure tone           | 
 |       !             |        !
 |     @ !             |        !
 |##############       |        !   
 |##############       |        !
  -------------->       ------------->

(e)                  (j)
 ^                     ^
 | Low-Pass            | High-pass
 | noise, pure tone    | noise, pure tone
 |   !                 |         ! 
 |  @!                 |         !
 |####                 |         ####             
 |####                 |         ####
  -------------->       ------------->
  Frequency            Frequency


 Key :-

 ### Indicates noise    @ indicates frequency
                          at which Zwicker tone
                          is heard

 ! Indicates frequency
 at which a tone is
 played

Explanation

The above patterns show very interesting effects, firstly experiments f to j give no Zwicker tone, and secondly the addition of another pure tone on top of, or at the edge of the noise frequency can produce the effect. The origin of the Zwicker tone has long been debated, but a recent paper (ref. 1) by Franosch, Kempter, Fastl and Hemmen published in Physical Review Letters offers an explanation. They explain the effect is due to both noise reduction circuits in the brain, and to asymmetric inhibition. This is rather different to the optical illusion equivalents (e.g. looking at a spinning disk with a spiral on, then your hand) which are due to habituation.

They base their explanation on a model of the brain where there are feature detector neurons, noise detector neurons, and output neurons, each of which correspond to a fairly narrow frequency range.

The noise detector neurons when activated by noisy input around the frequency range they work at, will inhibit the output neurons. There is also a lag time associated with them, their inhibition lasts for seconds after the sound has been turned off. Also this inhibition is asymmetric in that it is more more effective from low to high frequencies than from high to low.

The feature detectors pick up pure tones and both stimulate the output neurons and inhibit the noise detection neurons around the frequency they detect. This can be seen in example (d) above, the asymmetric inhibition of the noise detectors around the frequency of the tone effectively "burns a hole" in the noise spectrum. This makes the noise spectrum look more like b) or (c) to the brain, and produces a Zwicker tone lower in frequency than the tone played.

Furthermore there is a background level of activity present in the system, that is neurons are firing all the time, sometimes even exceeding a hundred times a second. You only hear a sound when the output neurons fire faster than this so called 'spontaneous' activity. The output neurons also inhibit firing to the neurons at a slightly higher frequency to themselves. (See diagram of the model below) The product of the lag time of the noise reduction neurons and their asymmetric inhibition is such that the activity of the output neurons will rise just above the spontaneous activity level around the frequency of the tone gap. Which is what produces a faint pure tone.

These competing processes are kind of hard to visualise, but the authors of the paper made a neural network that mimics their model. When this network is played noise and tones as above, its behaviour mimiced that of human subjects. Shown below is the asymmetric inhibition, with noise reduction model, again reproduced from their paper.

                    _----_ _----_       
                   |      *      *
                  OOO    OOO    OOO
                  OOO    OOO    OOO
                  OOO    OOO    OOO
                          *+
                          | \
                          |  \
                         ###  |
                         ###  |
                         ###  |
                         *+  /
                        / | /
                       /  |/
             ----------   |
            |             |
           @@@            |
           @@@            |
           @@@            |
          *   +           |
         /     \          |
        /       \         |
        :        :        :
       . .      . .      . .
      .   .    .   .    .   .
     .     .  .     .  .     .
    .       ..       ..       .
Key :-     
# = Noise detection neurons
O = Output neurons
@ = Feature detection neurons
* = Inhibitory fibres
+ = Excitatory fibres
. = Denotes frequency range of neurons                   

Okay so that's the model, if we now apply it to experiment (e) above, that is low-pass noise, with a tone right at the top edge of its frequency and see what happens. During the sound, the noise detection neurons suppress the output ones, except in the region of the pure tone. This 'hole burning' effect cuts the frequency response of the noise detect to less than the pure tone. Hopefully you can see it tails off before the '!' in the diagram below. The noise detectors at this frequency are therefore off before, during and after the experiment. The noise detectors lower in frequency than the burnt hole are active, suppresing output during and for a few seconds after the sound. When the sound is stopped the noise detectors are inhibiting the output neurons still, dropping their firing rate well below the spontaneous firing level. However the asymmetric nature of the inhibition means the output neurons that have been suppressed are generating less inhibition to neurons at a higher frequency, meaning the higher frequency ones are firing slightly faster, just enough to raise the output rate above the spontaneous threshold and give a pure tone!

 |                                             ^
 |  ::                                         |
 | :  :         @   ....                       |
 | :   :     ......:    :                      F
 | :    .....   **       :                     I
 |-:------------*-*------:----------------     R
 | :            *  *      ..                   I
 | :oooooooooooo*o  ****    ******             N
 | o           * o     ****      ********      G
 | o           *  o                            
 |o            *  o                            R
 |o   *       *   o                            A
 |o*** ********    o                           T
 |*________________o______________________     E


 |                   !
 |                   !
 |####################
 |####################____________________

      F  R  E  Q  U  E  N  C  Y


  Key :-
  --- = Marks the level of 'spontaneous' firing of output neurons i.e. before the experiment
  ... = Firing rate during stimulus
  *** = Immediately after stimulus  
  ooo = Rate of noise-dectection neurons
    @ = Frequency at which Zwicker tone is heard
    ! = Frequency of pure tone played
    # = White noise

Conclusion

So the whole upshot is that the Zwicker tone is an illusion produced by the parts of the brain designed to suppress background noise so that we can pay attention to important features in our environment. The authors of the paper suggest that tinnitus may arise from a long term malfunction of this system, and hope by understanding how the brain can generate phantom sounds, treat the condition. Also as a_scar_fairy suggests it explains why after loud rock and roll you get ringing in the ears... If anyone knows, let me know!

I myself also wonder if this effect could be put to use in a musical compostion, never having experienced the effect, I don't really have an idea of how noticable it would be. I suspect you could hear it in a quiet room with headphones. As there is a whole movement of music dedicated to really quiet sounds (can't remember what it's called though), we may well be hearing music played by "instruments" that were never even there...

References :-
1). Jan-Moritz P. Franosch, Richard Kempter, Hugo Fastl and J. Leo van Hemmen. Zwicker Tone Illusion and Noise Reduction in the Auditory System. Phys. Rev. Lett. 90:178103 (2003)

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