<p>Let us model hearing in the frequency domain as a <a href="https://en.wikipedia.org/wiki/Bark_scale" rel="nofollow noreferrer">Bark scale</a> with <a href="https://www.iue.tuwien.ac.at/phd/singulani/images/Picture23.png" rel="nofollow noreferrer">piecewise overlapping</a> <a href="https://en.wikipedia.org/wiki/Triangular_distribution" rel="nofollow noreferrer">triangular frequency distribution</a> <a href="https://en.wikipedia.org/wiki/Basis_function" rel="nofollow noreferrer">basis functions</a> like this one based on normal distributions
<a href="https://i.sstatic.net/z6tvD.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/z6tvD.png" alt="enter image description here" /></a>
where a piece of a single overlapping in the violet box is like in the following image.
<a href="https://i.sstatic.net/94sXe.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/94sXe.png" alt="enter image description here" /></a>
The blue and orange lines are from a small piece of the Bark scale where overlapping triangular frequency distributions exist.
The black, pink and green are three type of sounds (frequency distributions), all with the same mean frequency. It is obvious from the picture that the perceived response of any of the three sounds in the image are the same. The frequency of the sound is detected by the relative difference in intensity when the blue and orange basis functions are multiplied with the sound signal. Another observation is that that frequency variance (the width of the sound in the picture) is different among the three sounds but there is no way these overlapping triangular basis functions can detect that. Thus, the nervous system can arbitrarily understand the variance to be small or wide. For a wide variance the <a href="https://en.wikipedia.org/wiki/K%C3%BCpfm%C3%BCller%27s_uncertainty_principle" rel="nofollow noreferrer">uncertainty relation</a> will be able to make a more narrow determination of the sound in the temporal domain. The limit of the possible variance is determined by the width of the overlap of the triangular basis functions and the sound's distance to any of these overlap edges. This model can explain how the temporal resolution can be higher than with non overlapping basis functions and how perception can differ from individuals.</p>

CC BY-SA 4.0
2022-04-10T23:13:29.517Z
2022-04-28T09:29:02.650Z
2022-04-28T09:29:02.650Z
David Jonsson
<p>Majka et al. (2015) [<a href="https://www.europhysicsnews.org/articles/epn/pdf/2015/01/epn2015461p27.pdf" rel="nofollow noreferrer">PDF</a>] shows that some trained people can discern pitch differences faster than the <a href="https://en.wikipedia.org/wiki/Uncertainty_principle#Signal_processing" rel="nofollow noreferrer">uncertainty relation</a> permit. How can this be possible?</p>
<p><strong>Abstract</strong></p>
<blockquote>
<p>The human hearing sense is an astonishingly effective signal processor. Recent experiments [1, 2, 3] suggest that it is even capable of overcoming limitations implied by the time-frequency uncertainty relation. The latter, mostly known from quantum mechanics, requires that the product of uncertainties in time and frequency, Δt∙Δf , cannot be smaller than the limiting value Δt∙Δf = (1/4π), which holds when the signal is a harmonically oscillating function with a Gaussian envelope.</p>
</blockquote>
<h2>References</h2>
<p>Majka, M., Sobieszczyk, P., Gębarowski, R., &amp; Zieliński, P. (2015). Hearing overcome uncertainty relation and measure duration of ultrashort pulses. <em>Europhysics News, 46</em>(1), 27-31. <a href="https://doi.org/10.1051/epn/2015105" rel="nofollow noreferrer">https://doi.org/10.1051/epn/2015105</a></p>

CC BY-SA 4.0
2021-11-07T12:23:59.110Z
Welcome to Psychology.SE.  I was clicking on your link for the paper you cited and after a few clicks and not seeing the paper, realised that it was a PDF and now I have several copies.  I thought it would be helpful to highlight that with an edit for you.  Hope that is OK with you.  If not, feel free to edit it back.
Chris Rogers
CC BY-SA 4.0
2021-11-07T14:16:01.427Z
Have you read the rest of their paper or did you stop at the abstract?
Bryan Krause
CC BY-SA 4.0
2021-11-07T14:52:37.990Z
@BryanKrause Yes but without insight. I also wrote a program to test this. If you find an acceptable answer in their article please write it as an answer. I also doubt how realistic their conclusion is if they don't provide any assumption on present noise. Hearing is nonlinear and I wonder if that contributes.
David Jonsson
CC BY-SA 4.0
2022-01-08T15:48:34.863Z
@ChrisRogers I suggest using the same linking tradition as elsewhere on Stack Exchange.
David Jonsson
CC BY-SA 4.0
2022-01-08T15:58:53.727Z
@DavidJonsson maybe you could raise this in [meta] for this site's community to decide? Just because it works elsewhere, doesn't necessarily mean it works here.
Chris Rogers
CC BY-SA 4.0
2022-01-08T16:00:58.190Z
Please bear in mind that [there is this meta post](https://psychology.meta.stackexchange.com/q/8) for preferred referencing methods.
Chris Rogers
<hearing><reaction-time>
How can the uncertainty relation be exceeded in hearing?
David Jonsson
# How can the uncertainty relation be exceeded in hearing?

(Asked by: username_0 on 2021-11-07)

Majka et al. (2015) [[PDF](https://www.europhysicsnews.org/articles/epn/pdf/2015/01/epn2015461p27.pdf)] shows that some trained people can discern pitch differences faster than the [uncertainty relation](https://en.wikipedia.org/wiki/Uncertainty_principle#Signal_processing) permit. How can this be possible?

**Abstract**

> The human hearing sense is an astonishingly effective signal processor. Recent experiments [1, 2, 3] suggest that it is even capable of overcoming limitations implied by the time-frequency uncertainty relation. The latter, mostly known from quantum mechanics, requires that the product of uncertainties in time and frequency, Δt∙Δf , cannot be smaller than the limiting value Δt∙Δf = (1/4π), which holds when the signal is a harmonically oscillating function with a Gaussian envelope.

## References

Majka, M., Sobieszczyk, P., Gębarowski, R., & Zieliński, P. (2015). Hearing overcome uncertainty relation and measure duration of ultrashort pulses. *Europhysics News, 46*(1), 27-31. <https://doi.org/10.1051/epn/2015105>

**Tags:** hearing, reaction-time

> **Comments:**
> **username_1**: Welcome to Psychology.SE.  I was clicking on your link for the paper you cited and after a few clicks and not seeing the paper, realised that it was a PDF and now I have several copies.  I thought it would be helpful to highlight that with an edit for you.  Hope that is OK with you.  If not, feel free to edit it back.  
> **username_2**: Have you read the rest of their paper or did you stop at the abstract?  
> **username_0**: @BryanKrause Yes but without insight. I also wrote a program to test this. If you find an acceptable answer in their article please write it as an answer. I also doubt how realistic their conclusion is if they don't provide any assumption on present noise. Hearing is nonlinear and I wonder if that contributes.  
> **username_0**: @ChrisRogers I suggest using the same linking tradition as elsewhere on Stack Exchange.  
> **username_1**: @DavidJonsson maybe you could raise this in [meta] for this site's community to decide? Just because it works elsewhere, doesn't necessarily mean it works here.  
> **username_1**: Please bear in mind that [there is this meta post](https://psychology.meta.stackexchange.com/q/8) for preferred referencing methods.  

---

## 1 answers

### Answer by username_0 on 2022-04-10. Score: 1

Let us model hearing in the frequency domain as a [Bark scale](https://en.wikipedia.org/wiki/Bark_scale) with [piecewise overlapping](https://www.iue.tuwien.ac.at/phd/singulani/images/Picture23.png) [triangular frequency distribution](https://en.wikipedia.org/wiki/Triangular_distribution) [basis functions](https://en.wikipedia.org/wiki/Basis_function) like this one based on normal distributions
[![enter image description here](https://i.sstatic.net/z6tvD.png)](https://i.sstatic.net/z6tvD.png)
where a piece of a single overlapping in the violet box is like in the following image.
[![enter image description here](https://i.sstatic.net/94sXe.png)](https://i.sstatic.net/94sXe.png)
The blue and orange lines are from a small piece of the Bark scale where overlapping triangular frequency distributions exist.
The black, pink and green are three type of sounds (frequency distributions), all with the same mean frequency. It is obvious from the picture that the perceived response of any of the three sounds in the image are the same. The frequency of the sound is detected by the relative difference in intensity when the blue and orange basis functions are multiplied with the sound signal. Another observation is that that frequency variance (the width of the sound in the picture) is different among the three sounds but there is no way these overlapping triangular basis functions can detect that. Thus, the nervous system can arbitrarily understand the variance to be small or wide. For a wide variance the [uncertainty relation](https://en.wikipedia.org/wiki/K%C3%BCpfm%C3%BCller%27s_uncertainty_principle) will be able to make a more narrow determination of the sound in the temporal domain. The limit of the possible variance is determined by the width of the overlap of the triangular basis functions and the sound's distance to any of these overlap edges. This model can explain how the temporal resolution can be higher than with non overlapping basis functions and how perception can differ from individuals.


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