Talk:Sone

Role of perceived relative loudness
Is it true that humans will rate a sound as twice as loud if the sone level doubles? Or is that property true of phons and not sones? Or is it yet some other property, like pressure wave amplitude, or pressure intensity? Human perception of loudness must scale linearly in proportion to some measure, perhaps as yet to be defined. But whichmeasure?? As far as I can tell, Wikipedia is silent on this. Randallbsmith (talk) 21:35, 30 September 2013 (UTC)
 * Doubling of sones in intended to represent a doubling of perceived loudness; "sones" are that "some measure" you're looking for, though the relation between the objective and perceived values is not a precisely measurable thing, and is defined by convention after sufficient experimentation.  At high enough loudness, doubling the sones requires about a 10 dB intensity increase; or factor of 3.16 pressure increase. Dicklyon (talk) 23:19, 18 October 2020 (UTC)

More useful equations?
The given equation simply relates two rather obscure measures of loudness ($$N$$ and $$L_N$$.) If it's easy, I'd request the author(s) plop in some other equations as well, relating $$N$$ to more familiar basic physical wave properties (like amplitude, for example). Randallbsmith (talk) 15:59, 30 September 2013 (UTC)

Sones at 0 dB
Can someone explain how dBs relate to Sones below 40 dB? If an increase of 10 DB is a doubling of Sones, then 30 dB should be .5 Sones, 20 dB should be .25 Sones, 10 dB should be .125 Sones and 0 dB should be .0625 Sones. However the chart says the threshold of sound is 0 Sones, which is understandable if a Sone is a "perceived" sound level -- if you don't hear anything, it would be 0 Sones. If this is the case, how do the numbers map to Sones between 0 dB and 40 dB? How is the perceived level measured or calculated? -- &#x2611; Sam uelWantman 09:06, 9 February 2008 (UTC)


 * That's an excellent point. There's nothing wrong with your calculations, but I think the introduction is slightly misleading. There is no citation that I can see for the mapping of a factor 2 in sones to a 10 dB change in sound level, but my guess is that this mapping breaks down for very low levels of sound, close to the hearing threshold. Thunderbird2 (talk) 09:21, 9 February 2008 (UTC)


 * I think the part missing from the article is a description of where the sones value comes from. The single number comes from a summation of the sound pressures in each of the frequency bands, and is effected by things like prominent tones that are significantly louder than other sounds in the spectrum, or two prominent tones close to each other, or other spectral situations.  Also, which method of calculation was used?  Whereas overall sound pressure is a logarithmic summation of numbers (with or without weighting), loudness is much more complicated, and you can't try to equate or correlate dB's with sones.   That said, I'm not editing the entry because I don't know what to say.  (I know just enough to be dangerous...)  --Freqdomain (talk) 14:07, 3 June 2008 (UTC)


 * More information for computing the loudness for arbitrary sounds can be found in the norm ISO 532 B. This norm also contains a quantitative description of the relationships between the loudness level LN in phon and the loudness N in sone. For 1 kHz sinus signals the loudness level and the sound presure level are identical. According to this norm the following formula is given for loudness levels less than 40 phon or for loudnesses less than 1 sone:


 * $$L_N = 40 ( \frac{N}{sone} + 0.0005 )^{0.35} \text{ phon}$$


 * $$N = (( \frac{L_N}{40 phon} )^{2.86} - 0.0005) \text{ sone}$$


 * For these levels a reduction of the sound level by 10 dB leads to a stronger reduction of the loudness than at higer levels. For example:
 * A loudness level of 30 phon leads to a loudness of 0.44 sone (instead of 0.5 phon)
 * A loudness level of 20 phon leads to a loudness of 0.14 sone (instead of 0.25 phon)
 * A loudness level of 10 phon leads to a loudness of 0.018 sone (instead of 0.125 phon)
 * Skyhead E (talk) 22:17, 29 March 2010 (UTC)

auditory threshold
auditory threshold at 2 kHz ==> isn't it at 1kHz ?????? —Preceding unsigned comment added by 78.113.58.88 (talk) 16:37, 8 May 2008 (UTC)

Lack of References
I found the base page to be very informative, but from other interactions with Wikipedia, I was surprised to find no references for the data provided. When I came to the discussion page, I find out its part of a wikipedia project. Shouldn't that data be documented on the base page in addition to the discussion page? Charles W. Bash (talk) 22:42, 31 May 2008 (UTC)

Mathematical Symbol?
Thanks for the article! I did notice that the equation to calculate sones from phons is a little confusing. It looks like you use the symbol "ld" for log base 2. You might consider altering that equation. Ben Havrilesko 03 November, 2009  —Preceding undated comment added 22:28, 3 November 2009 (UTC).

How is the pronounced?
Is it (o as in song) or  (o as in bone)? -- Q Chris (talk) 12:30, 28 November 2012 (UTC)

too technical?
i'm not sure how to flag this article as such, but as a layman, I can't make heads or tails of this... — Preceding unsigned comment added by 173.16.173.3 (talk) 00:00, 27 August 2013 (UTC)

I would argue...
There are symmetry reasons in the nonlinear differential equations that argue strongly for cube root compressive behavior above 40 Phon.

Hence the factor 33.2 is off from the expected 30.

I would argue that it is impossible to accurately discern "twice as loud". But this is a close rule of thumb. And it is in using the "rule of thumb" that one gets 33.2 (10 dB increase for twice as loud). 33.2 pays primacy to 10 dB and "twice". And I argue that cube root compression is primal.

Using cube root behavior, the expected increase in Phon would be 9.5 dB instead of 10 dB, for that "twice as loud". An imperceptible distinction.

So to simplify, we have

Sones = 10^((Phons - 40)/30).

Using 30 instead of 33.2 keeps cube root behavior, and this matches analytic modeling to better than 2% everywhere above 35 Phon (= 35 dBSPL at 1 kHz). Using 33.2 produces much larger errors everywhere.

Below 40 Phons we get into the transition zone between cube root compressive behavior at commonly encountered sound levels, and the linear behavior at near-threshold levels. So the simple formula grows increasingly inaccurate below 40 Phon. An empty quiet auditorium registers about 30 dBSPL.

Nonlinear "EarSpring" equation for loudness perception of whole hearing (not just cochlear) model:

[d^2/dt^2 + 2*B * d/dt + k*(1 + gamma * )] y = F(t)

for B damping, k spring stiffness, gamma coeff of stiffness growth with average power of vibration, F(t) specific forcing function with time.

Here Sones(P) can be identified as the ratio of average vibrational power taken at sound level P phons, compared to the average power at 40 Phons, as measured in one critical band.

Symmetry arguments: https://arxiv.org/pdf/1408.2085.pdf (top of page 24)

EarSpring: https://www.icloud.com/iclouddrive/04cLSvZIf1gQRx9Zjrx71D5qg#EarSpring