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I cant understand how paper about the human eye (source number 5) can be related to the range at which the law is valid.
It's difficult to interpret any of these equations, since S is never defined. — Preceding unsigned comment added by 129.170.30.126 ( talk) 20:16, 15 August 2017 (UTC)
i agree. this page is a classic wikipedia demonstration of people posting over their heads. while it is possible, with scrutiny, to infer that (S zero) is the stimulus threshold as a physical quantity (power, mass, distance, time, etc.), the reader should not have to puzzle parse to do so. all mathematical symbols (other than the operation signs) need to be defined at the first place they appear, and then used uniquely (no multiple symbols for the same quantity). in the case of psychometrics, if it is relevant, then the classical or original formulation of a relationship needs to be stated separately from any modern or currently conventional definition.
i think the editors need to flag this page as having problems requiring help. "start quality" does not adequately warn the reader to be wary. Drollere ( talk) 18:11, 25 January 2020 (UTC)
I give up. I've read the page and I still couldn't tell you what the W-F law actually *is*. The article has an awful lot of discussion *about* the law, but I don't see anything that actually states what the law is. The law of gravity is that bodies are attracted to each other proportional to the product of their masses and inversely proportional to the distance between them, or F = Gm1m2/s^2. Murphy's law is that anything that can go wrong will go wrong. The Weber-Fechner law is....????? —Preceding unsigned comment added by 131.107.0.73 ( talk) 19:36, 26 August 2008 (UTC)
The Weber-Fechner law of logarithmic sensitivity may be valid for some of our senses, but modern theory of sound measurement is in disagreement with it. If the intensity is (in watts per square metre, ), the (intensity) level is
where is the threshold of hearing, and where is the logarithm base 10.
For simplicity, consider just a pure tone (sine wave) of 1000 Hz; then , and the unit dB is also called phon. According to Weber-Fechner, doubling the level should mean doubling the subjective loudness. However, experiments show that to double the subjective loudness, one should multiply the intensity by 10, or equivalently increase the level by 10 dB. It takes 10 violins to sound twice as loud as one violin! (Some sources give a value smaller than 10. The article sone mentions the value 3.16; this discrepancy is due to a misunderstanding - on my part, or on the part of the author of that article; I am not sure.) Therefore, the subjective loudness is better represented by
where . Choosing , the unit of this measure is called " sones".
Accoring to Weber-Fechner, the following should be a doubling sequence in terms of subjective loudness:
intensity | level | subjective loudness |
---|---|---|
5 dB | 0.0884 sones | |
10 dB | 0.125 sones | |
20 dB | 0.25 sones | |
40 dB | 1 sones | |
80 dB | 16 sones | |
160 dB | 4096 sones |
But the experimental results give the following doubling sequence instead:
intensity | level | subjective loudness | examples |
---|---|---|---|
0 dB | 0.0625 sones | limit of hearing | |
10 dB | 0.125 sones | Â | |
20 dB | 0.25 sones | Â | |
30 dB | 0.5 sones | Â | |
40 dB | 1 sones | ppp | |
50 dB | 2 sones | pp | |
60 dB | 4 sones | p | |
70 dB | 8 sones | Â | |
80 dB | 16 sones | f | |
90 dB | 32 sones | ff | |
100 dB | 64 sones | fff | |
110 dB | 128 sones | Â | |
120 dB | 256 sones | limit of pain |
The notations ppp = piano pianissimo, etc., are used in musical scores. Their correspondence to sound levels are approximate only.
-- Niels Ø 13:53, Mar 20, 2005 (UTC)
... in this article there was something about "Pythagoras finding out that every (n+1) tone is the "twelveth root of 2" * (n)tone. that is weird because the 12-tone-western music (that is what this root-thingy revers to i guess) was introduced around 2000 years after Pythagoras died...
Crucial to understanding marginalism. Christofurio
I'm trying to figure out the origin of the bel unit, now most commonly used as a decibel. I've discovered that it was originally derived from Fechner's law. This article describes it as so:
Physicists are sticklers for the dB being only used for 10·log intensity/power ratios (and not 20·log amplitude/voltage/pressure ratios). Since Fechner's law is about "perceived intensity", does it really refer to a ratio of a specific type of unit? — Omegatron 17:29, 6 January 2006 (UTC)
Fechner's interpretation depends on having some unit of sensation intensity. In my view, this gets lost by proceeding directly to an expression of the so-called law in terms of ratios. The implied unit is more difficult to interpret than a unit of a physical quantity. Let be a unit of perceptual intensity. Let be the measure of the posited sensation intensity associated with a stimulus whose physical magnitude is . I'm using non-italicized symbols to represent quantities rather than ratios of quantities (i.e. rather than measurements in some unit). I'm using italicized symbols only for ratios of quantities; i.e. for measurements in which some unit is implicit.
Making the perceptual unit explicit, according to Fechner's "law"
I think your question is whether it is possible to obtain measurements of sensation intensity relative to a fixed unit such as P? If so, I think the answer is far from clear as things currently stand.
There is only stochastic information about sensation intensity, such as the proportion of occasions on which differences between stimuli of different magnitudes are noticed under specified conditions. Thurstone argued that Weber's law and Fechner's law are only equivalent if the so-called discriminal dispersions are constant, which gives a unit (see law of comparative judgment). What this amounts to is that the sensation intensity associated with the so-called JND is the unit (or equivalently some multiple of this intensity is the unit). For one thing, why should we be able to obtain sensory units without controlling conditions when we cannot obtain physical units without using instruments deliberately designed to measure in a particular unit under controlled conditions? In my view it is still very much an open question. smhhms 06:40, 7 January 2006 (UTC)
This page and the page on Munsell's color notation conflict in their description of the perceived increase in luminance. This may be valid because the term used here is 'brightness' while the term used there is 'lightness,' but on the Munsell page, lightness changes with respect to the cube root of the actual intensity, rather than the logarithmic increase mentioned here. It should be noted that a cube root trend appears similar to a log, and that this is apparently used in CIELAB color space to help define the color axis. 74.74.223.195 ( talk) 20:28, 11 July 2008 (UTC)
Also, the page on Visual_magnitude says that it is a misconception that the eye responds on a logarithmic scale, but this page says it does. What's with that? 122.169.103.240 ( talk) —Preceding undated comment was added at 11:19, 23 October 2008 (UTC).
Regarding Color: I'm wondering about what data anyone might have relating color space perception to Weber's law? The article on color theory might have some useful insights and I will do some research, but if any editors are able to address perception of color as it does, or does not, follow the logarithmic scale as with loudness and brightness.
Regarding sound timbre, tone and metrics: How might this be addressed in terms of Weber's law, or related concepts. Timbre perception is complex having to do with harmonic content and so on. The question of signal to noise ratio is also something I'm wondering about, that is, how to relate Weber's law and related concepts to sound quality. With regard to perception of metrical units and rate of units, otherwise known as meter and tempo in music, does Weber's law apply to our perception of these elements?
I may not even be formulating these questions all that well, but, perhaps you have some insights to share which will help my own understanding and moreover help the article expand in a useful direction. Calicocat ( talk) 06:05, 20 July 2008 (UTC)
I'm not sure what this means. It seems inaccurate. It should be (re)considered, although I don't have time to parse it just this minute. 129.81.44.124 ( talk) 15:59, 26 August 2010 (UTC)DGHyman
I would presume that mental number lines have no inherent bias to be left to right, but predominantly take on that direction in cultures which write left to right. Has anyone studied this effect in populations that use the Arabic or Hebrew scripts? 4pq1injbok ( talk) 02:14, 11 October 2012 (UTC)
I'm too lazy to find reputable references which consider the two (Scoville scale and Weber-Fechner law) together, so here's some funny Finding On The Talk Page: the Scoville scale is clearly more concerned with representing magnitude rather than exact (up to the last digit) measure of capsaicin concentration (which is closely connected to spicyness, heat and, in extremes, pain sensations), and it begs for logarithmic units. — Preceding unsigned comment added by 213.227.200.124 ( talk) 01:48, 30 December 2014 (UTC)
The symbols in the equations currently need to be looked up by a non-mathematician. Understanding would be greatly promoted and encouraged if the formulae had their symbols briefly explained in terms of which quantities each symbol represents. For example if "K" represents a constant that is specific to the different human senses, and that can vary according to which sense it represents ... then saying so right after or before the formula in which "K" appears for the first time in the article would be helpful. Having a simple equation, but for which symbols are not locally defined ... interrupts learning. Thanks. Very interesting article and concepts. — Preceding unsigned comment added by 97.125.86.191 ( talk) 18:39, 13 June 2017 (UTC)
From the article: "if the weight of 105 g can (only just) be distinguished from that of 100 g, the JND (or differential threshold) is 5 g. […] this minimum required fractional increase (of 5/100 of the original weight) is referred to as the "Weber fraction""
I'm no expert, but the article on JNDs says that it's the same as the difference limen. Meanwhile, the literature seems to define the Weber fraction as the relative standard deviation of the error, and in a 1975 paper by Getty, I read that "the difference limen is a constant fraction (.68) of the value of the standard deviation". So that seems to mean that JND = Weber fraction * 0.68. In our example, I would therefore expect the Weber fraction to be 5% / 0.68 = 7.35%. Could somebody clarify?
-- Forlornturtle ( talk) 14:53, 30 August 2018 (UTC)
I think that this should be C class. Anyone with me? — Preceding unsigned comment added by Just4science! ( talk • contribs) 10:49, 5 March 2019 (UTC)
The current version of the section on Sound has three contradictory statements:
Anyone want to clear this up? Clean Copy talk 11:25, 28 March 2020 (UTC)
The lead now says:
(The emphasis is mine.) Clearly, you cannot infer Fechner's law from Weber's - you can ... extend? extrapolate? be inspired by? I'm not sure what's a good word here - but inference isn't, I think.-- Nø ( talk) 14:00, 19 March 2021 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||
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I cant understand how paper about the human eye (source number 5) can be related to the range at which the law is valid.
It's difficult to interpret any of these equations, since S is never defined. — Preceding unsigned comment added by 129.170.30.126 ( talk) 20:16, 15 August 2017 (UTC)
i agree. this page is a classic wikipedia demonstration of people posting over their heads. while it is possible, with scrutiny, to infer that (S zero) is the stimulus threshold as a physical quantity (power, mass, distance, time, etc.), the reader should not have to puzzle parse to do so. all mathematical symbols (other than the operation signs) need to be defined at the first place they appear, and then used uniquely (no multiple symbols for the same quantity). in the case of psychometrics, if it is relevant, then the classical or original formulation of a relationship needs to be stated separately from any modern or currently conventional definition.
i think the editors need to flag this page as having problems requiring help. "start quality" does not adequately warn the reader to be wary. Drollere ( talk) 18:11, 25 January 2020 (UTC)
I give up. I've read the page and I still couldn't tell you what the W-F law actually *is*. The article has an awful lot of discussion *about* the law, but I don't see anything that actually states what the law is. The law of gravity is that bodies are attracted to each other proportional to the product of their masses and inversely proportional to the distance between them, or F = Gm1m2/s^2. Murphy's law is that anything that can go wrong will go wrong. The Weber-Fechner law is....????? —Preceding unsigned comment added by 131.107.0.73 ( talk) 19:36, 26 August 2008 (UTC)
The Weber-Fechner law of logarithmic sensitivity may be valid for some of our senses, but modern theory of sound measurement is in disagreement with it. If the intensity is (in watts per square metre, ), the (intensity) level is
where is the threshold of hearing, and where is the logarithm base 10.
For simplicity, consider just a pure tone (sine wave) of 1000 Hz; then , and the unit dB is also called phon. According to Weber-Fechner, doubling the level should mean doubling the subjective loudness. However, experiments show that to double the subjective loudness, one should multiply the intensity by 10, or equivalently increase the level by 10 dB. It takes 10 violins to sound twice as loud as one violin! (Some sources give a value smaller than 10. The article sone mentions the value 3.16; this discrepancy is due to a misunderstanding - on my part, or on the part of the author of that article; I am not sure.) Therefore, the subjective loudness is better represented by
where . Choosing , the unit of this measure is called " sones".
Accoring to Weber-Fechner, the following should be a doubling sequence in terms of subjective loudness:
intensity | level | subjective loudness |
---|---|---|
5 dB | 0.0884 sones | |
10 dB | 0.125 sones | |
20 dB | 0.25 sones | |
40 dB | 1 sones | |
80 dB | 16 sones | |
160 dB | 4096 sones |
But the experimental results give the following doubling sequence instead:
intensity | level | subjective loudness | examples |
---|---|---|---|
0 dB | 0.0625 sones | limit of hearing | |
10 dB | 0.125 sones | Â | |
20 dB | 0.25 sones | Â | |
30 dB | 0.5 sones | Â | |
40 dB | 1 sones | ppp | |
50 dB | 2 sones | pp | |
60 dB | 4 sones | p | |
70 dB | 8 sones | Â | |
80 dB | 16 sones | f | |
90 dB | 32 sones | ff | |
100 dB | 64 sones | fff | |
110 dB | 128 sones | Â | |
120 dB | 256 sones | limit of pain |
The notations ppp = piano pianissimo, etc., are used in musical scores. Their correspondence to sound levels are approximate only.
-- Niels Ø 13:53, Mar 20, 2005 (UTC)
... in this article there was something about "Pythagoras finding out that every (n+1) tone is the "twelveth root of 2" * (n)tone. that is weird because the 12-tone-western music (that is what this root-thingy revers to i guess) was introduced around 2000 years after Pythagoras died...
Crucial to understanding marginalism. Christofurio
I'm trying to figure out the origin of the bel unit, now most commonly used as a decibel. I've discovered that it was originally derived from Fechner's law. This article describes it as so:
Physicists are sticklers for the dB being only used for 10·log intensity/power ratios (and not 20·log amplitude/voltage/pressure ratios). Since Fechner's law is about "perceived intensity", does it really refer to a ratio of a specific type of unit? — Omegatron 17:29, 6 January 2006 (UTC)
Fechner's interpretation depends on having some unit of sensation intensity. In my view, this gets lost by proceeding directly to an expression of the so-called law in terms of ratios. The implied unit is more difficult to interpret than a unit of a physical quantity. Let be a unit of perceptual intensity. Let be the measure of the posited sensation intensity associated with a stimulus whose physical magnitude is . I'm using non-italicized symbols to represent quantities rather than ratios of quantities (i.e. rather than measurements in some unit). I'm using italicized symbols only for ratios of quantities; i.e. for measurements in which some unit is implicit.
Making the perceptual unit explicit, according to Fechner's "law"
I think your question is whether it is possible to obtain measurements of sensation intensity relative to a fixed unit such as P? If so, I think the answer is far from clear as things currently stand.
There is only stochastic information about sensation intensity, such as the proportion of occasions on which differences between stimuli of different magnitudes are noticed under specified conditions. Thurstone argued that Weber's law and Fechner's law are only equivalent if the so-called discriminal dispersions are constant, which gives a unit (see law of comparative judgment). What this amounts to is that the sensation intensity associated with the so-called JND is the unit (or equivalently some multiple of this intensity is the unit). For one thing, why should we be able to obtain sensory units without controlling conditions when we cannot obtain physical units without using instruments deliberately designed to measure in a particular unit under controlled conditions? In my view it is still very much an open question. smhhms 06:40, 7 January 2006 (UTC)
This page and the page on Munsell's color notation conflict in their description of the perceived increase in luminance. This may be valid because the term used here is 'brightness' while the term used there is 'lightness,' but on the Munsell page, lightness changes with respect to the cube root of the actual intensity, rather than the logarithmic increase mentioned here. It should be noted that a cube root trend appears similar to a log, and that this is apparently used in CIELAB color space to help define the color axis. 74.74.223.195 ( talk) 20:28, 11 July 2008 (UTC)
Also, the page on Visual_magnitude says that it is a misconception that the eye responds on a logarithmic scale, but this page says it does. What's with that? 122.169.103.240 ( talk) —Preceding undated comment was added at 11:19, 23 October 2008 (UTC).
Regarding Color: I'm wondering about what data anyone might have relating color space perception to Weber's law? The article on color theory might have some useful insights and I will do some research, but if any editors are able to address perception of color as it does, or does not, follow the logarithmic scale as with loudness and brightness.
Regarding sound timbre, tone and metrics: How might this be addressed in terms of Weber's law, or related concepts. Timbre perception is complex having to do with harmonic content and so on. The question of signal to noise ratio is also something I'm wondering about, that is, how to relate Weber's law and related concepts to sound quality. With regard to perception of metrical units and rate of units, otherwise known as meter and tempo in music, does Weber's law apply to our perception of these elements?
I may not even be formulating these questions all that well, but, perhaps you have some insights to share which will help my own understanding and moreover help the article expand in a useful direction. Calicocat ( talk) 06:05, 20 July 2008 (UTC)
I'm not sure what this means. It seems inaccurate. It should be (re)considered, although I don't have time to parse it just this minute. 129.81.44.124 ( talk) 15:59, 26 August 2010 (UTC)DGHyman
I would presume that mental number lines have no inherent bias to be left to right, but predominantly take on that direction in cultures which write left to right. Has anyone studied this effect in populations that use the Arabic or Hebrew scripts? 4pq1injbok ( talk) 02:14, 11 October 2012 (UTC)
I'm too lazy to find reputable references which consider the two (Scoville scale and Weber-Fechner law) together, so here's some funny Finding On The Talk Page: the Scoville scale is clearly more concerned with representing magnitude rather than exact (up to the last digit) measure of capsaicin concentration (which is closely connected to spicyness, heat and, in extremes, pain sensations), and it begs for logarithmic units. — Preceding unsigned comment added by 213.227.200.124 ( talk) 01:48, 30 December 2014 (UTC)
The symbols in the equations currently need to be looked up by a non-mathematician. Understanding would be greatly promoted and encouraged if the formulae had their symbols briefly explained in terms of which quantities each symbol represents. For example if "K" represents a constant that is specific to the different human senses, and that can vary according to which sense it represents ... then saying so right after or before the formula in which "K" appears for the first time in the article would be helpful. Having a simple equation, but for which symbols are not locally defined ... interrupts learning. Thanks. Very interesting article and concepts. — Preceding unsigned comment added by 97.125.86.191 ( talk) 18:39, 13 June 2017 (UTC)
From the article: "if the weight of 105 g can (only just) be distinguished from that of 100 g, the JND (or differential threshold) is 5 g. […] this minimum required fractional increase (of 5/100 of the original weight) is referred to as the "Weber fraction""
I'm no expert, but the article on JNDs says that it's the same as the difference limen. Meanwhile, the literature seems to define the Weber fraction as the relative standard deviation of the error, and in a 1975 paper by Getty, I read that "the difference limen is a constant fraction (.68) of the value of the standard deviation". So that seems to mean that JND = Weber fraction * 0.68. In our example, I would therefore expect the Weber fraction to be 5% / 0.68 = 7.35%. Could somebody clarify?
-- Forlornturtle ( talk) 14:53, 30 August 2018 (UTC)
I think that this should be C class. Anyone with me? — Preceding unsigned comment added by Just4science! ( talk • contribs) 10:49, 5 March 2019 (UTC)
The current version of the section on Sound has three contradictory statements:
Anyone want to clear this up? Clean Copy talk 11:25, 28 March 2020 (UTC)
The lead now says:
(The emphasis is mine.) Clearly, you cannot infer Fechner's law from Weber's - you can ... extend? extrapolate? be inspired by? I'm not sure what's a good word here - but inference isn't, I think.-- Nø ( talk) 14:00, 19 March 2021 (UTC)