>As I don't have my books around here in Dessau, I can't give the exact
>explanation of the Weber-Fechner law. It says that to measure the
>physiologically perceived difference between certain light or sound
>impressions,
>you cannot compare just the amount of lux or db but have to use their
>logarithms.
The deciBell or dB is already expressed in a logarithm scale. This scale is
named for the American inventor Alexander Graham Bell.
dB = 10log(Ep/Eo)
Where Ep is the sound energy exprerienced and Eo is a standardized reference
energy level determined by experiment and the log is a base 10 common log.
Some scales use a multiplier of 20 rather than 10.
The Weber-Flechner law states that perception is proportional to the
logarithm of the impressed energy (*). For example, the ear's mechanical
system responds to the actual energy of the sound. The brain's perception
system responds to the logarithm of the sound energy. This includes pain
perception responses. Logs increase in value very, very slowly so, as an
example, rock musicians will happily play music so loud that it will destroy
their hearing and rock music fans will happily listen to music just as loud.
Photo emulsions respond to the impressed light energy and make "opaqueness,"
Visual perception responds (is proportional) to the log of the "opaqueness."
The exact nature and the values (numerical and aesthetic) of the constants of
proportionality are the subjects of much debate in many more fields than
photography. Some of the debate is scientific and some of it is not. Some of
both kinds of debate are valuable and some are not. You pay your money and
you hope the referees are competent.
The Weber-Flechner law should not be judged the same way as the laws of
Newtonian mechanics and should not be expected to be as precise or accurate,
but it does explain many things very well indeed.
Eugene Robkin
erobkin@uwcmail.uwc.edu
(*) A better statement would be that perception is a linear function of the
log of the impressed energy. This would allow for threshold phenomena which
is what the Eo part of the Ep/Eo is for. Howeve, the above covers the
ground well enough.