22 Jul
2010
22 Jul
'10
9:14 p.m.
On 07/21/2010 07:24 PM, Fons Adriaensen-2 wrote:
On Thu, Jul 22, 2010 at 01:05:01AM +0200, Philipp
Überbacher wrote:
Hi Fons, I'm a fool to even try to answer this question.
But I couldn't resist...
Let's suppose we have two sounds A and B,
and sound B has been measured as being twice as loud as A,
by somebody. In order to be able to say that, that person needs
some kind of reference measurement unit, the equivalent of a
measurement stick. That unit has to satisfy two requirements.
It has to be big enough, so that people can agree some difference
is being measured, and it has to be small enough, so that a multiples
of that unit fit into a realistic range. There is a requirement of maximum
precision (the smallest value we can measure), and a requirement of
minimum precision. The question is, what kind of measurement stick
is being used by that person.
First of all, we can assume that the length of that stick will be depend
on the range of possible input values that we observe, and that we want
to measure. If we want to measure the size of a road, we will probably
use kilometers, instead of meters. In the same way, when our ears want
to measure the amplitude of a sound, our ears will use smaller or bigger
units, depending on the ranges observed. What are the ranges we observe?
Let's assume that humans are perfect, and observe everything that we
can observe with SPL meters. We could do a statistical investigation
on a number of people, and make charts of everything they hear.
In these charts we would see what frequencies they are exposed to,
and what the minimum and maximum SPL's are for that frequencies.
After more analyses, we would have one chart that could be
representative for most people.
I think the word loudness is a problem here.
Afaik it usually refers to
how it is perceived, and twice the amplitude doesn't mean twice the
perceived loudness. It may mean twice the sound pressure level, energy,
or intensity (if we ignore analogue anomalies, as you wrote in some
other
answer).
Subjective loudness is a very complex thing, depending on the
spectrum, duration, and other aspects of the sound, and also
on circumstances not related to the sound itself.
For mid frequencies and a duraion of one second, the average
subjective impression of 'twice as loud' seems to correspond
to an SPL difference of around +10 dB.
I often wondered what criterion we use to determine which
objective SPL difference sounds as 'twice as loud'. We don't
have any conscious numerical value (there may be unconscious
ones such as the amount of auditory nerve pulses, or the amount
of neural activity), so what it this impression based on ?
The only thing I could imagine is some link with the subjective
impression of a variable number of identical sources. For example
two people talking could be considered to be 'twice as loud' as
one. But that is not the case, the results don't fit at all (it
would mean 3 dB instead of 10).
From that chart we could get an estimate of the size of
the measurement
unit. Frequencies with with bigger SPL variations would be measured
with bigger units, and visa versa. And from this we could deduce what
the minimum precision is for a certain frequency, when we say it is twice
as loud. To satisfy the requirement of maximum precision, we should
take into account the smallest observable differences for every frequency
in the spectrum.
now you can kill me :-)
Greetings,
Lieven