22 Jul
2010
22 Jul
'10
10:51 p.m.
Excerpts from fons's message of 2010-07-22 22:36:58 +0200:
On Thu, Jul 22, 2010 at 09:31:09PM +0200, lieven moors
wrote:
We may be comparing the wrong thing when we compare with the size of
objects to loudness.
It's relatively easy to say that the interval between sound B and C
is twice as long as the interval between A and B (given the
interval and the length of the sound is in a certain range). This is
probably closer to the object size comparison.
I wonder how well we can judge something like twice the
brightness.
--
Regards,
Philipp
--
"Wir stehen selbst enttäuscht und sehn betroffen / Den Vorhang zu und alle Fragen
offen." Bertolt Brecht, Der gute Mensch von Sezuan
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.
Not really. If A is 'twice' B, either A or B can act as the reference.
I'm pretty sure that if you'd do the experiment to find out when
people think that an object B is twice as big as another object A
(without introducing optical illusions), you'd find that it's quite
close to a factor of 2. This is because we can easily imagine two
A's side by side, which would be 'twice as big' as one A.
Can we do something similar with 'loudness' ? As I wrote, the
only option I see is to consider two equal sources to be 'twice
as loud' as one of them, but that doesn't work out.
Given this, what you write does make sense - there must be some
'stick' rather than a real comparison of A to B. But what is it
based on ? If most people do agree on some value for 'twice as
loud', even with a large variation, there must be some physical
ground for this. But what is it ? And a related question: iff
there is some 'unit' even a variable one depending on frequency
etc., why can't we imagine that unit ? Why don't we 'see' the
stick ?
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.
This is basically what has been done more than 50 years ago, with
the known results: the objective ratio corresponding to 'twice as
loud' depends on frequency, absolute level, etc.
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.
'Smallest observable difference' has been measured as well. It should
relate in some way to 'twice as loud', but I haven't verified this.
OTOH, knowing the smallest observable difference does not help to
define what 'twice as loud' is supposed to be.
Another poster mentioned that he found it quite difficult to work
out what 'twice as loud' means for him - and I do believe that is
touching on the real problem: if you start *thinking* about it
rather than just following your 'gut feeling', how sure can you
still be of your impression of 'twice as loud' ? How stable is it
in the face of doubt ?
Keep on thinking !