23 Jul
2010
23 Jul
'10
1:28 p.m.
On 07/22/2010 03:36 PM, Fons Adriaensen-2 wrote:
As I said above, I think it
plays a major role, in our ability to
measure things
Could you elaborate on this a little bit more?
Greetings,
Lieven
On Thu, Jul 22, 2010 at 09:31:09PM +0200, lieven moors
wrote:
Yes,
but we can never agree that A is twice B, unless we agree on
how precise the measurement could/should be.
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.
I don't think this is easy. Imagine a ruler lying on your desk, and
try to imagine the point where the ruler would become twice as
long. I think you will find that your brain is continually adjusting
that distance, and that it requires significant effort.
It also occurs to me, that by doing this, I am actually
determining the smallest observable difference, and that this
distance is proportionate to the length of the ruler.
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.
It could work if we would agree on it. But apparently our brains
have made up their own mind :-)
That's why I propose to reconsider how we look at measurement.
The process of measuring might not be as simple as we think.
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 ?
When we see the length of something, we don't see the stick either.
The only thing we see is that one thing is longer than the other.
The stick is just a short thing, which we can compare to all other
things. But even when you agree on such a reference, you still have to
go through the process of measuring.
The problem of 'twice as loud', shows us that we can measure things
even without an agreed-on unit. Somehow we are able to dynamically
create that unit when we need it.
This is how it could work for example:
we have a range, and something within that range: | x
|
we try to cut the range in halves and keep the part with x: | x |
The precision of cutting in halves is based on the smallest
observable difference between the two halves, and is
proportionate to the size of the range. (yes I know this is
a problematic statement, I have to think more about this)
We do the same thing
again: | x |
Now, if we would halve the range again, we would be unable
to distinguish x from that point, and we have some kind of
measuring
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 !
Ciao,
--
FA
There are three of them, and Alleline.
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23 Jul
23 Jul
6:29 p.m.
New subject: twice as loud
On Fri, Jul 23, 2010 at 01:28:37PM +0200, lieven moors wrote:
I don't think this is easy. Imagine a ruler lying
on your desk, and
try to imagine the point where the ruler would become twice as
long. I think you will find that your brain is continually adjusting
that distance, and that it requires significant effort.
True, but it will be somewhere between say 1.8 and 2.2.
Not 1.5, not 3. The problem here is just one of precision.
For sound this is quite different. Except by imagining or
remembering '2 of the same' there seems no way to even just
define what 'twice as loud' is supposed to mean.
This is how it could work for example:
...
Now, if we would halve the range again, we would be unable
to distinguish x from that point, and we have some kind of
measuring
stick: |
| | | |
Transporting this to the audio domain, given two similar
sounds A and B with a B having a higher level than A, you
could adjust a third one X so it appears to be 'halfway'
between A and B. If you do this with A much smaller than
B, would you expect X to be close to 'half a loud as B' ?
Ciao,
--
FA
There are three of them, and Alleline.
6:36 p.m.
New subject: twice as loud
On 07/23/10 18:29, fons(a)kokkinizita.net wrote:
For sound this is quite different. Except by imagining
or
remembering '2 of the same' there seems no way to even just
define what 'twice as loud' is supposed to mean.
Brightness and color temperature would be a better analogy than
distance, as the human perception continuosly adapts to changes.
Flo
--
Machines can do the work, so people have time to think.
public key DA43FEF4 x-hkp://wwwkeys.eu.pgp.net
6:42 p.m.
New subject: twice as loud
On 07/23/2010 06:29 PM, fons(a)kokkinizita.net wrote:
On Fri, Jul 23, 2010 at 01:28:37PM +0200, lieven moors
wrote:
If A would be very close to silence, yes.
I don't think this is easy. Imagine a ruler
lying on your desk, and
try to imagine the point where the ruler would become twice as
long. I think you will find that your brain is continually adjusting
that distance, and that it requires significant effort.
True, but it will be somewhere between say 1.8 and 2.2.
Not 1.5, not 3. The problem here is just one of precision.
For sound this is quite different. Except by imagining or
remembering '2 of the same' there seems no way to even just
define what 'twice as loud' is supposed to mean.
This is how it could work for example:
...
Now, if we would halve the range again, we would be unable
to distinguish x from that point, and we have some kind of
measuring
stick: |
| | | |
Transporting this to the audio domain, given two similar
sounds A and B with a B having a higher level than A, you
could adjust a third one X so it appears to be 'halfway'
between A and B. If you do this with A much smaller than
B, would you expect X to be close to 'half a loud as B' ?
10:23 p.m.
New subject: twice as loud
On Fri, Jul 23, 2010 at 06:42:11PM +0200, lieven moors wrote:
On 07/23/2010 06:29 PM, fons(a)kokkinizita.net wrote:
I'd be *very* surprised if that would turn out to be true.
I bet that if B is A + 40 dB, X would turn out to be
close to A + 20 dB. And if B is A + 60 dB, X will be
close to A + 30 dB. In both cases A is very small
conpared to B (at most 1/10000 in power).
Ciao,
--
FA
There are three of them, and Alleline.
Transporting this to the audio domain, given two
similar
sounds A and B with a B having a higher level than A, you
could adjust a third one X so it appears to be 'halfway'
between A and B. If you do this with A much smaller than
B, would you expect X to be close to 'half a loud as B' ?
If A would be very close to silence, yes.
24 Jul
24 Jul
2:58 p.m.
New subject: twice as loud
On 07/23/2010 10:23 PM, fons(a)kokkinizita.net wrote:
On Fri, Jul 23, 2010 at 06:42:11PM +0200, lieven moors
wrote:
Let's put it differently. If you only had sound B, and you
were asked to position a similar sound X halfway between
total silence, and the level of sound B, wouldn't that be the
same as asking that sound X has half the loudness of sound
B, or as asking that sound B has double the loudness of
sound X?
Greetings,
Lieven
On 07/23/2010 06:29 PM, fons(a)kokkinizita.net
wrote:
I'd be *very* surprised if that would turn out to be true.
I bet that if B is A + 40 dB, X would turn out to be
close to A + 20 dB. And if B is A + 60 dB, X will be
close to A + 30 dB. In both cases A is very small
conpared to B (at most 1/10000 in power).
Ciao,
Transporting this to the audio domain, given two
similar
sounds A and B with a B having a higher level than A, you
could adjust a third one X so it appears to be 'halfway'
between A and B. If you do this with A much smaller than
B, would you expect X to be close to 'half a loud as B' ?
If A would be very close to silence, yes.
10:31 p.m.
New subject: twice as loud
On Sat, Jul 24, 2010 at 02:58:36PM +0200, lieven moors wrote:
On 07/23/2010 10:23 PM, fons(a)kokkinizita.net wrote:
So with e.g. A = B - 60 dB we could end up with X at
B - 30 dB (two steps of 30dB which are supposed to be
near equal subjectively), while with A = silence we would
have X somewhere between -6 and -10 dB relative to B
(these are the extremes of common values for 'twice as
loud'). How low can A be before this inconsistency turns
up ? Or more important: how reliable is such an idea of
'halfway' ?
The simple fact is that on a logarithmic scale the whole
concept of 'half' or 'double' is **meaningless**. That is
because such a scale depends on an arbitrary reference
value, and changing that value shifts the whole scale by
a constant amount without changing the underlying reality.
Two levels that are e.g. 10 and 20 on one scale (hence the
second is 'double' the first) could be as well be 80 and 90
just by changing the reference value for the log scale.
Of course half/double still makes sense in the original
domain. But if the perceptual scale is logarithmic, they
are perceived as a constant difference, not as a ratio.
Ciao,
--
FA
There are three of them, and Alleline.
On Fri, Jul 23, 2010 at 06:42:11PM +0200, lieven
moors wrote:
Let's put it differently. If you only had sound B, and you
were asked to position a similar sound X halfway between
total silence, and the level of sound B, wouldn't that be the
same as asking that sound X has half the loudness of sound
B, or as asking that sound B has double the loudness of
sound X? On 07/23/2010 06:29 PM, fons(a)kokkinizita.net
wrote:
I'd be *very* surprised if that would turn out to be true.
I bet that if B is A + 40 dB, X would turn out to be
close to A + 20 dB. And if B is A + 60 dB, X will be
close to A + 30 dB. In both cases A is very small
conpared to B (at most 1/10000 in power).
Ciao,
Transporting this to the audio domain, given two
similar
sounds A and B with a B having a higher level than A, you
could adjust a third one X so it appears to be 'halfway'
between A and B. If you do this with A much smaller than
B, would you expect X to be close to 'half a loud as B' ?
If A would be very close to silence, yes.
10:42 p.m.
New subject: twice as loud
On Sat, 2010-07-24 at 22:31 +0200, fons(a)kokkinizita.net wrote:
On Sat, Jul 24, 2010 at 02:58:36PM +0200, lieven moors
wrote:
I had this discussion for the Richter scale. I don't have knowledge of
math. Isn't it possible to give a value, e.g. for physics (electrics and
optics) there's a value of square root 2. Isn't there such a similar
simple value for log scales?
On 07/23/2010 10:23 PM, fons(a)kokkinizita.net
wrote:
So with e.g. A = B - 60 dB we could end up with X at
B - 30 dB (two steps of 30dB which are supposed to be
near equal subjectively), while with A = silence we would
have X somewhere between -6 and -10 dB relative to B
(these are the extremes of common values for 'twice as
loud'). How low can A be before this inconsistency turns
up ? Or more important: how reliable is such an idea of
'halfway' ?
The simple fact is that on a logarithmic scale the whole
concept of 'half' or 'double' is **meaningless**. That is
because such a scale depends on an arbitrary reference
value, and changing that value shifts the whole scale by
a constant amount without changing the underlying reality.
Two levels that are e.g. 10 and 20 on one scale (hence the
second is 'double' the first) could be as well be 80 and 90
just by changing the reference value for the log scale.
Of course half/double still makes sense in the original
domain. But if the perceptual scale is logarithmic, they
are perceived as a constant difference, not as a ratio.
Ciao,
On Fri, Jul 23, 2010 at 06:42:11PM +0200, lieven
moors wrote:
Let's put it differently. If you only had sound B, and you
were asked to position a similar sound X halfway between
total silence, and the level of sound B, wouldn't that be the
same as asking that sound X has half the loudness of sound
B, or as asking that sound B has double the loudness of
sound X? On 07/23/2010 06:29 PM, fons(a)kokkinizita.net
wrote:
> Transporting this to the audio domain, given two similar
> sounds A and B with a B having a higher level than A, you
> could adjust a third one X so it appears to be 'halfway'
> between A and B. If you do this with A much smaller than
> B, would you expect X to be close to 'half a loud as B' ?
>
>
>
If A would be very close to silence, yes.
I'd be *very* surprised if that would turn out to be true.
I bet that if B is A + 40 dB, X would turn out to be
close to A + 20 dB. And if B is A + 60 dB, X will be
close to A + 30 dB. In both cases A is very small
conpared to B (at most 1/10000 in power).
Ciao,
25 Jul
25 Jul
1:24 a.m.
New subject: twice as loud
On 07/24/2010 10:31 PM, fons(a)kokkinizita.net wrote:
On Sat, Jul 24, 2010 at 02:58:36PM +0200, lieven moors
wrote:
That is assuming that our experience of loudness
corresponds to the continuous logarithmic scale
with which we measure SPL's. I suspect that this
is not the case. Our ears have minimum and
maximum SPL values they can observe/tolerate,
and I think that this range is the 'unconscious'
reference for measurement of loudness.
So we might have to adapt the 'steepness' of the
logarithmic curve to that range.
On 07/23/2010 10:23 PM, fons(a)kokkinizita.net
wrote:
So with e.g. A = B - 60 dB we could end up with X at
B - 30 dB (two steps of 30dB which are supposed to be
near equal subjectively), On Fri, Jul 23, 2010 at 06:42:11PM +0200, lieven
moors wrote:
Let's put it differently. If you only had sound B, and you
were asked to position a similar sound X halfway between
total silence, and the level of sound B, wouldn't that be the
same as asking that sound X has half the loudness of sound
B, or as asking that sound B has double the loudness of
sound X?
On 07/23/2010 06:29 PM, fons(a)kokkinizita.net
wrote:
> Transporting this to the audio domain, given two similar
> sounds A and B with a B having a higher level than A, you
> could adjust a third one X so it appears to be 'halfway'
> between A and B. If you do this with A much smaller than
> B, would you expect X to be close to 'half a loud as B' ?
>
>
>
>
If A would be very close to silence, yes.
I'd be *very* surprised if that would turn out to be true.
I bet that if B is A + 40 dB, X would turn out to be
close to A + 20 dB. And if B is A + 60 dB, X will be
close to A + 30 dB. In both cases A is very small
conpared to B (at most 1/10000 in power).
Ciao,
while with A = silence we would
have X somewhere between -6 and -10 dB relative to B
(these are the extremes of common values for 'twice as
loud'). How low can A be before this inconsistency turns
up ? Or more important: how reliable is such an idea of
'halfway' ?
I would say it's the only reliable thing in this context,
because it's the very thing we want to measure.
The simple fact is that on a logarithmic scale the
whole
concept of 'half' or 'double' is **meaningless**. That is
because such a scale depends on an arbitrary reference
value, and changing that value shifts the whole scale by
a constant amount without changing the underlying reality.
Two levels that are e.g. 10 and 20 on one scale (hence the
second is 'double' the first) could be as well be 80 and 90
just by changing the reference value for the log scale.
Yes, but changing the base does change the underlying
reality.
Of course half/double still makes sense in the
original
domain. But if the perceptual scale is logarithmic, they
are perceived as a constant difference, not as a ratio.
I think we are aware of the original domain, in de sense
we are approaching the limits of our hearing. What
we interpret as half/double as loud depends on the
position within that range.
regards,
Lieven
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