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On 07/22/2010 03:36 PM, Fons Adriaensen-2 wrote:
<blockquote
cite="mid:tag:old.nabble.com,2006:post-29241238@localhost.localdomain"
type="cite"><base
href="http://old.nabble.com/Re%3A-twice-as-loud-tp29240719p29241238.html">
<title>Re: twice as loud</title>
<base href="http://old.nabble.com/linux-audio-dev-f13235.xml"> On
Thu, Jul 22, 2010 at 09:31:09PM +0200, lieven moors wrote:
<br>
<br>
> Hi Fons, I'm a fool to even try to answer this question.
<br>
> But I couldn't resist...
<br>
<br>
:-)
<br>
<div class="shrinkable-quote"><br>
> Let's suppose we have two sounds A and B,
<br>
> and sound B has been measured as being twice as loud as A,
<br>
> by somebody. In order to be able to say that, that person needs
<br>
> some kind of reference measurement unit, the equivalent of a
<br>
> measurement stick. That unit has to satisfy two requirements.
<br>
> It has to be big enough, so that people can agree some difference
<br>
> is being measured, and it has to be small enough, so that a
multiples
<br>
> of that unit fit into a realistic range. There is a requirement of
maximum
<br>
> precision (the smallest value we can measure), and a requirement
of
<br>
> minimum precision. The question is, what kind of measurement stick
<br>
> is being used by that person.
</div>
<br>
Not really. If A is 'twice' B, either A or B can act as the reference.
<br>
</blockquote>
Yes, but we can never agree that A is twice B, unless we agree on<br>
how precise the measurement could/should be. <br>
<br>
<blockquote
cite="mid:tag:old.nabble.com,2006:post-29241238@localhost.localdomain"
type="cite"><br>
I'm pretty sure that if you'd do the experiment to find out when
<br>
people think that an object B is twice as big as another object A
<br>
(without introducing optical illusions), you'd find that it's quite
<br>
close to a factor of 2. This is because we can easily imagine two
<br>
A's side by side, which would be 'twice as big' as one A.</blockquote>
<br>
I don't think this is easy. Imagine a ruler lying on your desk, and<br>
try to imagine the point where the ruler would become twice as<br>
long. I think you will find that your brain is continually adjusting<br>
that distance, and that it requires significant effort.<br>
It also occurs to me, that by doing this, I am actually<br>
determining the smallest observable difference, and that this<br>
distance is proportionate to the length of the ruler.<br>
<br>
<blockquote
cite="mid:tag:old.nabble.com,2006:post-29241238@localhost.localdomain"
type="cite"> <br>
Can we do something similar with 'loudness' ? As I wrote, the <br>
only option I see is to consider two equal sources to be 'twice
<br>
as loud' as one of them, but that doesn't work out.
<br>
</blockquote>
<br>
It could work if we would agree on it. But apparently our brains<br>
have made up their own mind :-)<br>
That's why I propose to reconsider how we look at measurement.<br>
The process of measuring might not be as simple as we think.<br>
<br>
<blockquote
cite="mid:tag:old.nabble.com,2006:post-29241238@localhost.localdomain"
type="cite"><br>
Given this, what you write does make sense - there must be some
<br>
'stick' rather than a real comparison of A to B. But what is it
<br>
based on ? If most people do agree on some value for 'twice as
<br>
loud', even with a large variation, there must be some physical
<br>
ground for this. But what is it ? And a related question: iff <br>
there is some 'unit' even a variable one depending on frequency
<br>
etc., why can't we imagine that unit ? Why don't we 'see' the
<br>
stick ?
<br>
</blockquote>
<br>
When we see the length of something, we don't see the stick either.<br>
The only thing we see is that one thing is longer than the other.<br>
The stick is just a short thing, which we can compare to all other<br>
things. But even when you agree on such a reference, you still have to<br>
go through the process of measuring.<br>
The problem of 'twice as loud', shows us that we can measure things<br>
even without an agreed-on unit. Somehow we are able to dynamically<br>
create that unit when we need it.<br>
<br>
This is how it could work for example:<br>
<br>
we have a range, and something within that range: | x
|<br>
<br>
we try to cut the range in halves and keep the part with x: | x
|<br>
The precision of cutting in halves is based on the smallest <br>
observable difference between the two halves, and is<br>
proportionate to the size of the range. (yes I know this is <br>
a problematic statement, I have to think more about this)<br>
We do the same thing
again: | x |<br>
Now, if we would halve the range again, we would be unable<br>
to distinguish x from that point, and we have some kind of <br>
measuring
stick: |
| | | |<br>
<br>
<br>
<blockquote
cite="mid:tag:old.nabble.com,2006:post-29241238@localhost.localdomain"
type="cite">
<div class="shrinkable-quote">> First of all, we can assume that
the length of that stick will be depend
<br>
> on the range of possible input values that we observe, and that we
want
<br>
> to measure. If we want to measure the size of a road, we will
probably
<br>
> use kilometers, instead of meters. In the same way, when our ears
want
<br>
> to measure the amplitude of a sound, our ears will use smaller or
bigger
<br>
> units, depending on the ranges observed. What are the ranges we
observe?
<br>
> Let's assume that humans are perfect, and observe everything that
we
<br>
> can observe with SPL meters. We could do a statistical
investigation
<br>
> on a number of people, and make charts of everything they hear.
<br>
> In these charts we would see what frequencies they are exposed to,
<br>
> and what the minimum and maximum SPL's are for that frequencies.
<br>
> After more analyses, we would have one chart that could be
<br>
> representative for most people.
</div>
<br>
This is basically what has been done more than 50 years ago, with
<br>
the known results: the objective ratio corresponding to 'twice as
<br>
loud' depends on frequency, absolute level, etc.
<br>
<br>
> From that chart we could get an estimate of the size of the
measurement
<br>
> unit. Frequencies with with bigger SPL variations would be
measured
<br>
> with bigger units, and visa versa. And from this we could deduce
what
<br>
> the minimum precision is for a certain frequency, when we say it
is twice
<br>
> as loud. To satisfy the requirement of maximum precision, we
should
<br>
> take into account the smallest observable differences for every
frequency
<br>
> in the spectrum.
<br>
<br>
'Smallest observable difference' has been measured as well. It should <br>
relate in some way to 'twice as loud', but I haven't verified this.
<br>
OTOH, knowing the smallest observable difference does not help to <br>
define what 'twice as loud' is supposed to be.</blockquote>
As I said above, I think it plays a major role, in our ability to
measure things<br>
Could you elaborate on this a little bit more?<br>
<br>
Greetings,<br>
<br>
Lieven<br>
<br>
<blockquote
cite="mid:tag:old.nabble.com,2006:post-29241238@localhost.localdomain"
type="cite"><br>
Another poster mentioned that he found it quite difficult to work
<br>
out what 'twice as loud' means for him - and I do believe that is
<br>
touching on the real problem: if you start *thinking* about it <br>
rather than just following your 'gut feeling', how sure can you
<br>
still be of your impression of 'twice as loud' ? How stable is it
<br>
in the face of doubt ?
<br>
<br>
Keep on thinking !
<br>
<br>
Ciao,
<br>
<br>
-- <br>
FA
<br>
<br>
There are three of them, and Alleline.
<br>
<br>
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