On 07/22/2010 03:36 PM, Fons Adriaensen-2 wrote:

Re: twice as loud On Thu, Jul 22, 2010 at 09:31:09PM +0200, lieven moors 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.

Not really. If A is 'twice' B, either A or B can act as the reference.

Yes, but we can never agree that A is twice B, unless we agree on
how precise the measurement could/should be.

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.

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

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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