Re: [LAD] twice as loud

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:
>
> > 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 !

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
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