[LAD] twice as loud

[fons at kokkinizita.net]

On Sat, Jul 24, 2010 at 02:58:36PM +0200, lieven moors wrote:

> On 07/23/2010 10:23 PM, fons at kokkinizita.net wrote:
> > On Fri, Jul 23, 2010 at 06:42:11PM +0200, lieven moors wrote:
> >
> >   
> >> On 07/23/2010 06:29 PM, fons at 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,
> >
> >   
> 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?

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.