Re: [LAD] twice as loud

On Sat, 2010-07-24 at 22:31 +0200, fons@email-addr-hidden wrote:
> On Sat, Jul 24, 2010 at 02:58:36PM +0200, lieven moors wrote:
>
> > On 07/23/2010 10:23 PM, fons@email-addr-hidden wrote:
> > > On Fri, Jul 23, 2010 at 06:42:11PM +0200, lieven moors wrote:
> > >
> > >
> > >> On 07/23/2010 06:29 PM, fons@email-addr-hidden 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,
>

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?

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Received on Sun Jul 25 00:15:03 2010