[LAD] twice as loud

[Charles Henry]

On Mon, Jul 26, 2010 at 11:30 PM, Jens M Andreasen
<jens.andreasen at comhem.se> wrote:
>
> On Sun, 2010-07-25 at 14:24 +0200, Philipp Überbacher wrote:
>
>> It would be strange but funny if an estimate of sound A just about
>> masking sound B would correspond to 'twice as loud'.
>
> Masking appears somewhere in the 30 to 40dB range - which is way beyond
> "twice as loud".

Right.  The two are not related and they're in wholly different orders
of magnitude.  I'd be reluctant to put a number on it, though...

Because psychoacoustics just hasn't been defined in a way to make hard
numbers stick.  The tendency in psychoacoustic experimental design is
to use discrete conditions (which gives better experimental power) in
order to show that an effect exists.  But this way, any given
experiment can't produce results that cover the whole space.
Generalization and extrapolation are limited.

A psychoacoustic relationship is a map between a set of acoustically
presented signals and a set of sensory experiences.  Loudness, pitch,
timbre are the three terms used to describe sounds in psychoacoustics,
which might lend one to think they are orthogonal or separable.  The
problem of describing the non-linear psychoacoustic map is that
relations don't apply the same way to different neighborhoods in the
spaces involved.  With appropriate techniques and *lots* of data, we
could come up with models that describe the curvature of those maps
locally at each point in the space.  What we think of as loudness is
just one way of assigning a scale to a path in the space which
connects sounds of similar pitch and timbre.

Masking is an interesting effect to look at topologically.  Consider
that points in the set of sensory experiences may be more or less
distant from each other based on their degree of similarity.

Although acoustically, we can have a metric that separates all signals
from each other, two sounds (psychological) may be in-distinguishable
from each other.  The topology on this space is determined by a
pseudo-metric in which d(p1,p2)=0 => p1 and p2 are indistinguishable
from each other.  This generates a coarse topology with smallest open
sets consisting of sounds that are indistinguishable from each other.

Describing the masking effect means finding the inverse image of the
psychoacoustic map where a collection of distinct acoustic signals map
onto points in the same open set.

Suppose we have two signals s1 and s2, and we construct a third sound
s3=s1+a*s2.  For some range of values of a, s3 can be made
indistinguishable from s1.  This describes just *one* local dimension
along which s1 masks s2, as long as a*s2 also corresponds to a
non-zero point in the psychoacoustic image.

Well, I just wanted to get a few ideas out there to have some fun with
this discussion :)  I'm a late-comer since I had some other
obligations to attend to last week.

Best,
Chuck