Re: [LAD] twice as loud

On Mon, Jul 26, 2010 at 11:30 PM, Jens M Andreasen <jens.andreasen(a)comhem.se> wrote: 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