Correct presentation is an interesting concept, and I can’t resist the temptation to make analogies to photography. If we’re going to print a photograph of a sunny beach scene, and we want it to look natural and realistic, are we just going to linearly map the light that hit the sensor on to the paper? That’s impossible without compressing everything, because the photographic paper has drastically less dynamic range capability than the real beach scene. A linear compression looks bad, so we use curves. The film in the camera develops with a curve, and the print film is also developed with a curve. If you shoot digital, curves are still used. There’s a mid-band of shades that actually track as steeply as they should, but the deeper blacks and brighter brights are compressed, so the curve typically has an "S" shape to it, flatter on both ends. This gives a "correct" presentation because of how our eye adjusts for contrast. It turns out we really don’t see that much contrast all at once. Our eyes are constantly adjusting in bright daylight, and even still we end up reaching for sunglasses because it’s more intensity than our eyes can comfortably handle. So the S curve makes the printed beach scene look realistic, with good, natural contrast. It doesn’t look compressed, even though it is. This works because our eyes automatically adjust their contrast sensitivity within limits.
With hifi it’s a little different, but there are similar limitations that have to be adjusted for to make things perceptually "correct." You could call the "S" curve in a photo distortion. Or you could call it a correction for perceptual purposes. If you don’t use the S curve in photos and just linearly compress across the entire range, the photos typically end up looking rather flat and lifeless, although detail in shadows and highlights can be excellent - at the expense of noise becoming very visible in shadows. Also if there’s any clipping in the highlights it’ll really show up and look bad. This sounds somewhat similar to the complaints people make about solid state amps. Maybe tube amps employ something similar to an S curve to make up for limits to how only two speakers can interact with our ears when trying to convey a realistic sound space, with proper tone, and also to compensate for limits inherent in recording techniques.
