Modeling the human perception of noise Add together some sinusoids with irrational or "nearly" irrational frequency ratios, and you get something pseudoperiodic. If there aren't too many, you can hear that it has only pitched components, even if you can't isolate them by ear.

If there are enough of them playing together, it will sound like steady noise.

The same goes with random transients. If they're separated in time well enough, you can hear them as distinct sounds. If they become very dense it sounds like steady noise.

Is there a model that predicts when a long-playing signal sounds like steady noise, and when it sounds merely rough or dissonant?
As with any perceptual model, the answer is not exactly cut and dry.  In my research, I’ve found that many of the hearing models I’ve encountered are based on band pass filter banks.  These banks are numerous and tightly spaced.  The more adjacent banks that are stimulated, the ‘noiseyer’ the signal would sound.

There are examples of inharmonic signal analysis that take noise into account, such as: https://pdfs.semanticscholar.org/b5bf/98425051f47b0685e75da986ee166e41d6ec.pdf.  I’ve never tried to implement such a structure, but as I understand it, you analyze the peaks in the output of a frequency transform to create a ‘deterministic’ signal.  You then subtract the deterministic signal from the original to get the ‘residual’ noise.  You would then perform further analysis on the residual.  I assume that this isn’t exactly what you were looking for in terms of a model, but I figured it may be informative.