Quotes from http://physicsworld.com/cws/article/news/2013/jan/31/human-hearing-is-highly-nonlinear , originally published in Phys. Rev. Lett. 110, 044301 – Published 23 January 2013.
"The information available from Fourier analysis is bound by an uncertainty relation called the Gabor limit. This says that you cannot know the timing of a sound and its frequency – or pitch – beyond a certain degree of accuracy. The more accurate the measurement of the timing of a sound, the less accurate the measurement of its pitch and vice versa."
"Oppenheim and Magnasco discovered that the accuracy with which the volunteers determined pitch and timing simultaneously was usually much better, on average, than the Gabor limit. In one case, subjects beat the Gabor limit for the product of frequency and time uncertainty by a factor of 50, clearly implying their brains were using a nonlinear algorithm."
In other words, conventional analysis of non-linear distortions in an audio system tell you absolutely nothing about how it sounds, because human hearing beats measurement by a healthy margin.