It turns out that the listening task associated with hearing distortion is not that simple.
Instead of trying to detect an audible sound that is not in the recording, your task may be to detect a minor level shift in a sound that is already in the recording.
Lets say that the recording contains a organ pedal note whose fundamental frequency is say 40 Hz. We know that:
(1) The recorded real world organ note is composed of both the fundamental and a number of harmonics
(2) The fundamental is far weaker than some of its harmonics especially the second and third harmonics.
The recording of the organ pedal note might have 20% fundamental, 60% second harmonic, and 20% remaining harmonics.
If there is 10% second order distortion at the fundamental frequency or 40 Hz, then the second harmonic created by the distortion is 2% or 10% of 20%. Add that to the second harmonic in the recording, and we are now trying to detect the difference between roughly 60% second harmonic and 62% second harmonic. That is a mere 0.3 dB difference. At 80 Hz, a 0.3 dB dB difference is difficult or impossible to hear because the ear just isn't so sensitive to differences at low frequencies.