Thus spake Jim Lesurf:
Snipped
I've now found the HFN letter by Baxadall [1] I had in mind when I
made some earlier comments. This used some microphones and a speaker
to add controlled amounts of distortion to the sound of a 'live'
piano. To sum up the results, he found that listeners could hear
distortion at levels around 2 percent with fair reliability, but by
the time it was down to 0.5 percent they showed no signs of being
able to hear it.

Yet if the same distortion was recorded and replayed without the piano
playing, it was easily audible.

At 0.5%? I'm sorry but I don't understand why Baxendall went the route of
adding distortion to a live recording. Surely the temporal relationship
between the live fundamental tones & the added harmonics would be smeared,
let alone the phase relationship (& vary with listening position) unless it
was just to refute a dodgy theory.

His test was for the 'Bob Stuart Hypothesis' that added distortions
might have an effect when accompanied by the sound they altered even
if the distortion in isolation was inaudible. This was a
counter-hypothesis to PJW using nulling to argue that when you nulled
amp distortion and got no audible result, then the distortion must
have no audible effect.

I don't understand the postulates behind the Bob Stuart Hypothesis.

Thus Baxandall's test supported PJW and refuted Bob Stuart's
hypothesis.

As I would expect.

The result was in line with some similar tests using 'grunge boxes'
which I have read about where even long-term use showed no signs of
the listeners being able to hear distortion at the same levels as
Baxandall found to show no sign of being audible.

I suspect we are fairly tolerant to harmonics. Piano is particularly good
instrument at revealing frequency modulation artefacts such as wow or
flutter (as it happens.)