None of my speakers or systems distort pitch in any way - they reproduce pitch accurately. They might not reproduce amplitude relations between harmonics totally accurately, but they do not distort pitch.
No, because an error in guitar tunings are reflected in incorrect pitch relationships that are audible without reference to any other sound, because a guitar tuning is not an absolute thing, it is a relation between the strings of the guitar, so you reference the pitch of each string against the pitch of the other strings, not against something you have to retain in your memory. A change in *colour* (in terms of frequency response or distortion) isn't referenced to anything except you recollection, so is harder to detect after a delay.
Pitch is referenced to the fundamental apart from the harmonics. The notes on the music staff reference the fundamental and are oblivious to harmonics. But harmonics are direct mathematical multiples of the fundamental. So this begs the obvious question: in audio, exactly how can harmonic distortion be compartmentalized separately from the fundamental? I doubt the two are separate from each other. If the two are intertwined (how can they not be?), then HD and pitch are interrelated.
Toole knows a few things about this. He posits one of the benefits of improved reverberant field is improved pitch sensitivity. The ear gets a "second look" at the pitch (Geddes says ideally 10-20ms later), thus solidifying the first on-axis impression. IMO this "second look" at the pitch also lowers stress and increases the illusion of live music. Over the past 1.5 years I've had the luxury of turning on-off the reverberant field section of my loudspeaker.(which comprises two separate full range speakers per ch).
Perhaps one could envision the orchestra and chorus of Beethoven's 9th or a huge Wagner piece and imagine all these instruments playing inter related pitches, and imagine that there is more to pitch portrayal than is commonly believed to be the case.
Regarding the two guitars, I asked if time passing would affect one's ability to judge which guitar was more properly tuned vs. the other, or meant to if I did not.