I personally do believe that there is something fundamentally different about perfect pitch perception, and think of it more like discussions around aphantasia or maybe synesthesia. I followed along with this guy's research years ago on his quest to understand and obtain perfect pitch [0] and was pretty obsessed myself. I had a number of friends with perfect pitch and would do random experiments and quiz them ("ooh, you're drunk, can you tell what note this is?" etc).
From that link:
> For the same reason, absolute listeners do not perceive pitch "height". They do not perceive pitches as "higher" or "lower" or physically "next to" each other. As musicians, of course, absolute listeners learn that, metaphorically, pitches are "higher" and "lower" than each other, because they can see these relationships on a page of sheet music. They also learn that, theoretically, "distance" between notes exists, because you can count the semitones that separate them, and you can see the "distance" between keys on an instrument. But, to an absolute listener, neither "height" nor "distance" has any direct perceptual reality.
> For example, when a non-absolute listener hears a guitar slide, we literally hear something moving down. But an absolute listener's experience is nearer to the color-changing rectangle above. They hear a series of discrete pitches, changing—not moving—from one to another. Although they know the sound has "descended" from their knowledge of the musical scale, the sound does not give them a literal experience of downward movement as it does to non-absolute listeners.
The link has a gif of a box moving through the color spectrum which helps understand the point.
From that link:
> For the same reason, absolute listeners do not perceive pitch "height". They do not perceive pitches as "higher" or "lower" or physically "next to" each other. As musicians, of course, absolute listeners learn that, metaphorically, pitches are "higher" and "lower" than each other, because they can see these relationships on a page of sheet music. They also learn that, theoretically, "distance" between notes exists, because you can count the semitones that separate them, and you can see the "distance" between keys on an instrument. But, to an absolute listener, neither "height" nor "distance" has any direct perceptual reality.
> For example, when a non-absolute listener hears a guitar slide, we literally hear something moving down. But an absolute listener's experience is nearer to the color-changing rectangle above. They hear a series of discrete pitches, changing—not moving—from one to another. Although they know the sound has "descended" from their knowledge of the musical scale, the sound does not give them a literal experience of downward movement as it does to non-absolute listeners.
The link has a gif of a box moving through the color spectrum which helps understand the point.
[0] http://www.aruffo.com/eartraining/