[jancsika]

The Barbershop example is orthogonal to what I'm describing. There, the singers are (apparently) choosing to sweeten particular chords to get certain relationships in the partials. That's something you can listen for and hear without having perfect pitch.

What I'm saying is that there seems to be a disconnect between the various theories of tuning systems and the way humans perceive melodic interval distances. It seems like people who have perfect pitch do a good, consistent job of organizing their memory of sounds into frequency bins. It also seems like what they are not doing is memorizing an idealized set of integer ratios-- or even any interval relationships in particular-- and then singing those intervals back in melodies.

If they could do the latter then you'd expect them to sing those intervals in melodic patterns that end up on a frequency measurably different from where they started. People with perfect pitch obviously have the ability to know when that happens, but I don't hear them describe that conundrum. It makes me speculate that what they are doing is leaping around "frequency lily pads" from memory rather than iterating over a list of well-defined intervals.