Problems with ancient musical scales
borisreitman.medium.com
borisreitman.medium.com
However, I have never heard a student with perfect pitch complain or even inquire about internal inconsistencies in tuning that would lead to comma drift. E.g., "Hey, I was practicing singing C-G-D-A-E-C and I ended up slightly off from the C I started with. What gives?" I've never heard of a student stumbling upon anything like this independent of reading a text about the problems of tuning systems.
I don't have perfect pitch, but as a guitarist I often tune my 3rd string to be a little bit flat (relative to equal temperament), because many chords I play have their major 3rd on that string and it sounds better to have it closer to just temperament.
Regarding singing, one of the reasons that Barbershop music has such a beautiful/smooth sound is because the vocalists sing the intervals of chords in just temperament, despite the fact that the bass note moves around in equal temperament. This is covered well by the Wikipedia page: https://en.wikipedia.org/wiki/Barbershop_music.
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.
In many ways you get more sophisticated expression from older systems because they are more tuned to both empirical physics and biology, rather than abstracted CONSTRUCTED for convenience.
https://www.youtube.com/watch?v=fzee0jwMqpw
(Bonus mind-melter: Double Harmonic Major. https://www.youtube.com/watch?v=7-HZXm61Cv4 )
Our modern tonal systems make sense, but to me microtonal ones have more spice to them. Even stuff like Aphex Twin constantly uses "incorrect" tunings (analog gear is like that) and this makes up a signifikant part of the sound.
Or listen to stuff by Wendy Carlos. Just otherworldly
Yet the humanity is found in all of the tiny imperfections of the art, not the mathematical symmetries on offer.