IMO "perfect pitch" is a complete fallacy, since in most cases it only applies for A being around 440 Hz and 12-tone equal temperament. In the past, when I didn't know better, I thought it was some magical superpower, but I now hate this term.
So, a bit of a background of where I come from and what I know:
My parents got me into piano from very early on, and I played for most of my childhood all the way until the end of high school. I picked up this ability through the years. A lot of people, both at church and in my music classes, noticed this and said that I have "perfect pitch".
This worked out quite well for most of my life, until around September–October of 2022. During that time, I got back into classical music. Along the way, I learned about historical tunings (Pythagorean, meantone, and unequal well temperaments) and after exploring music in alternate tunings I had realised that the way I had been approaching music was completely wrong.
And now, to answer your questions:
Are the frequencies C4 260hz and A4 440hz actually noticeably different to someone with “perfect pitch”[?]
Yes, though the exact frequency of middle C depends on the tuning. If we're keeping pure octaves and 440 Hz for A, then 12-TET puts middle C at 261.626 Hz. In 19-TET middle C is 264.022 Hz, which is noticeably higher than that in 12-TET, and 31-TET would put middle C at 263.092 Hz. This is why specifying any sort of pitch range from note to note is actually extremely ambiguous—the frequency of any note varies significantly depending on the chosen tuning, reference frequency, stretching or compressing of octaves, and a whole host of other things, many of which I don't even know about right now.
What did they learn differently growing up to notice the difference in these tones?
I think it comes from them being constantly exposed them to the same frequencies over and over again.
There is a noticeably higher incidence of people with "perfect pitch" among communities that speak tonal languages like Chinese and Vietnamese from a young age. Since tonal languages use pitch changes to differentiate between syllables, people who speak tonal languages from a young age are already used to paying a lot of attention to pitch, and this helps when learning music.
I could understand learning to recognize tones in comparison to one another (intervals), as those have a clear difference in sound but I’m having trouble understanding how one can recognize them individually.
Because you don't have this ability. However, you will be better off than people with this "ability" (myself included) in many instances.
How can a tone be recognized as different without another tone to compare it to? We constantly see different colors and are always naturally comparing them with one another.
I think it's because people with "perfect pitch" have associated very specific frequencies with certain notes.
Same with colours—we differentiate them based on wavelength. Often times, with very small differences, it's hard to differentiate between notes unless you play intervals. For example, not many people can tell the difference between a perfect fifth from A to E in 12-TET and those in 19-TET if you just play the individual notes. But when you play them together, the difference becomes audible, since, for example, there is a bigger difference between the third harmonic of A and the second harmonic of E in 19-TET than in 12-TET. Things like differences in beating start to appear and it is through these things that we can tell a difference.
To me, if I tune my guitar to eadgbe there’s virtually no difference (except maybe bass, tenor, soprano, etc voice classifications), than if I tune my piccolo guitar to adgcea. Same concept as if a song is in the key of C Major vs the key of F major. What difference does it make which tones are used to tune an instrument/form a scale as long as the intervals are the same. What then, would be the purpose of “perfect pitch”?
To me, I've associated certain keys with certain "moods" or settings. If we're still assuming 12-TET, then to me E♭ major (assuming meantone tunings) sounds best at night in a downtown setting, G major sounds best in the morning, while B♭ major and C major are fairly universal between times of day and setting. That's why I save many copies of the songs I listen to—key signature is very important to me since there is a specific set of key signatures that sound best to me for any given setting.
But this way of associating key signatures with mood or whatever gets significantly more complicated when we venture beyond 12-TET. For example, in meantone (nowadays represented by 19, 31, 43, 50, and 55-TET) and Pythagorean (now 53-TET), B major and C♭ major are distinguished, F♯ major and G♭ major are distinguished, and C♯ major and D♭ major are also distinguished. It is the differences in where notes sit and the sizes of the various intervals that causes this.
For example, I think B♭ major sounds brighter in 31-TET than in 12-TET, while B major sounds darker and more mellow, since D, G, C, F, and all of the flats sit higher than they do in 12-TET, while E, B, and the sharp notes sit lower. In Pythagorean the opposite is true.
In alternative tunings, you also have key signatures that have double sharps and double flats, sometimes triple sharps and triple flats, that are redundant in 12-TET but are necessary. They will also sound radically different than their nearest neighbours in 12-TET, and I would have a hard time knowing what their "mood" or whatever would be like without actually listening to them.
Why is A4 considered between 432hz and 446hz? https://pages.mtu.edu/~suits/notefreqs.html
Before electronics existed, tuning frequencies varied widely. In the past, the reference pitch for A tended to be lower than where it is now, and even though it was sometimes higher than where it is now, it has generally risen over the years. 440 Hz as a convention was agreed upon in the late 1930's and made official in 1955.
It's important to note that A = 440 Hz is merely a convention and is not universal. Many Baroque orchestras, for example, tune to A = 415 Hz, since tuning frequencies in the Baroque era were mostly lower than they are now, and 415 Hz was chosen as a compromise where it's something that people can agree on and that more accurately reflects the performance practices of the era.
This is also why I still don’t exactly understand what microtones are either. How many distinct tones can we supposedly hear and rationalize as being different. As with color, there’s only red, orange, yellow, green, blue, violet and of course the shades (brown, pink, white, black etc) but there’s only about 12 that we can perceive as different.
Strictly speaking, microtones are intervals smaller than a semitone (chromatic or diatonic) or not present in standard tuning, such as subminor, neutral, and supermajor thirds.
I understand that how we calculate frequencies is logarithmic, as in, as we get to higher frequencies it takes more hz to reach the next tone. But how many recognizable tones are there for these perfect pitch folks, can they differentiate microtones too or are those just a part of our 12 tones, does anybody have any information on that?
This depends on ear training and music education.
From my experience, most people who are musically inclined could tell the difference between a near-just minor third in 19-TET and the rather flat minor third in 12-TET, or between a near-just major third of 31-TET and 12-TET's rather sharp major third, and even many untrained people could tell as well.
Though, minor thirds in 19-TET and 31-TET would likely sound too wide to most people, and major thirds too narrow, since they've never heard what justly-tuned minor and major thirds sound like in their lives.
Most people in the western world also aren't familiar with intervals past the 5-limit. For example, they don't know what the 7th, 11th, and 13th harmonics sound like, so intervals like 7/6 (the septimal subminor third), 8/7 (the septimal whole tone), and 9/7 (the septimal supermajor third) would likely sound very strange.