December 23rd, 2020
It is of great surprise to (almost) everyone when a person can precisely name the note of a sound they just heard, let alone, from an instrument. It is really a very rare skill to have, but let's discuss why it really does not make much sense, why it just represents the social frame in which you are born in and how all this may be related to synesthesia.
Perfect pitch or absolute pitch refers to the ability of any person who can figure out the name of the corresponding note for any given sound. This can go from identifying any note on a piano o guitar, to even hitting a glass with a spoon, the claxon of a car and maybe even a snap from your fingers. It also varies in precision, since some can just barely say it is a G, while others can hone down to cents of semitones.
This remarkable ability exists in a small fraction of the population and appears to be the result of an innate predisposition, combined with musical exposure and training, probably within a critical period during childhood. 
This rare skill (1 in 10.000 people), while it is quite flashy and makes for a very good showcase at parties and events alike, is not of much use. This opinion, however, is polarizing in the musicians community.
Ones say that it is really useful since you can hop on any song anytime and be much more useful and proficient when working in improvised situations. Others say that there's really no use, since a skilled player will be able to find the key quite fast without the need for identifying it right away, and that relative pitch is the real important skill to develop.
To clarify for those unfamiliar, relative pitch refers to the ability to identify the relationship between two or more notes. That is, given an A and then a C#, one can identify that as a major third, but they do not need to know the original pitches of the sounds. They are able to tell the relationship between them, without caring about the actual pitches alone.
This is said to be a much more useful skill since it allows you to pretty much navigate through your instrument much more precisely and with much more control, but I think that that just comes from overall skill from practicing. The real use of relative pitch comes in super handy when trying to analyze any song. That becomes much easier to accomplish since you can pretty much work it out in one or two runs.
Without entering too much in the extensive and boring topic of how useful or useless these skills are, one thing is true: perfect pitch is born, and relative pitch is made.
When I say it is born I mean it is only at a very young age, when the human brain is sufficiently prone to stimuli, that you can develop it. It is said that only 8-year-old kids or younger can actually develop it, of course if present in the right environment. Many tries have been made with adults, with little to no success in developing it. That is why it is such a rare skill: you have to have an initial predisposition to music, fine ears and and a family that educates you into that.
On the other hand, relative pitch can be easily trained by any interested musician. I myself enjoy making relative pitch exercises and, eventually, I was able to decompose the overall harmonic structure of a song on the fly, which I think is quite a cool and exciting exercise to do.
Nevertheless, the part that most interest me is the one involving education. That is, you not only need a very fine ear and music exposition. You have to be told what is an A before you can actually identify it.
I want you to look at the back of your phone and think: what color is it? You'll probably have absolutely no trouble in identifying that your phone is black, white, green or whatever... that is if you don't have those shiny cases/glass backs. The point is that you have no trouble telling what color it is. Perfect pitch people feel the same way when doing their thing.
That said, when you look at a tomato, your fridge or your headphones you just do not simply think "Wow, this fridge is white" or "This tomato is red". Of course, you don't even question one's ability to tell colors, since you take it for granted. I know I am forgetting colorblindness, but for the purpose of this explanation we won't consider it, since it really does not matter for the actual point I wanna make. What I mean is that this is an active exercise, you have to really be thinking about the color of something. Same happens with perfect pitch people.
But... why exactly are we able to do that? If you really think about it... why is green green?
The color green itself (or any color for that matter) does not exist. For those of you who don't know, colors are just mere slices of the visual spectrum that end up in our eyes. It is our brain who colors them, but the color itself is just a representation that we've made up from reality. And even more so, the name we gave it.
This means that while we both may be looking at a strawberry and consistently tag it as "red", your red may differ from my red. But what it is certain is that the particular frequency of the electromagnetic energy from the light getting to our eyes is always the same, and thus we can deterministically identify it as such.
Moreover, since we can measure that correctly, to make it easier for us we gave it a name! In English is green, and in Spanish, verde. We assigned a certain stimulus an arbitrary name.
The implications of this are huge, since we've just inherited what some random people some long time ago decided to name things in order to being able to refer to them properly and univocally. That is where the concept of language was born, but that is a topic for another day.
This whole introduction was just to set up my main point: perfect pitch works exactly the same as this. Random wavelengths of air pressure that end up in our ears are assigned an arbitrary name. For some reason, if this wiggly air vibrates at 440 Hz, someone decided to call it A.
Really there is absolutely NO DIFFERENCE WHATSOEVER about these two concepts. Arbitrary names to arbitrary stimuli. We could have called the 440 Hz-wiggly-air "tomato", but we decided to call it "A".
The last concept I want to introduce is synesthesia. This is believed to be a very light disorder in which the different nerves that come out of the spinal chord are not correctly separated into their standalone form upon gestation inside the mother's uterus, causing several senses to trigger when the source is only meant for one.
I myself suffer from this on a very high degree, so I can tell you from my experience first hand. When I hear music, I can very precisely see things. The things I see cannot be associated with anything you and I can find in the real world, so I cannot make up a reference for you to imagine it, but it is there. Other senses like taste and smell trigger visual effects too.
That said, I usually describe these stimuli with very graphic terms. For example, upon eating a piece of pure black chocolate, I can immediately tell a very yellow feeling, and I tend to say the flavour is very sharp and edgy. When listening to music, the stimuli are so intense that I just cannot concentrate on anything else, it occupies every portion of my brain. (that may also have to be related with the fact that I am a musician and make all sorts of analysis, but the visions caused by music really are intense)
Music alone does not trigger this, individual sounds can too, as expected. And the descriptions I give about them are a bit off also, tending to be very graphic.
There are many different kinds of synesthesia, relating every possible pair of senses, but there are more common ones like color–graphemic synesthesia, where people literally color numbers, days, months... concepts like these. I find Monday to be light blue and the number 2 being red, just to name some examples. And just in my close circle lots of people have it, so I guess that number can only grow when considering a larger population.
This is usually quite useful, since it is being constantly demonstrated of how the use of color in any kind of learning process can lead to a much faster and better understanding of the topic at hand.
However, this is quite different. It is much more likely to be caused by some sort of exposition of these particular (and arbitrary) combinations in early phases of one's childhood, leading to a very strong association that will, most probably, last forever.
From here, you might already see where I am going.
These exercises I just so exhaustively described define the human need for association. Since the developing of the first languages, we name everything we see in order to give it an identifying tag to which we can refer to. This means that there really is no difference between telling two colors apart versus telling two notes apart. These are just names, and that just defines the context in which you were born.
For me, I say La and Verde, but for others is A and Green. Different names for the same thing, but those names mean the same. For that matter, people that can identify colours, or even, can associate colors to other social constructs have the same ability. Perfect pitch is really another form os colour-graphemic synesthesia. But we can arbitrarily call it sound-graphemic synesthesia. And that is because there is no difference between these two kinds of associations.
This means that if we had a better default musical education in schools and the notes were taught from a very young age, the ratio of perfect pitch people would rise significantly. Probably not enough for it to be 'standard' as the colour-telling ability is, but much higher for sure.
Really, all boils down to the concept of taking something out of the real world, process it through our senses (lots of biases and perspective taking part of it) and give it a name. We just created a social construct, a handle for us to easily grasp reality with our mind.
Maybe we've been sleeping on this concept (synesthesia) too much when it is really the most essential part for language creation and, consequently, human communication. But, all in all, we can give it the name we want.
: —Drayna, D.T. (2007) Absolute pitch: A special group of ears. Proceedings of the National Academy of Sciences of the United States of America, 104 (37):14549-50.