Unless you have a really good reason, I advise against learning absolute perfect pitch. If you do, it will drive you absolutely nuts to hear almost any music (since it will almost never be perfectly tuned).
Imagine for a moment that you could see all decimal numbers to 100 places, and it turned out that almost never was any number used by anyone else exactly x.0. Suddenly your world becomes full of "insignificant" but very distracting/annoying .9999887424151515 garbage. That, at least for me, is what absolute perfect pitch is like. (And thankfully, it can fade away as an ability just as it can arrive as one.)
Relative perfect pitch, which simply means you can accurately perceive relative distances between pitches, is very useful. I would expect that most experienced musicians (and some inexperienced but ?gifted? people) have this. It is also attainable, as nearly every other skill is.
Once again, this is incorrect: absolute pitch (also known as perfect pitch, but there is no such thing as "absolute perfect pitch) does not necessarily imply or bestow the ability to perceive differences in pitch that are very small (say, 5 cents). Many people can identify a C# or an A-flat or what have you, but without the ability to tell whether that pitch is very very slightly flat or sharp. They nevertheless are said to have "perfect" pitch.
I have that doubt. But is it not same as not hearing pitch? I would be surprised if I could train to cent accuracy. And what about Just Intonation vs Equal Temperament?
If relative pitch is correct every tone would be shifted. I can imagine picture made entirely out of unusual colors — no red, yellow, orange, but red-orange, yellow-orange.
Imagine for a moment that you could see all decimal numbers to 100 places, and it turned out that almost never was any number used by anyone else exactly x.0. Suddenly your world becomes full of "insignificant" but very distracting/annoying .9999887424151515 garbage. That, at least for me, is what absolute perfect pitch is like. (And thankfully, it can fade away as an ability just as it can arrive as one.)
Relative perfect pitch, which simply means you can accurately perceive relative distances between pitches, is very useful. I would expect that most experienced musicians (and some inexperienced but ?gifted? people) have this. It is also attainable, as nearly every other skill is.